Student Workbook for Research and Evaluation in Counseling, 2e
Student Workbook
to accompany
Research and Evaluation in Counseling
2nd edition
By Bradley T. Erford
Loyola University Maryland
© 2015. Cengage Learning. All rights reserved.
1
Student Workbook for Research and Evaluation in Counseling, 2e
Contents
Preface …………………………………………………………………………………
3
Activities
A Quick Math Review…………………………………………………………. 4
Chapter 1 The Nature and Importance of Inquiry…………………………… 15
Chapter 2 Characteristics of a Research Study……………………………… 17
Chapter 3 Locating, Reviewing and Writing Research……………………… 20
Chapter 4 Outcomes Research in Counseling……………………………….. 22
Chapter 5 Qualitative Approaches to Research……………………………… 24
Chapter 6 Qualitative Research Design……………………………………… 27
Chapter 7 Quantitative Research Design in Counseling…………………….. 29
Chapter 8 Using Action Research and Single Subjects Research Design …... 35
Chapter 9 Needs Assessment………………………………………………… 39
Chapter 10 Program Evaluation and Accountability………………………….. 40
Chapter 11 Collecting Data……………………………………………………. 43
Chapter 12 Describing Data…………………………………………………… 47
Chapter 13 Deriving Standardized Scores…………………………………….. 50
Chapter 14 Statistical Hypothesis Testing…………………………………….. 53
Chapter 15 Using SPSS for Introductory Statistical Analysis…………………. 55
Chapter 16 Univariate Inferential Statistics…………………………………… 57
Chapter 17 Correlation and Regression……………………………………….. 59
Chapter 18 Nonparametric Tests of Statistical Inference ……………………. 63
Chapter 19 Multivariate Statistical Analysis………………………………….. 68
Answer Keys
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Chapter 19
2
The Nature and Importance of Inquiry…………………………… 74
Characteristics of a Research Study……………………………… 74
Locating, Reviewing and Writing Research……………………… 74
Outcomes Research in Counseling……………………………….. 75
Qualitative Approaches to Research……………………………… 75
Qualitative Research Design……………………………………… 76
Quantitative Research Design in Counseling…………………….. 77
Using Action Research and Single Subjects Research Design …... 78
Needs Assessment………………………………………………… 79
Program Evaluation and Accountability………………………….. 79
Collecting Data……………………………………………………. 80
Describing Data…………………………………………………… 82
Deriving Standardized Scores…………………………………….. 83
Statistical Hypothesis Testing…………………………………….. 84
Using SPSS for introductory Statistical Analysis…………………. 84
Univariate Inferential Statistics…………………………………… 84
Correlation and Regression……………………………………….. 85
Nonparametric Tests of Statistical Inference ……………………. 86
Multiple Statistical Analysis……………………………………… 87
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
Preface
This student workbook was written to accompany Research and Evaluation in Counseling (2nd
edition) by Bradley T. Erford. The workbook chapters correspond to the text chapters. Each
chapter in this workbook includes activities to help students review and master the content of the
text and help extend the learning of students beyond the textual readings through some
experiential tasks that can be enacted both within and outside the classroom. Some activities may
be appropriate for homework assignments or even additional course requirements. These
activities are only meant as a start. Instructors are encouraged to alter and modify them to meet
the individual and group needs of students. Answer keys for the activities are located at the end
of the workbook.
© 2015. Cengage Learning. All rights reserved.
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Student Workbook for Research and Evaluation in Counseling, 2e
A Quick Math Review
THE NUMBER WORLD
POSITIVE AND NEGATIVE NUMBERS
FRACTIONS, PERCENTS, AND DECIMALS
EXPONENTS
ORDER OF OPERATIONS
ALGEBRA
I’m not very good in math.” This sentence is uttered by countless students in an infinite
number of classrooms from elementary schools to high schools and, yes, even more so
in colleges and universities. Math, often considered a four-letter word, has suffered
through a long history of intolerance perpetuated by the belief that if your parents
weren’t very good in math, then “genetically” neither are you! This section reviews
some rules and skills that will help you survive a research course. Who knows—you
may even end up liking math! What follows are the basic principles of mathematics that
will serve as the basis for the statistical concepts later in this chapter.
THE NUMBER WORLD
Within the number world, just like our world, there are families of numbers. Some
numbers belong to more than one family, such as the whole numbers and the natural
numbers.
Real Numbers are the set of numbers that consists of the positive numbers, negative
numbers, and zero: –232.41, 0, 6, 9.3.
Rational Numbers are any real number that can be written as a fraction where the
numerator and denominator are integers (the denominator cannot be zero). The resulting
2
3
decimal either repeats itself in some form or terminates:– 14 , 119
.
5
17
Irrational Numbers are any real number that cannot be written as a fraction using
two integers. The resulting decimal neither repeats nor ends: 2 = 1.41421356237 . . . ,
3 = 1.73205080756 . . . , 5 = 2.23606797749 . . . , π = 3.141592653589 . . . , e =
2.718281828459045235 . . . .
Integers include the set {. . . , –2, –1, 0, 1, 2, . . .}. (The “. . .” means to infinity—in
this case, in both positive and negative directions.)
Whole Numbers include the set {0, 1, 2, 3, . . .}.
Natural Numbers include the set {1, 2, 3, . . .}.
4
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Student Workbook for Research and Evaluation in Counseling, 2e
POSITIVE AND NEGATIVE NUMBERS
In an ideal world, there would be no debt and, therefore, no need for negative numbers.
Thanks to the invention of credit cards and bank loans, however, we’re all seeing a little
red! The sign in front of a number tells you where it is located in reference to zero.
Negative numbers are to the left of zero, and positive numbers are to the right. For
visual learners, it is helpful to look at a number line.
The farther you move to the left, the smaller the numbers become. This means that
negative 5 (–5) is smaller than negative 2 (–2). In accounting terms, being “in the
black” means one has made money (which is a positive!). The farther one is “in the
red,” the more money one has lost (which is a negative!). The farther into the red one
goes, the more money is owed (e.g., deeper in debt, deeper into the negative territory).
Concept 1. If a number or expression is written without a sign, it is positive.
Ex. 5 and +5 represent the same value. 5 = +5
Concept 2. When adding numbers with the same sign, add the numbers to get
your answer.
Then take the sign of the original numbers as the sign of your answer.
Positive + Positive = Positive
Negative + Negative = Negative
Ex. 4 + 7 = 11
Ex. –3 + –6 = –9
Concept 3. When adding two numbers with opposite signs, subtract the two
numbers (ignoring the signs) to get your answer.
To assign a prefix to your answer, look at the original two numbers. Use the sign of the
number that is farthest from zero on the number line—in other words, the number that is
the largest if they had no signs. It is clearer to see in these examples.
Ex. –4 + 8 = 4
Ex. 5 + –8 = –3
A concrete way of understanding these examples is to go a number line. To demonstrate
the first example (–4 + 8 = 4), start at 0 and move 4 spaces to the left. You should now
be at –4. Now, move 8 spaces to the right (positive). You should now be at +4, the
correct answer. Repeat this exercise for the second example (5 + –8 = –3).
Concept 4. Adding a negative number is the same as subtracting a positive
number.
Ex. 6 + (–4) = 2 is the same as 6 – (+4) = 2
Concept 5. Subtracting a negative number is the same as adding a positive
number.
Two negatives (or subtraction signs) in a row equal a positive.
Ex. 13 – (–5) = 18 is the same as 13 + (+5) = 18
Concept 6. When adding several numbers of mixed signs, follow these steps:
1. Add all of the positive numbers together. This answer is positive.
2. Add all of the negative numbers together, ignoring their signs for the moment. This
answer is negative.
3. Then “add” your two answers by following Concept 3.
Ex. 18 – 5 + 3 –7 + (–2) + 4
1. Add the positives: 18 + 3 + 4 = 25
2. Add the negatives: 5 = 7 + 2 = 14 or –14
3. Add these numbers: 25 + (–14) = 11
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Student Workbook for Research and Evaluation in Counseling, 2e
Concept 7. When multiplying or dividing numbers with the same sign, the
answer is always positive.
Positive × Positive = Positive
Negative × Negative = Positive
Positive ÷ Positive = Positive
Negative ÷ Negative = Positive
Ex. 4 × 7 = 28
(-3)(-9) = 27
-8 · -4 = 32
Notice that there are three different ways of indicating multiplication: an “×” sign,
a dot, or no sign if the numbers are in parentheses. Sometimes parentheses are used to
enclose a single number or expression.
Ex. 18 ÷ 6 = 3
(–45) ÷ (–5) = 9
Concept 8. When multiplying or dividing numbers with opposite signs, the
answer is always negative.
The order in which the signs appear does not matter.
Positive × Negative = Negative
Ex. (6) (–5) = –30
Positive ÷ Negative = Negative
-5 x 6 = -30
Concept 9. Multiplying any number by zero will ALWAYS equal zero.
Ex. 0 × 8 = 0
–4 · 0 = 0
Concept 10. Multiplying any number by one will give you back that number.
Ex. (1)(8) = 8
(–3)(1) = –3
Concept 11. Dividing by zero is NOT possible in the real number system.
Try it. Enter 11 divided by 0 into your calculator. It should say you have an error. If
within a problem you find you are dividing by 0 (0 is on the bottom of a fraction), go
back and check your work. Mostly likely, there is a mathematical error.
PRACTICE SET FOR CONCEPTS 1–11:
1. –4 + 7 +5 –8 + 1 =
3.
–81
–9
2. (8)(–4) =
4. 5 + 7 – (–8) – 4 + 6 =
=
FRACTIONS, PERCENTS, AND DECIMALS
When working with fractions, you will need to learn some basic vocabulary. The top
number is referred to as the numerator, and the bottom number is called the
denominator. To help you remember which is which, transpose the letters in
denominator so it looks like “demon-inator,” and demons belong underneath! Fractions,
percentages, and decimals are just three ways of representing the same value.
Concept 12. Comparing decimals.
Each place in a decimal number represents a value. As with money, the more you have
to the left of the decimal point, the greater the value. The numbers to the right of the
decimal point, however, are fractions of numbers.
The farther out to the right you go, the smaller the decimal value.
1
Ex. 0.01=
and 0.0.001= 1 (one hundredth and one thousandth, respectively).
100
1000
So 0.001 is smaller than 0.01
6
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Student Workbook for Research and Evaluation in Counseling, 2e
236
Ex. 0.0236 =
and 0.154 =
154
(236 ten thousandths and 154 thousandths,
10000
1000
respectively). So 0.0236 is smaller than 0.154
Concept 13. Rounding decimals.
When rounding decimals, first decide how many places to which you plan to round.
Typically, rounding to two decimal places is acceptable in most statistical studies, but
the rules apply to rounding for any place value. Look one place past where you plan to
round, and apply the phrase “Five or above, give it a shove. Four or below, leave it
alone.” This phrase tells you what to do with the number you are rounding.
Ex. Round to two decimal places:
3.14159
Look at the third-place number (thousandths). This is a 1. Since 1 is “four or
below,” leave the second decimal place alone. Cut off the rest of the numbers. Your
answer is 3.14.
Ex. Round to two decimal places:
6.32815
Look at the third-place number (thousandths). This is an 8. Since 8 is “five or
above,” give the second decimal place number a shove to the next number. Your answer
is 6.33.
Concept 14. Simplifying fractions.
Simplifying a fraction means to find a number that divides evenly into both the
numerator and the denominator.
42
12
Ex.
12
3
1
= 4 = =1
8
8
2
2
4
Ex.
42
7
1
= 6 = =2
18
18
3
3
6
In the preceding example, 4 is the largest number that divides into both 12 and 8. When
you divide 12 by 4, you get 3, and when you divide 8 by 4, you get 2. Therefore, your
3
1
answer is , which is the same as the mixed number 1 . If you don’t come up with
2
2
the largest divisor right away, then continue to find numbers that go into both the
numerator and denominator, and divide until you are out of numbers that go into both.
42
The same process is used for the second example,
. In this example, the number can
18
7
1
be divided by 6, thus simplifying to and, finally to 2 , which is the mixed number
3
3
equivalent written in lowest terms.
Concept 15. Adding, subtracting, multiplying, and dividing decimals.
Plain and simple: Use a calculator! In this century, there is no reason to be without one.
Concept 16. Adding and subtracting fractions.
Before you can add or subtract fractions, their denominators must be the same number.
If they are already the same, then add or subtract just the numerators, and leave the
denominators alone.6
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7
Student Workbook for Research and Evaluation in Counseling, 2e
Ex.
3
+
4
4
4
=
7
4
=1
10
3
Ex. 3
4
6
4
1
− 3 = 3 = 13
If the denominators are not the same, then make them the same without changing
the value of the fraction. Do this by multiplying both the numerators and denominators
by a number that will make the denominators equal.
1 3 3
. =
2 3 6
3+5 8 4
1
Ex.
= = =1
5 1 5
6
6 3
3
+ . =
6 1 6
Notice how multiplying by or does not change the value of the fraction—just the look!
3 3 9
. =
4 3 12
9–4 5
Ex.

12 12
1 4 4
– . =
3 4 12
Concept 17. Multiplying fractions.
When multiplying fractions, follow these steps:
1. Multiply the numerators together.
2. Multiply the denominators together.
3. Simplify if necessary.3
Ex.
. 3 = 51 𝑥 32 = 15
= 7 12 .
2
3 2
6
3
. =
=
4 5 20 10
Ex 5 2
Note: You can make any whole number a fraction by placing the number one
underneath it.
Concept 18. Dividing fractions.
Dividing fractions is the same as multiplying by the reciprocal. In other words, leave the
first fraction alone, flip the second fraction, and multiply using Concept 6.
1 2 1 5 5
2 1 2 6 12
Ex. ÷ = . =
Ex. ÷ = . =
=4
4 5 4 2 8
3 6 3 1 3
Concept 19. Rewriting fractions, percents, and decimals.
a. Fractions to Decimals: Fractions are just another way of representing division.
Using your calculator, take the numerator (top number), and divide it by the
5
denominator (bottom number). To change to a decimal, enter 5 divided by 8
8
(5 ÷ 8) into your calculator. This gives you 0.625.
b. Fractions to Percents: First change your fraction to a decimal, and then
multiply the decimal by 100% to get your percent.
Ex.
4
5
8
= 0.8, (0.8)(100%) = 80%
Ex.
5
= 0.625, (0.625)(100%) = 62.5%
8
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Student Workbook for Research and Evaluation in Counseling, 2e
c. Percents to Decimals: Remove the percent sign, and then use your calculator
to divide the number by 100. This usually results in the same number, except
the decimal place has moved to the right two places.
Ex. 43.5% =
43.5
%=
100
43.5
Ex. 6.3% 
= 0.435
100
6.3
= 0.063
100
d. Percents to Fractions: Remove the percent. Place the number over 100, and
simplify if necessary.
Ex. 22% =
22
100
=
11
Ex. 250% =
50
250
100
=
5
=2
2
1
2
e. Decimals to Percents: Multiply by 100!
Ex. .26 × 100% = 26%
Ex. 3.91 × 100% = 391%
f. Decimals to Fractions: Leave decimals as decimals. It is rare they will ever
need to be fractions!
PRACTICE SET FOR CONCEPTS 12–19:
Round the following numbers to two decimal places:
A. 8.9315
B. 104.39842
Simplify the following fractions:
A.
16
–30
B.
=
=
12
24
Perform the indicated operations on the following fractions:
A.
2

3
C.
3
B.
=
2
6 2
.
5
3
=
2
4
5
 =
D.
=
–
5 3
6
1
2
Complete the table by rewriting the number given as a fraction, decimal, and percent.
FRACTION
DECIMAL
PERCENT
2
5
0.7
35%
7
8
EXPONENTS
Exponents are used to represent repeated multiplication. It is shorthand for multiplying
several of the same numbers or letters in a row.
Ex. 3 · 3 · 3 · 3 · 3 · 3 = 36 = 729
Ex. x · x · x = x3
The general form of an exponent looks like an, where a is called the base, and n is
called the exponent. The entire term is called a power.
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9
Student Workbook for Research and Evaluation in Counseling, 2e
a represents the number to be multiplied ←
an
→ n tells you how many
times to multiply the number by itself
Concept 20. If there is no exponent number, it is the same as a 1 there to hold
the spot.
Ex. m = m1
Concept 21. When multiplying powers with the same base, add the exponents.
Ex. 23 · 22 = 25 = 32
Ex. x2 · x4 · y2 · y3 · x = x7y5
(3 + 2) =5
(x : 2 + 4 +1 = 7, y : 2 + 3 = 5)
(Note: If it is possible to multiply out the base (because it is a number and not a letter), then
by all means, multiply it out.)
Concept 22. When an exponent is raised to another exponent, multiply the two
exponents.
The exponent on the outside of the parentheses is distributed to each base on the inside.
Ex. (x3)2 = x6
Ex. (3y3)2 = (3)2(y3)2 = 9y6
Concept 23. When dividing powers that have the same base, subtract the
exponents.
6
6
6
6.6.6.6.6.6 2
Ex.
* Since 1 the first four 6’s on the top and
=
6
4
6
6.6.6.6
6
bottom cancel out to equal 1; there
are only two 6’s left on top.
Ex.
7
7
4
3
7
4–3
1
7 7
Ex.
3
3
12a
12 a
3a 2
=
. 1 =
1
8
2
8a
a
Concept 24. A nonzero number raised to the zero power is equal to one.
In other words, any number (or letter) raised to the power of zero cancels out to become
the value of 1.
Ex. 50 = 1
Ex. 6a4b0c3 = 6a4(1)c3 = 6a4c3
PRACTICE SET FOR CONCEPTS 20–24:
Simplify the following:
1. a2 · a4 · a =
5
6m
3.
2
8m
2. (4x2y3)2 =
4. (3b4c0d2)3 =
Concept 25. Radicals.
Radicals are the inverse operation of exponents. For example, addition is the inverse
operation of subtraction because one operation undoes or cancels out the other.
Therefore, to cancel out the operation of raising a number to the second power, one
would take the square root of that number. It is easier to see with numbers:
Ex. 52 = 25 and
10
25 = 5
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Student Workbook for Research and Evaluation in Counseling, 2e
The general form of a radical (sometimes called a root) is m a , where m represents
the root (or “shelf” number), and a is called the radicand. More often than not, m is 2
and left off of the shelf. So, if there is no number on the shelf, assume it is 2. This is
asking you to think of what number times itself will give you the radicand. For
example, 36 is asking for a number that when multiplied by itself will give you 36.
The answer is 6 because 62 is 36. A common mistake is to take half of the radicand. If
one did that with 36 , one would have 18 and 182 is not 36!
ORDER OF OPERATIONS
Concept 26. PEMDAS.
An order must be followed when performing operations (addition, subtraction,
multiplication, and division) on numbers so that everyone comes out with the same
answer. Here’s what could happen if there were NO order:
Ex. 4 + 3 · 2 =
or
4+3·2=
7 · 2 = 14
4 + 6 =10
14
10
In the first expression, 4 and 3 were added before multiplying by 2. In the second
expression, 3 and 2 were multiplied before adding to 4. Which way is correct?
To determine what order to perform operations, follow this simple phrase, “Please
Excuse My Dear Aunt Sally.” In PEMDAS, each letter represents an operation and the
order of the sentence explains what comes first!
Ex. 6(4 + 1)2 – 7 · 2
Parentheses
Ex. 3 – 4(2 · 5) + 52
6(5)2 – 7 · 2
Exponents
3 – 4(10) + 52
6(25) – 7 · 2
Multiply/Divide
3 – 4(10) + 25
150 – 14
Add/Subtract
3 – 40 + 25
136
–12
If an operation is not included, then skip it and go onto the next! Just as with reading,
work left to right when you are multiplying and dividing, or when you are adding and
subtracting.
Ex. 9 – 12 ÷ 4 + 6 · 4
9 – 3 + 24
There are no parentheses or exponents; therefore,
multiply/divide from left to right.
Now add/subtract from left to right.
6 + 24
30
PRACTICE SET FOR CONCEPT 26:
Solve.
1. 14 ÷ 7 + 32 =
2. 2 · 32 – 9 =
3. 5 (4 + 2) – 12 =
4. 42 ÷ 3 + 32 · (12 – 8) + 3 =
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Student Workbook for Research and Evaluation in Counseling, 2e
ALGEBRA
Algebra is an often misunderstood math subject. Most students believe that there is a
concrete explanation and practical use for algebra when, in fact, it is highly unlikely that
you’ll be asked to solve an equation or graph a line unless you are in the math field!
Algebra is more accurately described as a “workout for your brain.” You lift weights to
strengthen your muscles, and you exercise to strengthen your heart and lungs. Doing
these activities can help you be healthy and live longer. Well, algebra is strengthening
your thinking skills and your problem-solving abilities. Doing algebra will help the
brain think quicker and more effectively. This applies to all thinking activities done
throughout the day! Now, here’s the one concept that throws off all of the math we’ve
ever learned:
x is called a variable, and it represents a number.
In a way, this goes against everything you have ever studied: 5 is a number, and x is
a letter! It is called a variable because it can represent any number, and that number
may change or, in other words, vary. Variables are not only used in algebra but also in
statistics and research design. Remember: A variable is something that has many
possible values. Terms that do not change are called constants. An example of a
constant is ten (10). The number 10 will always be 10; it won’t ever be 3. For example,
in the expression x + 7, x is the variable and 7 is the constant. The variable x represents
any number that you want to put in its place. What can be even more confusing is that
just about any letter can be used as a variable (i.e., x, y, z, i, w, a). Let’s apply this idea.
Concept 27. Evaluating formulas.
Ex. Using the formula for the perimeter of a rectangle, P = 2l + 2w (where P =
perimeter, l = length of the rectangle, and w = width of the rectangle), find P if l = 3 and
w = 5.
P = 2 (l) + 2 (w)
P = 2(3) + 2(5)
Use the rules of PEMDAS to find the answer.
P = 6 + 10 = 16
Ex. Using the formula for compound interest, A = P(1 + r)t (where A equals compound
interest, P equals the principle borrowed, r equals the interest rate, and t equals the
number of years on the loan). Find A if P = 100, r = 6%, and t = 5.
A = P (1 + r )t
A = 100 (1 + 0.06)5
A = 100 (1.06)
Use the rules of PEMDAS to find the answer
5
A = 100 (1.34) = 134 (The borrower will owe $134 when the loan comes due.)
Concept 28. Distributive property.
This property is named such because the number outside the parentheses is “distributed”
to each number or letter on the inside.
a(b + c) = ab + ac
or
(b + c)a = ba + ca
This property also works when subtraction is on the inside of the parentheses and
regardless of how many terms are inside.
12
Ex. 3(x +5) = 3x +15
helpful!)
(Hint: Sometimes drawing arrows to each term is
Ex. 4 + (2x –6 + 3y)(–3)
Notice that –3 is the distributor because it is
immediately next to the larger set of parentheses.
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Student Workbook for Research and Evaluation in Counseling, 2e
= 4 + –6x + 18 – 9y
The 4 out front is not the distributor because it is
separated by the plus sign.
= 22 – 6x – 9y
Concept 29. Inequalities.
Not all things are created equal in the number world. A set of symbols was designed so
that we can describe nonequivalent relationships. These may look familiar!
> Greater Than
≥ Greater Than or Equal To
< Less Than
≤ Less Than or Equal To
≠ Not Equal To
≈ Approximately
Think of the line underneath the inequality symbol as half of an equal sign. It is
saying that the answer could also be equal to the number. You may remember inequality
symbols being compared with an alligator with teeth or “Pac-man.” These symbols, or
creatures, would “eat” the larger of the numbers. So whichever way the symbol’s mouth
opened was the larger number. Although an inequality can be read in either direction, it
is typically read from left to right. A graph is also used to illustrate the values identified
by the inequality.
Ex. x < 9
Read as, “x, or all the values that are less than 9.”
This can also be read as, “9 is larger than x.”
5 6 7 8 9 10 11
Ex. y ≥ –5
Read as, “y, or all the values that are greater than or equal to negative
5.” This can also be read as, “negative 5 is less than or equal to y.” –6 –5 –4 –3 –2 –1 0
Concept 30. Graphing Inequalities.
Symbol
Type of Circle
Explanation
<, less than
>, greater than
Open Circle
This means the number is not included in the answer set.
≤, less than or equal to
>, greater than or equal to
Closed Circle
This means the number is included in the answer set.
In other words, if there is an equal sign, this means to close the circle because the
answer could be equal to the number given. If there is no equal sign, the circle is open,
and the answer is not in the number given. In x < 9, possible values of x include all of
the negative numbers, 0, and all of the numbers until you reach 9. This includes 8.999,
but not 9. In y ≥ -5, possible values of y include all of the positive numbers, 0, and
negative numbers through and including –5. Negative six (–6) or –5.0001 would not be
possible values.
Concept 31. Approximately (≈).
This symbol is used most often when rounding decimals. It was created to acknowledge
that these answers are not “equal” but have been rounded and, therefore, are an
approximation of the answer.
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13
Student Workbook for Research and Evaluation in Counseling, 2e
Concept 32. Venn Diagrams.
Venn diagrams, named for John Venn in the 1880s, are used to express relationships
visually. These relationships can be used for any subject from math to English. The
extent to which the circles overlap defines how closely these topics correlate.
14
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Student Workbook for Research and Evaluation in Counseling, 2e
ACTIVITIES
CHAPTER 1 The Nature and Importance of Inquiry
Activity 1.1 Match the concepts in the left-hand column with the descriptions in the right-hand
column.
___ 1. sample
___ 2. constructivism
___ 3. reliability
___ 4. positivism
___ 5. independent variables
___ 6. objectivity
___ 7. population
___ 8. random sampling
___ 9. generalizability
___ 10. dependent variables
___ 11. validity
___ 12. replication
a. The search for nature’s laws through observation and
comparison via experiments that seek to explain
phenomena through cause-and-effect relationships.
b. Removed as far as possible from the research itself.
c. The greatest good for the greatest number of people.
d. Understanding and building, rather than discovering,
meaning from experiences.
e. Subset of the target population to be studied.
f. Degree to which the conclusions drawn from the data
gathered are consistent with those data.
g. Those that depend on the independent variable for their
response.
h. Those believed to affect the behavior of another variable.
i. Participants to study.
j. Consistency of findings from one study to the next.
k. The assignment of participants to treatment and control
groups.
l. Estimate of how consistently the instruments we use to
gather the data perform.
Activity 1.2 Determine whether the following concepts or scenarios are best described as
quantitative (A) or qualitative (B) methods.
1. ______ studying college students with personality disorders
2. ______ studying cancer survivors
3. ______ interviews
4. ______ instruments that allow subjects to express their feelings, emotions, and attitudes.
5. ______ survey instrument
6. ______ case study
7. ______ personality inventory
8. ______ ethnography
9. ______ essays
10. ______ subjectivity
11. ______ objectivity
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15
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 1.3 Match the concepts in the left-hand column with the descriptions in the right-hand
column.
____ 1. quasi-experimental
____ 2. ethnography
____ 3. quantitative
____ 4. case study
____ 5. theory
____ 6. qualitative
____ 7. empiricism
a. A lens through which researchers view the phenomenon
they want to study.
b. The in-depth study of one subject at a time.
c. Rely on mathematical calculations to characterize the
data collected.
d. Becomes a part of the study.
e. Some features of the experimental design might be
compromised in order to achieve groups that can be studied
in a timely and efficient manner.
f. Claims all knowledge comes from experiences that can
be tested against the experiences of others.
g. Rely on words to characterize the data collected.
Activity 1.4 Provide bulleted descriptions in the right-hand column to describe the major
characteristics of the research method listed in the left-hand column.
Research Method
Description
Experimental
Correlational
Survey
Observational
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Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 2 Characteristics of a Research Study
Activity 2.1 Match the concepts in the left-hand column with the descriptions in the right-hand
column.
___ 1. cluster sampling
___ 2. nondirectional hypothesis
___ 3. simple random sampling
___ 4. random sampling
___ 5. hypothesis
___ 6. operational definitions
___ 7. stratified random sampling
___ 8. sample
___ 9. directional hypothesis
___ 10. population
___ 11. convenience sampling
___ 12. conceptual definitions
a. Indicate precise steps required to measure a variable
accurately.
b. A tentative explanation for a phenomenon.
c. A large group of individuals to whom the results of the
study are to be generalized.
d. Randomly selecting a portion of the population to
comprise the sample.
e. Used to ensure that certain characteristics of participants
are reflected in the final sample in the same proportion that
they occur in the population.
f. Individuals selected to take part in the study.
g. Allows us to understand and communicate in general
terms; often found in the dictionary.
h. Gathering participants that are available and willing to
participate.
i. Predicts a difference will occur without indicating which
group will perform higher.
j. Randomly assigning selected participants to various
treatment conditions.
k. The researcher selects units of participants either
randomly or conveniently.
l. Predicts a difference and the direction.
Activity 2.2 Number the following characteristics in the basic order (1-12) that they occur in
the research process.
____ literature review
____ implications/applications
____ formulation of a hypothesis
____ procedures
____ definitions
____ interpretation
____ data collection
____ sample
____ statement of the research problem or question
____ results/conclusions
____ data analysis
____ methodology
© 2015. Cengage Learning. All rights reserved.
17
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 2.3 Match the concepts in the left-hand column with the descriptions in the right-hand
column.
___ 1. comprehensive sampling
___ 2. procedures
___ 3. descriptive statistics
___ 4. purposeful sampling
___ 5. parametric tests
___ 6. extreme-case sampling
___ 7. snowball sampling
___ 8. data analysis
___ 9. typical-case sampling
___ 10. multistage sampling
___ 11. nonparametric tests
___ 12. inferential statistics
a. Selecting interesting, extreme or outlier cases with
interesting perspectives.
b. The process of analyzing collected data and describing
any statistical procedures conducted.
c. Used in large scale surveys in which initial stratified
random samples of larger entities are followed by simple
random samples of smaller entities.
d. Describe and summarize data.
e. The detailed description of the process of the study and
the materials used in the study.
f. Used in ethnographic or other qualitative methodologies
when the researcher is interested more in diverse data
sources than generalizability of results.
g. Selecting normal or typical cases.
h. Used to evaluate hypotheses about the shapes of
distributions and are only applied to nominal or ordinal
data.
i. Selecting numerous participants with diverse
characteristics and perspectives.
j. Locates one participant and then develops a referral
network to locate other likely participants.
k. Help predict the probability of occurrence of some casual
or association event with some degree of confidence.
l. Used to evaluate hypotheses when the dependent variable
is measured using an interval or ratio scale and when
certain other assumptions are met.
Activity 2.4 Determine whether the following are more closely related to parametric tests (P) or
nonparametric tests (N).
1. ______ chi square
2. ______ normally distributed scores
3. ______ interval or ratio scale
4. ______ Mann-Whitney u
5. ______ nominal or ordinal data
6. ______ t-tests
7. ______ are more powerful under normal circumstances
8. ______ ANOVA
18
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 2.5 True (T) or False (F).
1. ______ Much of the research in counseling is conducted on large groups of people and
involve measurements that can be counted.
2. ______ The scientific method is basically the testing of ideas to discover answers to some
research problem or question.
3. ______ The planning of research is a linear process.
4. ______ The hypothesis is the foundation of any quality research project.
5. ______ A literature review involves an analysis of all relevant articles, journals, or books that
pertains to the researcher’s current research topic.
6. ______ A hypothesis can be viewed as a prediction, educated guess, or a statement of what
specific results or outcomes the researcher expects.
7. ______ Quality hypotheses are concrete formulations of behavioral phenomena.
8. ______ Research questions and hypotheses are often categorized according to purpose, such
as descriptive, associational or difference.
9. ______ A general rule is that the smaller the sample size, the greater the statistical power.
10. _____ The main reason procedures are documented is so people know they did not lie about
how they conducted the research.
11. _____ How a sample is collected affects the degree to which inferences can be made about
the population.
12. _____ Random selection and stratification are meant to minimize or eliminate bias.
© 2015. Cengage Learning. All rights reserved.
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Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 3: Locating, Reviewing, and Writing Research
Activity 3.1 Put the following steps in the correct order of occurrence (1-5) when constructing a
literature review.
______ Organize the quality and relevant literature.
______ Identify the topic of inquiry.
______ Write the literature review.
______ Locate literature pertinent to the topic.
______ Critically evaluate the selected literature.
Activity 3.2 True (T) or False (F).
1. ______ Professional counselors evaluate existing research and produce new research in an
effort to improve professional practice.
2. ______ An informative and lengthy research report is crucial.
3. ______ When writing a literature review it is important to use as few sources as possible.
4. ______ A literature review should demonstrate the benefits and drawbacks to prior research
efforts.
5. ______ A primary source is general information that supports the argument.
6. ______ The goal of most research is to expand on or improve existing research.
7. ______ When beginning the actual process of searching for literature, reading about the topic
first in a basic reference book (e.g., encyclopedia) can be helpful.
8. ______ Librarians, online library catalogs, online journal databases, and secondary sources
from reference lists are the most commonly used methods of locating literature.
9. ______ The reliability of published information is often related to an author’s quality of
credentials, experience in the field, and provable results in works for a specific article/book.
10. _____ Published research pretty much guarantees that the research is sound.
11. _____ When writing a literature review it is important to be informative, forthright and
logical.
12. _____ A literature review is mainly a presentation of previous findings; it should not be a
presentation of the author’s position.
13. _____ When writing a literature review it is good to use many direct quotes.
14. _____ When writing a literature review, each paragraph should begin with a reference to a
particular study, summarize the study, and move on to the next paragraph were the same pattern
is repeated.
Activity 3.3 In outline form, explain what you would include for each of the three parts of a
literature review.
1. Introduction
2. Body
3. Summary/Conclusion
20
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 3.4 Match the concepts in the left-hand column with the descriptions in the right-hand
column.
___ 1. literature
___ 2. body
___ 3. transition words
___ 4. headings
___ 5. introduction
___ 6. target audience
___ 7. summary
___ 8. seriation
a. A series or list of items.
b. Help the reader understand the organization of the paper.
c. Final section of a literature review.
d. An inanimate object that does not have the ability to
show something.
e. Determines the tone of the writing.
f. Then, next.
g. First part or section of a literature review.
h. Second part or section of a literature review.
© 2015. Cengage Learning. All rights reserved.
21
Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 4 Outcomes Research in Counseling
Activity 4.1 True (T) or False (F).
1. _____ Counseling can cause harm to clients.
2. _____ Treatment length is not related to counseling effectiveness.
3. _____ Clients are more likely to stay in counseling if the professional counselor administers
complete psychological evaluations, are perceived as trustworthy and competent, and are
perceived as skillful.
4. _____ Gender, socioeconomic class, race and age are all related to the treatment outcome.
5. _____ Group counseling has not been found to be effective.
6. _____ Comprehensive school counseling programs appear to be effective in improving
student academic performance, social skills, and behavior.
7. _____ About 20% of adults, children and adolescents have a mental disorder and most of
them seek and receive help.
8. _____ Clinical trial studies are the most common outcome research conducted.
9. _____ Counseling is very effective.
10. _____ Outcomes research cannot be trusted.
Activity 4.2 Match the concepts in the left-hand column with the descriptions in the right-hand
column.
___ 1. clinical trial studies
___ 2. effect size
___ 3. meta-analysis
a. When outcomes research is not relevant to practitioners.
b. Rely on comparison groups.
c. When researchers examine and summarize robust trends
and findings across studies, clients and contexts.
___ 4. outcomes research
d. A meaningful quantitative index.
___ 5. qualitative analysis
e. Provide a counselor with a recommended treatment
regimen.
___ 6. research-practice disconnect f. A specific quantitative technique that allows empirical
studies to be collapsed into a meaningful quantitative index.
___ 7. therapeutic alliance
g. Clinical trials, qualitative reviews, and meta-analytic
reviews.
___ 8. treatment manuals
h. Collaborative relationship between a client and
professional counselor.
Activity 4.3 List the seven variables identified by the American Psychological Association
(Steering Committee, 2002) believed to help make counseling effective:
1.
2.
3.
4.
5.
6.
7.
22
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 4.4 Using criteria specified in the text, write what each effect size means for each of
the meta-analytic studies below (i.e., no effect, small effect, medium effect, or large effect of
treatment).
Source
1. Bachar (1998)
2. Cuijpers (1998)
3. Horvath & Symonds (1991)
4. Shirk & Karver (2003)
5. Whiston, Sexton & Lasoff (1998)
6. Wilson, Gottfredson & Najaka (2001)
7. Prout & Prout (1998)
8. Prout & DeMartino (1986)
9. Orlinsky, Grawe & Parks (1994)
10. Shapiro & Shapiro (1982)
Effect
Size (d)
.80
.77
.26
.24
.45
~ .10
.97
.58
.20
1.12
© 2015. Cengage Learning. All rights reserved.
What the effect size means
23
Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 5 Qualitative Approaches to Research
Activity 5.1 Match the concepts in the left-hand column with the descriptions in the right-hand
column.
___ 1. saturation
___ 2. observer effect
___ 3. focus group
___ 4. inductive process
___ 5. observer expectation
___ 6. observation
___ 7. mixed methodology inquiry
___ 8. purposive selection
___ 9. documentary evidence
___ 10. observer bias
___ 11. researcher bias
a. When data is used to construct theory and/or lead to a
deeper understanding of an issue or phenomenon.
b. How the researcher’s worldview and presence in the
study influences the research design.
c. When the researcher watches participants in a natural
setting and documents what occurs.
d. The impact of the observer on the participants.
e. When research designs may combine or use both areas of
inquiry at various points of a study.
f. Typically consist of six to 12 members who can provide
insight about a particular issue.
g. When the observer’s personal attitudes and values affect
the observation or the researcher’s interpretation of the
observation.
h. Continuing to sample participants in a setting until no
new information is present or refutes the findings of
previous data.
i. When the researchers knowledge about the participants
leads her to expect certain behaviors.
j. Similar to the term sample.
k. Written, oral, visual, or cultural artifacts.
Activity 5.2 Describe the difference between the following types of interviews:
1. Structured interview: ____________________________________________________
________________________________________________________________________
________________________________________________________________________
2. Unstructured interview: __________________________________________________
________________________________________________________________________
________________________________________________________________________
3. Semi-structured interview: ________________________________________________
________________________________________________________________________
________________________________________________________________________
4. How are these three types of interviews similar? ______________________________
_______________________________________________________________________
_______________________________________________________________________
24
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 5.3 Match the concepts in the left-hand column with the descriptions in the right-hand
column.
___ 1. applicability
a. A single sheet summary of questions or reflections from
a single contact with a case.
___ 2. document summary forms
b. Demonstrating the believability and assurance that
conclusions make sense in a qualitative inquiry.
___ 3. persistent observation
c. Used to present data in an organized manner for the
purposes of various stages of analysis.
___ 4. trustworthiness
d. The extent to which the findings of an inquiry are
applicable in other settings and with other participants.
___ 5. consistency
e. Summary sheets that put a document into context.
___ 6. contact sheet
f. Infers that the researcher invests enough time to establish
trust with participants and eventually learn the culture,
climate, and socialization process inherent in human nature
and the phenomena under investigation.
___ 7. data displays
g. Questions about the replication and repetition of themes
if the method of inquiry were applied with the same or
similar research participants.
___ 8. prolonged engagement
h. The investigation’s credibility, transferability,
dependability, and confirmability.
___ 9. triangulation
i. Entails accessing multiple opportunities for the researcher
to identify characteristics within various situations that are
most relevant to the phenomenon under investigation.
___ 10. credibility
j. The use of multiple and different sources, methods,
investigators, and theories to gather information that is
pertinent to the study and the participants.
Activity 5.4 Fill in the empty boxes with information addressing each prompt as it applies to
qualitative and quantitative methods.
Qualitative Methods
Quantitative Methods
Purpose
Research Design
Approach
Hypotheses
Data Collection
Sampling
Nature of Data and Analysis
Use of Results
© 2015. Cengage Learning. All rights reserved.
25
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 5.5 Describe the following types of sampling methods.
1. Comprehensive sampling: ________________________________________________
________________________________________________________________________
________________________________________________________________________
2. Theoretical sampling: ____________________________________________________
________________________________________________________________________
________________________________________________________________________
3. Purposive-iterative sampling: _____________________________________________
________________________________________________________________________
________________________________________________________________________
4. Snowball sampling: _____________________________________________________
________________________________________________________________________
________________________________________________________________________
5. Maximum variation sampling: _____________________________________________
________________________________________________________________________
________________________________________________________________________
6. Homogenous sampling: __________________________________________________
________________________________________________________________________
________________________________________________________________________
7. Typical case sampling: ___________________________________________________
________________________________________________________________________
________________________________________________________________________
8. Extreme sampling: ______________________________________________________
________________________________________________________________________
________________________________________________________________________
9. Critical case sampling: ___________________________________________________
________________________________________________________________________
________________________________________________________________________
10. Convenience sampling: _________________________________________________
_______________________________________________________________________
_______________________________________________________________________
26
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 6 Qualitative Research Designs
Activity 6.1 Match the concepts in the left-hand column with the descriptions in the right-hand
column.
___ 1. member checking
___ 2. bracketing
___ 3. field notes
___ 4. audit trail
___ 5. participant observer
___ 6. negative case analysis
___ 7. life-world
___ 8. case study
___ 9. ethnography
___ 10. grounded theory
___ 11. triangulation
a. One way ethnographic researchers record data.
b. Collecting multiple forms of data.
c. A combination of feelings, thoughts, and self-awareness
experienced by an individual at any given moment.
d. A systematic procedure used to generate a theory that
explains a process, action, or interaction.
e. A people or cultural group.
f. Process includes looking for negative cases.
g. Involves returning to the field to check interpretations
with the informants.
h. An intentional process of naming values, biases, and
interests of the researcher.
i. When researchers become participants in the interactions
and in the communities that they study.
j. A way to trace what was done in a study, when, and why.
k. An in-depth exploration of a bounded system based on
extensive data collection.
Activity 6.2 Put the following stages in the order that they occur (1-3) in data analysis.
___ Axial coding
___ Open coding
___ Selective coding
Activity 6.3 Describe each of the following stages of the coding process.
1. Open coding: __________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Axial coding: _________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. Selective coding: _______________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
© 2015. Cengage Learning. All rights reserved.
27
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 6.4 Describe the purpose and key characteristics of each of the following types of
qualitative research approaches.
1. Ethnography: ________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Case Study: _________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. Phenomenology: _____________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4. Grounded Theory: ____________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Activity 6.5 Describe the following types of case studies:
1. Intrinsic case study
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Instrumental case study
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. Collective case studies
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
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© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 7 Quantitative Research Design in Counseling
Activity 7.1 Match the concepts in the left-hand column with the descriptions in the right-hand
column.
___ 1. population generalizability
___ 2. no-treatment control group
___ 3. random error
___ 4. internal validity
___ 5. placebo control groups
___ 6. ecological generalizability
___ 7. external validity
___ 8. experimental design
___ 9. quasiexperimental design
___ 10. nonexperimental design
___ 11. control of procedure
___ 12. single-case design
a. How the experiment is implemented.
b. Generalizability.
c. The degree to which results of a study can be applied to
other settings or conditions.
d. When researchers manipulate variables or introduce a
treatment to one subject or group over time and intently
study effects.
e. The degree to which the sample is representative of the
population of interest on the particular characteristic or
variable being studied.
f. Unpredictable fluctuations in instruments, participants, or
conditions.
g. A researcher’s ability to determine if a causal
relationship exists between the independent variable and
dependent variable.
h. Participants are given a treatment unrelated to the real
treatment.
i. Used to describe participant characteristics or behaviors,
and do not involve the application of any treatment to
participants.
j. Control group participants receive no treatment at all.
k. Does not use random assignment as a means of control.
l. Can be used to make cause-effect determinations.
Activity 7.2 Explain the three main types of evidence that researchers use to determine the
internal validity of the study.
1. Content-related evidence: ______________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
2. Criterion-related evidence: _____________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
3. Construct-related evidence: ____________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
© 2015. Cengage Learning. All rights reserved.
29
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 7.3 True (T) or false (F).
1. ___ Quantitative research primarily deals with descriptions.
2. ___ Through observation and manipulation of variables, quantitative researchers seek to
establish relationships between variables to explain the possible causes.
3. ___ Validity is the process of verifying that the research instruments and the results accurately
reflect the research question in order to make correct conclusions and inferences.
4. ___ External validity is the extent to which extraneous variables have been controlled or
accounted for, to ensure that the inferences or conclusions drawn from the results of the data are
accurate.
5. ___ Exercising more control over the variables in a research study tends to decrease the
generalizability or external validity of the results.
6. ___ Nonexperimental research does not manipulate any variables or test hypotheses, but rather
merely obtains data to determine specific characteristics of a group or to describe a phenomenon.
7. ___ Researchers using correlational designs seek to describe the direction and degree to which
two or more variables are related through the use of a correlation coefficient.
8. ___ A positive correlation indicates a contradictory relationship, with low scores on one
variable being associated with high scores on the other variable, or vice versa.
9. ___ Correlational studies do not indicate any cause and effect relationship among variables;
instead they indicate the magnitude or the direction of the relationships.
Activity 7.4 Generally speaking, what are the four ways to minimize threats to validity?
1. ___________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
2. ___________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
3. ___________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
4. __________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
30
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 7.5 Explain the following methods of control in experimental research:
1. Randomization: ______________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Random assignment: __________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
_____________________________________________________________________________
3. Matching: ___________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4. Participants as their own control: _________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
5. Analysis of covariance: ________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
© 2015. Cengage Learning. All rights reserved.
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 7.6 Explain the following threats to internal validity.
1. Selection: ___________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. History: ____________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. Maturation: __________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4. Mortality: ___________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
5. Instrumentation: ______________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
6. Testing: ____________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
7. Location: ___________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
8. Implementation: ______________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
32
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 7.7 What are some possible ways to control for the following threats to internal
validity.
Threats to
Internal Validity
Possible Ways to Control Threat
1. selection
2. history
3. maturation
4. mortality
5. testing
6. instrumentation
7. experimenter bias
8. statistical regression
Activity 7.8 List and explain the four general threats to external validity.
1. Placebo effects: _______________________________________________________
______________________________________________________________________________
2. Hawthorne effect: _______________________________________________________
______________________________________________________________________________
3. Order effects: __________________________________________________________
______________________________________________________________________________
4. Treatment interaction effects: _____________________________________________
______________________________________________________________________________
© 2015. Cengage Learning. All rights reserved.
33
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 7.9 Match the concepts in the left-hand column with the descriptions in the right-hand
column.
___ 1. survey research
a. Used to survey different samples from a population
whose members may change over time.
___ 2. panel study
b. Includes members of a particular population who do not
change over the course of the study.
___ 3. cohort study
c. A statistical procedure for examining the results of
several research studies on the same topic and determining
the congruence and divergence of outcome data.
___ 4. descriptive studies
d. Describe the characteristics of a population by selecting
a representative sample of respondents to research.
___ 5. casual-comparative studies
e. When questions are asked in person.
___ 6. trend study
f. Used to investigate the relationship among two or more
variables without attempting to manipulate them.
___ 7. correlational designs
g. Describe an existing phenomenon by using numbers to
characterize individuals or groups.
___ 8. interview
h. Includes the same sample of individuals surveyed at
different times.
___ 9. action research
i. Look at the degree and direction of the relationship
between variables.
___ 10. meta-analysis
j. Observe and describe some current condition; but rather
than introduce treatments, researchers look to the past to try
to identify possible causes.
___ 11. correlational research design k. Focuses on specifying a problem and creating an action
plan to address the problem.
34
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 8 Using Action Research and Single Subject
Research Designs
Activity 8.1 Match the concepts in the left-hand column with the descriptions in the right-hand
column.
___ 1. alternating treatment design
___ 2. problem evaluation
___ 3. behavioral processes
___ 4. duration recording
___ 5. nonsystematic observation
___ 6. changing criterion design
___ 7. event recording
___ 8. interaction element
___ 9. problem analysis
___ 10. latency recording
___ 11. momentary time sampling
___ 12. multiple baseline
a. Order of consequences and how those may affect the
observed behavior.
b. Assessment, definition of the problem, and the formation
of goals.
c. Empirical evaluation and data-based conclusions.
d. Narrative recording and contingency analysis.
e. Recording involving counting the frequency of
occurrences of the observed behaviors within a designed
observation period.
f. Recording that estimates of the average time that has
elapsed from beginning to the end of the behavior.
g. Measures the elapsed time between the occurrence of the
signal and the beginning of the behavior.
h. Occurs when the observer records occurrences of the
target behavior in the beginning or final portion of the
interval period.
i. A-B-C
j. A design that emulates an A/B simple phase change; in
that there is a baseline and only one treatment
implemented.
k. Used to measure more than one treatment method on a
single dependent variable.
l. A design with two or more replicated simple phase
changes, duplicated across two or more series categorized
by time, setting, subject or any combination thereof.
Activity 8.2 The Data-based Problem Solver Model is divided into four different sequential
phases. Put the correct number (1-4) beside each phase below to indicate the proper order.
___ Problem Analysis (PA)
___ Problem Evaluation (PE)
___ Problem Solution (PS)
___ Problem Identification (PI)
© 2015. Cengage Learning. All rights reserved.
35
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 8.3 Match the concepts in the left-hand column with the descriptions in the right-hand
column.
___ 1. problem solution
a. Within series, between series, and combined series
design.
___ 2. non-systematic observation b. Phase where counselors formulate appropriate research
questions relative to identifying the client’s problems.
___ 3. spot checking
c. Phase where counselors are concerned with the
development of an intervention.
___ 4. stability
d. When the behavior we see is consistent and
representative of the client’s normal state of operation
without any treatment
___ 5. momentary time sampling
e. Narrative recording and contingency analysis.
___ 6. problem identification
f. A chain of events where there is an antecedent,
behaviors, consequence and possible function.
___ 7. single subject design
g. When the observer records occurrences of the target
behavior in the beginning or final portion of the interval
period.
___ 8. sequence analysis
h. Cuts down on “drift” that may occur between observers.
___ 9. review of permanent products i. When one measures or evaluates the product of the
behavior.
___ 10. reversal design
j. Continuously evaluating interventions and conducting
measurements over a designated amount of time.
___ 11. time-series methodology
k. The key to accuracy in all types of systematic
observation.
___ 12. reliability of observations l. A design where the baseline data is collected in the initial
phase, followed by the treatment phase.
Activity 8.4 Which of the following describe group designs (G) and single subject research
designs (S):
___ 1. Compare differences within and between experimental conditions. Participants have been
randomly assigned.
___ 2. Compare different experimental conditions presented to the same participants of a group
over time.
___ 3. Requires a large number of homogenous participants.
___ 4. Permits experimental analysis with one participant or a small number of participants.
___ 5. Requires the use of relational and inferential statistics to evaluate the results.
___ 6. Relies on visual inspection of the data on a graph to describe the meaningfulness of
results.
36
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 8.5 Determine whether the concepts in the left-hand column represent systematic
observations (S) or non-systematic observations (N).
1. ______ interval recording
2. ______ finite response
3. ______ narrative recordings
4. ______ event recording
5. ______ duration recording
6. ______ sequence analysis
7. ______ latency recording
8. ______ momentary time sampling
9. ______ review of permanent products
Activity 8.6 Fill in the outline below for each phase of the Data-based Problem Solver Model
as it aligns with traditional research and clinical practice.
Phase
Phase I – Problem
Identification
Traditional Research
1.
Clinical Practice
1.
Phase II – Problem
Analysis
1.
1.
2.
2.
3.
3.
4.
Phase III – Problem
Solving
1.
1.
Phase IV – Problem
Evaluation
1.
1.
2.
2.
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37
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 8.7 Briefly describe the following types of designs:
1. Single subject research designs: _________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Within series designs: _________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. A-B-C design: _______________________________________________________________
______________________________________________________________________________
_____________________________________________________________________________
4. Changing-criterion design: _____________________________________________________
______________________________________________________________________________
_____________________________________________________________________________
5. Reversal design: _____________________________________________________________
______________________________________________________________________________
_____________________________________________________________________________
6. Parametric design: ____________________________________________________________
______________________________________________________________________________
_____________________________________________________________________________
7. Between-series design: _________________________________________________________
______________________________________________________________________________
_____________________________________________________________________________
38
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 9 Needs Assessment
Activity 9.1 Match the characteristics below with the correct type of assessment: (D) Data
driven needs assessment or (P) Perception based needs assessment.
___ 1. more traditional
___ 2. deals with real needs
___ 3. surveys
___ 4. objective
___ 5. prominently used in educational settings
___ 6. asks for perspectives, wants and needs
___ 7. consumers help prioritize needs and direct a program’s focus
___ 8. analysis of program data
___ 9. standardized and objective sources of information
___ 10. biased
Activity 9.2 Indicate whether each statement is a goal (G) or objective (O):
___ 1. To become better at math.
___ 2. Demonstrate their knowledge of addition by getting eight of the ten problems correct.
___ 3. Increase grades.
___ 4. Students will be able to name three effective ways to cope with anger that they can use
outside of group.
___ 5. Learn how to interact better with others.
___ 6. Learn ways to effectively deal with their anger.
___ 7. Get an A on the next test by using the newly learned study skills.
___ 8. Pass the next math test by meeting with a tutor twice a week.
___ 9. Students will be able to identify whether their method of dealing with their anger is
effective.
___ 10. Decrease the number of fights within the relationship.
___ 11. Stop smoking.
___ 12. Demonstrate their knowledge of the story by retelling it in their own words.
Activity 9.3 Answer the following questions about needs assessment:
1. Who should be assessed?
_____________________________________________________________________________________________
_____________________________________________________________________________________________
2. When should needs be assessed?
_____________________________________________________________________________________________
_____________________________________________________________________________________________
3. What needs should be assessed?
_____________________________________________________________________________________________
_____________________________________________________________________________________________
4. How should needs be assessed?
_____________________________________________________________________________________________
_____________________________________________________________________________________________
© 2015. Cengage Learning. All rights reserved.
39
Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 10 Program Evaluation and Accountability
Activity 10.1 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. comprehensive assessment
___ 2. criterion-referenced
___ 3. triangulated
___ 4. disaggregated data
___ 5. focused assessments
___ 6. norm-referenced
___ 7. informal assessments
___ 8. program goals
___ 9. scale of measurement
___ 10. surveys
a. Compares a score to a predetermined standard or level of
performance.
b. Allows the identification of programmatic strengths and
weaknesses and the determination of equity in subgroup
performance.
c.. Compares a score to the standardization sample to
determine where that score falls within a distribution of
scores.
d. Compared across groups.
e. Collect demographic data and evaluate multiple facets of
a program.
f. Usually short, one-page surveys that assess a specific
topic of concern.
g. Uses available sources of information and can be
completed quickly.
h. Measure opinions, attitudes and behaviors, and generate
a lot of useful data in a short period of time.
i. Nominal, ordinal, interval.
j. Standards.
Activity 10.2 True (T) or False (F).
1. ___ No program can meet the needs of an entire population.
2. ___ Needs assessments help answer the question: What are the needs of those being served?
3. ___ Students are not stakeholders.
4. ___ It is a good idea to invite principals, supervisors and funding sources to become members
of the advisory committee.
5. ___ Data driven needs assessment refers to information derived through the administration of
tests or other standardized and objective sources of information.
6. ___ Disaggregation means that total group scores have been broken down into specific
subpopulation scores so that differences between and among subgroups can be analyzed.
7. ___ Surveys are examples of perception-based needs assessment.
8. ___ Observation is an example of a formal assessment.
Activity 10.3 Put the following stages of the counseling program evaluation cycle in sequential
order of occurrence (1–5):
______ Outcomes assessment
______ Program implementation
______ Communicate results
______ Program monitoring and refinement
______ Program planning
40
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 10.4 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. perception data
___ 2. formative evaluation
___ 3. summative evaluation
___ 4. value-added assessment
___ 5. accountability
___ 6. evaluation
___ 7. results data
___ 8. No Child Left Behind Act
___ 9. needs assessment
___ 10. ASCA National Model
___ 11. stakeholders
a. The measurement of worth based upon the evidence
collected.
b. Increased the scrutiny of educational programming,
particularly targeting the outcomes of educational practices
on student achievement.
c. Anyone who may benefit from, is involved in, or
interested in the program.
d. An end-of-program evaluation; is very frequently
performed, sometimes even mandated by funding agencies
or administrators.
e. Provides important information that will help shape and
guide the provision of counseling programs and services.
f. The beliefs of stakeholders about the need for, or impact
of, services provided by the school counselor.
g. Refers to the outcomes of programs and interventions
provided in the comprehensive school counseling program.
h. Highlights three main categories of accountability data
for use by professional school counselors to advocate for
program effectiveness and impact.
i. Involves demonstrating responsibility for one’s actions.
j. A way of gathering information about program
implementation and effectiveness during the course of the
program.
k. Seeks to determine and document what a program adds
to what participants already possess.
Activity 10.5 What are the purposes and benefits of program evaluation in counseling?
1. ___________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
2. ___________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
3. ___________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
4. ___________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
5. ___________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
© 2015. Cengage Learning. All rights reserved.
41
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 10.6 Describe each of the stages of the counseling program evaluation cycle.
1. Program planning: ____________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Program implementation: _______________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. Program monitoring and refinement: ______________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4. Outcomes assessment: _________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
5. Communicate results: __________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Activity 10.7 The four types of information that professional school counselors use to provide a
foundation when developing programs and services for populations served are:
1. ___________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
2. ___________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
3. ___________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
4. ___________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
42
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 11 Collecting Data
Activity 11.1 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. equal intervals
a. Used to measure variables that, theoretically, can be divided to
provide a more precise measurement of some psychological
characteristic.
___ 2. ordinal scales
b. Leave little to no room for disagreement.
___ 3. quantitative variables c. Display named categories, which also fall in an ordered
sequence.
___ 4. measurement
d. Have ordered response categories and the magnitude between
each category choice is of an equal interval.
___ 5. discrete scales
e. Ordered, equal interval, and has an absolute zero point.
___ 6. continuous scales
f. Assigning numbers to characteristics of an individual so that the
numbers accurately describe the presence, amount, or degree of the
characteristic the individual possesses.
___ 7. interval scales
g. Simply classify or categorize a client characteristic into
nonordered, exhaustive and mutually exclusive categories.
___ 8. absolute zero point
h. The mathematical distance between the numbers must be
accurately reflected in the distances between scale descriptors.
___ 9. ratio scale
i. Can be structured, semi-structured or unstructured.
___ 10. nominal scale
j. Designated score on some scales indicating the total absence of
some characteristic.
___ 11. interviews
k. Permit comparisons of people in terms of order.
___ 12. qualitative variables l. Place people in unordered categories.
Activity 11.2 True (T) or false (F).
1. ____ Measurements of client characteristics give professional counselors a time- and costefficient method of discovering the best way to help clients and students.
2. ____Measurement of physical characteristics is more difficult and less precise than the
measurement of psychological characteristics.
3. ____ Measurements of psychological constructs are best thought of as approximations or
estimates, rather than precise measurements.
4. ____ Standardization is not essential to measurement procedures.
5. ____The four types of measurement scales are nominal, ordinal, interval, and rational scales.
6. ____ Nominal scales are the simplest type of scale to understand and use, and are extremely
useful.
7. ____ Nominal scales have no magnitudes, equivalent intervals, or absolute zero points.
8. ____ High school class rank is an example of an ordinal scale.
9. ____ No absolute comparisons can be made with interval scales.
© 2015. Cengage Learning. All rights reserved.
43
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 11.3 Describe the four types of measurement.
1. Nominal scales: ______________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Ordinal scales: _______________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. Interval scales: _______________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4. Ratio scales: _________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Activity 11.4 Determine whether the following are characteristics of nominal (N), ordinal (O),
interval (I) or ratio (R) scales.
1. ___ Numbers to name categories.
2. ___ Numbers categorize, order and indicate equal distances.
3. ___ Inferential statistics are usually applied to this data.
4. ___ Variables are discrete and qualitative.
5. ___ Height, weight, Kelvin temperature scale.
6. ___ Provide ratio comparisons.
7. ___ Named categories that fall in an ordered sequence.
8. ___ Numbers do not possess the characteristic of equal distance between given points.
9. ___ Analyzed using nonparametric statistical tests.
10. ___ A researcher can add and subtract the data but cannot multiply or divide it.
11. ___ Simplest scale to use.
12. ___ Use numbers to categorize, order, represent equal distances, and have a true zero point.
13. ___ Class rank, places in a race, Likert scale.
14. ___ Sex, marital status, U.S. geographic area of residence.
15. ___ Celsius and Fahrenheit temperature scales, standardized intelligence or achievement
tests.
16. ___ All mathematical operations can be used with ratio data.
44
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 11.5 Describe the following methods for collecting data:
1. Interviews: __________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Observations: ________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. Written questionnaires, surveys and rating scales: ___________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4. Program records and schedules: __________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
5. Standardized and educator-made tests: ____________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
6. Performance indicators: _______________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
7. Products and portfolios: ________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
© 2015. Cengage Learning. All rights reserved.
45
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 11.6 Describe the following instruments used to gather data.
1. Open-ended items: ____________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Forced-choice items: __________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. Ranking items: _______________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4. Checklist items: ______________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
5. Binary option items: ___________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
6. Likert items: _________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
7. Guttman-type items: ___________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
8. Semantic differential items: _____________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
46
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 12 Describing Data
Activity 12.1 Under what circumstances might you use each of the following graphing or
frequency distributions?
1. Bar graphs: _________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
2. Histograms: ________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
3. Frequency polygon: __________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
4. Stem-and-leaf plots: __________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
5. Box-and-whisker plot: ________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
Activity 12.2 A class of 20 students took a test and received the following scores: 81, 99, 53,
76, 77, 88, 82, 89, 91, 93, 64, 77, 82, 71, 95, 21, 73, 82, 84, and 92. Using the set of data above
find the following measures of central tendency:
1. Mean:
2. Median:
3. Mode:
Activity 12.3 Using the same set of data in Activity 13.2 now find the following measures of
variability.
1. Range:
2. Semi-interquartile range:
© 2015. Cengage Learning. All rights reserved.
47
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 12.4 Match the following frequency distributions and graphs to their correct names:
histogram, frequency polygon, box-and-whisker plot, stem-and-leaf plot, bar graph.
10
20
10
8
8
15
Frequency
Count
Count
6
10
4
6
4
2
5
2
Mean = 11.98
Std. Dev. = 6.09613
N = 50
0
0
4.00
1.00
2.00
3.00
6.00
5.00
8.00
7.00
age
1. _____________
/
0
10.00
14.00
17.00
20.00
24.00
9.00
12.00
15.00
18.00
22.00
25.00
5.00
hrstv
10.00
15.00
20.00
25.00
hrstv
2. _______________
3. ________________
/
0 3
0* 67889
1 02233444
1* 5688
2 0
4. _____________
5. _____________
Activity 12.5 Below are names of graphs. Draw a graph that goes along with the names.
Positively skewed
Negatively skewed
Normal curve
Platykurtic
Leptokurtic
Mesokurtic
48
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 12.6 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. measures of variability
___ 2. positively skewed
___ 3. correlation statistics
___ 4. median
___ 5. curve smoothing
___ 6. mean
___ 7. standard deviation
___ 8. range
___ 9. attenuated standard deviation
___ 10. grouped frequency distribution
___ 11. central tendency
___ 12. negatively skewed
___ 13. descriptive statistics
___ 14. mode
___ 15. inferential statistics
a. Involves guessing within the bounds of what is
known.
b. Graphical displays or common statistics that help
to describe and understand data.
c. Arithmetic average of a set of scores.
d. Scores are grouped into convenient class
intervals.
e. Reveal how strongly two sets of scores are
related.
f. Middlemost score.
g. Tells what the distribution looks like as scores
away from the middle are explored.
h. Gives an idea of what the center or middle of a
distribution looks like.
i. Most frequently occurring score in a set of scores.
j. Help predict human behaviors and reach likely
conclusions.
k. Distance between the highest and lowest scores
in a distribution.
l. When a distribution has a lot of low scores.
m. When a distribution has a lot of high scores.
n. Square root of the variance.
o. Unbiased estimate.
© 2015. Cengage Learning. All rights reserved.
49
Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 13 Deriving Standardized Scores
Activity 13.1 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. CEEB score
___ 2. deviation IQ
___ 3. interpretative range
___ 4. normal curve
___ 5. z-score
___ 6. scaled score
___ 7. quartile
___ 8. T score
___ 9. stanine
___ 10. percentile rank
___ 11. normal curve equivalent
___ 12. standard score
a. A bell-shaped, mathematically defined, smooth curve in
which the mean, median, and mode lie at the exact center.
b. When the mean of a distribution of scores is 50 and the
standard deviation is 10.
c. Scores used on most intelligence, achievement, and
perceptual skills tests.
d. Declares that the mean of a distribution of scores is 100
and the standard deviation is 15.
e. Standardized scores with a mean of 50 and a standard
deviation of 21.06.
f. A system that divides the normal curve into nine
equidistant segments.
g. Scores with a mean of 10 and a standard deviation of 3;
frequently used to report subtest or subscale scores.
h. Standardized scores used on the Scholastic Assessment
Test (SAT) with M = 500 and SD = 100.
i. Indicate the percentage of observations that fall below a
given score on a measure plus one-half of the observations
falling at the given score.
j. Method for dividing a percentile rank distribution into
four portions.
k. Can help convey performance information to individuals
who may be unsophisticated in test score interpretation.
l. Has a mean of zero, a standard deviation of one, and is
computed from the raw score distribution.
Activity 13.2 Answer the following questions using the standardized score chart and normal
curve figure from the text.
1. What percentage of the population falls between one standard deviation above and below the
mean based on the normal curve? __________________________________________________
2. What percentage of the population falls between two standard deviations above and below the
mean based on a normal curve? ___________________________________________________
3. What percentage of the population falls between three standard deviations above and below
the mean based on a normal curve? ________________________________________________
4. How many scores fall below the mean based on a normal curve? _______________________
5. How many scores fall above the mean based on a normal curve? _______________________
50
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 13.3 Kayla took a test and received a raw score of 35. The sample of scores has a
mean of 40 and a standard deviation of 15.
1. What is the formula for computing a z-score?
2. What would Kayla’s z-score be?
3. What formula would you use to transform her z-score to a standard score (M = 100; SD = 15)?
4. What would Kayla’s standard score be?
Activity 13.4 Using the following standard scores, find the corresponding percentile ranks and
interpretative ranges.
Test
IQ
Oral Reading
Reading Comprehension
Math Computation
Math Problem Solving
Written Expression
Spelling
Science
Social Studies
Standard
Score
123
111
93
99
130
72
62
95
101
Percentile Rank
© 2015. Cengage Learning. All rights reserved.
Interpretative Range
51
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 13.5. Answer the following questions.
1. How would you explain what percentile ranks are to parents or caregivers?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. How would you explain what interpretative ranges are to parents or caregivers?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. How would you explain the IQ and oral reading scores in activity 14.4 to a parent?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
52
© 2015. Cengage Learning. All rights reserved.
Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 14 Statistical Hypothesis Testing
Activity 14.1 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. non-directional test
a. The hypothesis that is rejected or retained using inferential
statistics and is often the opposite of what the researcher believes
to be true.
___ 2. directional test
b. The researcher hypothesizes that a given score will be either
higher or lower than the chosen level of significance.
___ 3. alpha level
c. The likelihood of rejecting the null hypothesis given that the null
hypothesis should be rejected.
___ 4. null hypothesis
d. The researcher predicts the two groups will differ, but does not
predict which group will be higher.
___ 5. alternative hypothesis e. Lies in one or both tails of the sampling distribution and
indicates the sample values most unlikely to occur at the given
level of significance.
___ 6. rejection range
f. The amount of type I error the researcher is willing to allow in
the study.
___ 7. inferential
g. Generally the research hypothesis; a statement of what occurs if
the null hypothesis is rejected.
___ 8. inference
h. Determines the probability that the null hypothesis is true.
___ 9. significance tests
i. Used to infer correlation and causation.
___ 10. statistical power
j. Making a judgment on a population parameter based on
sampling.
Activity 14.2 True (T) or false (F).
1. ___ Hypothesis testing in univariate statistics is used to determine whether or not any change
in the dependent variable is due to change in the independent variable or simply due to chance.
2. ___ Inferential statistics are about a population, so the hypotheses are created using parameter
statistics.
3. ___ In hypothesis testing, the null hypothesis is always tested.
4. ___ If the null hypothesis is rejected, then no statistical group differences were found.
5. ___ Studies that lack sufficient power are more likely to make a type I error.
6. ___ The level of significance in a study is directly related to the amount of type I error allowed
in a study.
7. ___ Scores that are below the stated level of significance and critical value are considered to
be statistically significant.
8. ___ The more power in a study, the greater the chance of identifying a non-significant
difference when there actually is a significant difference.
9. ___ The easiest method of increasing power in a study is to increase sample size.
10. ___ For social sciences, power is usually deemed sufficient at .80.
11. ___ As probability of making a Type I error increases, the probability of making a Type II
error also increases.
12. ___ Power is the same as confidence.
© 2015. Cengage Learning. All rights reserved.
53
Student Workbook for Research and Evaluation in Counseling, 2e
Activity 14.3 Order the following steps (1-7) that a researcher uses when conducting hypothesis
testing.
________ Calculate the test statistic and probability values.
________ Write the results.
________ Select an appropriate statistic.
________ Identify the null and alternative hypothesis.
________ Evaluate the outcome for statistical significance.
________ Establish a level of significance.
________ Evaluate practical significance.
Activity 14.4 Explain the six ways that statistical power can be increased.
1. Increasing alpha: _____________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Increasing sample size: ________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. Increasing the effect size: _______________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4. Minimizing error: _____________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
5. Using a one-tailed test when appropriate: __________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
6. Using a parametric test: ________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Activity 14.5 Explain the difference between Type I error and Type II error.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
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CHAPTER 15: Using SPSS for Introductory Data Analysis
Activity 15.1 True (T) or False (F).
1. ___ Before you can perform any statistical analyses, you must create or open a database.
2. ___ SPSS not only manages data and performs statistical analyses, but it also interprets the
results.
3. ___ There are often multiple approaches available in SPSS that produce the same results.
4. ___ Learning to use SPSS requires an investment of time and effort.
5. ___ The spreadsheet rows represent the individual cases and the columns represent the
variables.
6. ___ It is useful to define the variables first.
7. ___ Using longer names and labels to describe the variable helps SPSS format output more
efficiently.
8. ___ For categorical variables, one should provide numeric codes.
9. ___ At its heart, SPSS is really a command processor; that is, all procedures are actually run
based on a series of text commands that are generated by the menu options.
10. ___ The most important thing to do after entering data is to make sure it was entered
correctly.
11. ___ The data rarely needs to be transformed in some way before performing any statistical
analyses.
12. ___ Categorical variables and scale variables should be summarized in the same way.
13. ___ When one wishes to know whether the mean for the target population differs from some
hypothesized value, a single-sample t test is run.
14. ___ SPSS uses the same procedure for linear regression whether there is one predictor or
many.
Activity 15.2 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. descriptive statistics
___ 2. correlation
___ 3. variable
___ 4. frequencies
___ 5. t test
___ 6. nonparametric test
___ 7. SPSS
___ 8. extreme value
a. A phenomenon that accompanies another phenomenon;
is related in some way to it.
b. Measures whether there is a difference between two
means.
c. A score at either of the two extremes.
d. Evaluates hypotheses about the shapes of distributions
and is used with nominal or ordinal data.
e. A commonly used statistical computer package.
f. Describes and summarizes data collected on a variable or
the relationship between variables.
g. Any characteristic, behavior, event, or other
phenomenon that can vary.
h. The number of observations in each category, score or
grouped score interval.
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 15.3 Following the procedures listed in Chapter 11, use SPSS to enter the data and run
the following statistical analyses.
1.
2.
3.
4.
5.
Compute a coefficient alpha reliability for the scale items 1-11.
Compute a Pearson r for “hours watching TV” and “hours studying.”
Compute a Pearson r for “hours watching TV” and “current GPA.”
Compute a Pearson r for “hours studying” and “current GPA.”
Compute an independent t-test with “gender” as the independent variable and “current GPA”
as the dependent variable.
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Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 16 Univariate Inferential Statistics
Activity 16.1 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. model assumptions
a. Concerned about the estimation of with-in group
differences.
___ 2. univariate
b. Specific tests for paired observations.
___ 3. repeated measures
c. Used in hypothesis testing when the groups being studied
are normally distributed.
___ 4. degrees of freedom
d. The magnitude of the difference between a group mean
and grand mean.
___ 5. parametric statistics
e. Focused on the measurement of one variable.
___ 6. post hoc analysis
f. Conducted when two or more independent variables are
examined across a single dependent variable.
___ 7. treatment effect
g. Calculated to provide an estimate of the normal curve
given the number of groups and sample size of each group.
___ 8. normality
h. Conducting research with sample sizes being equal in all
groups.
___ 9. factorial ANOVA
i. A specific set of conditions that must be met for the
statistical test to be deemed appropriate and meaningful.
___10. homogeneity of variances
j. Concerned with the distributions of the groups being
compared in a study.
__ 11. balanced design
k. The statistical tests conducted to indicate exactly where
statistically significant differences exist.
Activity 16.2 Explain the purpose of the following inferential statistical techniques and the
specific hypothetical question each answers.
Type of
Purpose
Answers the Question
Test
z-test
t-test
ANOVA
ANCOVA
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 16.3 True (T) or False (F).
1. ___ When comparing samples, the researcher needs to account for sample size and the number
of groups being compared.
2. ___ To determine whether or not the observed score is statistically significant at the .05 level
of significance, the observed score must be less than the critical value.
3. ___ In a dependent t-test means are compared between two randomized groups.
4. ___ In an independent t-test the means are compared from the same sample across time.
5. ___ Unlike the t-test, the F-test is calculated using squared deviations.
6. ___ When statistically significant differences are found in an ANOVA, what is really known
is that statistically significant differences exist among the groups.
7. ___ Statistical significance refers to the probability that the rejection of the null hypothesis
occurred outside the realm of chance.
8. ___ Cohen’s d is used to determine the effect size for the differences between two groups.
9. ___ Practical significance is always measured in standard deviation units.
10. ___ Statistical analyses may lend credibility and evidence to a particular process or
procedure.
11. ___ Analysis of covariance (ANCOVA) is a statistical analysis that combines ANOVA and
regression.
Activity 16.4 What are some similarities among the z-test, t-test, ANOVA, and ANCOVA?
1. ___________________________________________________________________________
___________________________________________________________________________
2. ___________________________________________________________________________
___________________________________________________________________________
3. ___________________________________________________________________________
___________________________________________________________________________
4. ___________________________________________________________________________
___________________________________________________________________________
5. ___________________________________________________________________________
___________________________________________________________________________
6. ___________________________________________________________________________
___________________________________________________________________________
58
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Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 17 Correlation and Regression
Activity 17.1 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. reliability
___ 2. tau-equivalent
a. All conditional distributions have equal variances.
b. The output for linear regression with two or more
predictors.
___ 3. covariance
c. r = 1.0.
___ 4. homoscedasticity
d. Indicates the degree to which the measures are free of
error.
___ 5. test-retest reliability
e. Indicates what proportion of the variance in one of the
variables is associated with the variance in the other
variable.
___ 6. multiple regression
f. The average cross-product of the deviation scores.
___ 7. correlation
g. Line of best fit.
___ 8. perfect positive correlation h. Measure the same trait and their true scores have equal
variances in the population of respondents.
___ 9. coefficient of determination i. r = -1.0.
___ 10. perfect negative correlation j. Measure of relationship.
___ 11. regression line
k. Stability of test data.
Activity 17.2 Based on the following Pearson correlation coefficients (r), label whether the
magnitudes are very high, high, moderate, low, or very low correlations according to the criteria
provided in the text.
1. ____________ r = .63
2. ____________ r = -.73
3. ____________ r = .98
4. ____________ r = .31
5. ____________ r = -.65
6. ____________ r = .56
7. ____________ r = -.93
8. ____________ r = .19
9. ____________ r = .48
10. ___________ r = .82
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 17.3 Draw graphs below to illustrate each of the following concepts.
1. Positive slope
2. Negative slope
3. Negative correlation
4. Positive correlation
5. Perfect positive correlation
6. Perfect negative correlation
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 17.4 True (T) or False (F).
1. ___ The Pearson r is a measure of the linear relationship between two variables
2. ___ The Pearson r is used to determine the degree to which the individual differences in one
variable can be associated with the individual differences in another variable.
3. ___ Correlation not only indicates the relationship between two variables but it indicates
causation.
4. ___ When there is a correlation between two variables, the linear relationship between them
cannot be used to predict values on one of the variables from values on the other variable.
5. ___ A positive correlation between two variables is when high X values relate to low Y values.
6. ___ A negative correlation between two variables is when low X values relate to high Y
values.
7. ___ A positive slope is when the direction of the dots in a scatterplot is from the lower left to
the upper right.
8. ___ The closer the dots are to a straight line, the weaker the correlation.
9. ___ The Pearson r takes on values from -1.0 to 1.0.
10. ___ When r = 0 it means there is no correlation.
11. ___ The Pearson r is sample dependent.
12. ___ The size of the Pearson r is affected by factors such as the sample size, range of X and Y
values in the sample, and nature of the relationship between X and Y.
Activity 17.5 True (T) or false (F).
1. ___ Two variables, X and Y, may correlate.
2. ___ A correlation between X and Y may be mediated by Z.
3. ___ Two variables may correlate because they are both affected by a third variable.
4. ___ When the effect of Z is removed from X and Y, the resulting correlation is referred to as
semipartial correlation between X and Y.
5. ___If the correlation between X and Y is spurious, their partial correlation is zero.
6. ___ In general, which correlation to use depends on the specific research question being asked.
7. ___ One situation for potential use of partial correlations is when the correlation between two
variables is mediated by other variables.
Activity 17.6 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. spurious correlation
___ 2. partial correlation
___ 3. semipartial correlation
a. When the effect of Z is removed from X and Y.
b. When the correlation between X and Y exists solely
because it is affected by a common cause, Z.
c. When a third variable, Z, is removed from X, but not
from Y.
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 17.7 Determine whether the following are characteristics of a partial correlation (P) or
a semipartial correlation (S).
1. ______ When the effect of Z is removed.
2. ______ Controlling for Z.
3. ______ Interest is on the correlation between two variables, while removing the effect of other
variables from one of the two variables only.
4. ______ When the correlation between two variables is mediated by other variables.
5. ______ When Z is removed from X, but not from Y.
6. ______ When the correlation between X and Y exists solely because it is affected by a
common cause, Z.
7. ______ Spurious correlation.
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Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 18 Nonparametric Tests of Statistical Inference
Activity 18. 1 Answer the following questions.
1. What are nonparametric tests? ___________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Nonparametric tests are applied under what two kinds of conditions? ____________________
______________________________________________________________________________
______________________________________________________________________________
3.Why are parametric tests more powerful than nonparametric test? _______________________
______________________________________________________________________________
______________________________________________________________________________
4. When do nonparametric tests begin to show advantages in statistical power over their
parametric counterparts? _________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Activity 18.2 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. Kolmogorov-Smirnov
a. An approach to testing whether two or more samples
differ in their distribution without assuming normality.
___ 2. resampling-based
b. Leads to the expectation that the groups will have
identical variances.
___ 3. nonparametric tests
c. Involves ranking the data.
___ 4. fully nonparametric inference d. Used to analyze nominal or ordinal data, or when the
assumptions required for parametric analysis have been
violated.
___ 5. Mann-Whitney U
e. Serves as a test of the null hypothesis that two samples
come from identical populations.
___ 6. parametric test
f. Estimates a referent distribution of a test statistic by
constructing a corresponding null statistic under the null
hypothesis.
___ 7. homoscedasticity
g. Assumes away everything but differences in location.
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 18.3 True (T) or False (F).
1. ___ Loglinear models are often applied to more advanced ANOVA models.
2. ___ Poisson regression is used when a count variable is regressed onto a set of continuous
and/or categorical predictors.
3. ___ Generalized Estimating Equations (GEE) are used for nominal data.
4. ___ When error distributions are normal or at least symmetric, then nonparametric tests are
more powerful than parametric tests.
5. ___ Kolmogorov-Smirnov tests are more powerful than the Bootstrap, Permutation, or RankBased methods.
6. ___ The basic idea behind resampling-based nonparametric methods is to estimate a referent
distribution of a test statistic by constructing a corresponding null statistic under the null
hypothesis.
7. ___ Permutation-based methods resample without replacement to create a referent
distribution.
8. ___ Nonparametric bootstrap tests are similar to the permutation approach, except the
resamples are generated by drawing with replacement from the data.
9. ___ The major similarity between bootstrap and permutation methods is that they both
resample with replacement so that the same data value can be in a resample twice.
10. ___ Ranks are never considered preferable to the actual data.
11. ___ When using a parametric test if two groups have identically skewed distributions with
the same variance, then any differences would be due to differences in location.
12. ___ A rank-based test may be considered a robust alternative because it is testing a null
hypothesis similar in concept to the parametric null.
13. ___ The most commonly used parametric procedures test differences in location because
other distributional differences are assumed not to exist.
14. ___ Data transformations can alter the fundamental nature of the data and the null hypothesis
being tested, thus complicating interpretation.
Activity 18.4 Determine whether the following are characteristic of parametric tests (P) or
nonparametric tests (N).
1. ___ chi square
2. ___ bootstrap
3. ___ normally distributed scores
4. ___ interval or ratio scale
5. ___ resampling-based methods
6. ___ permutation-based methods
7. ___ Mann-Whitney U
8. ___ nominal or ordinal data
9. ___ t-tests
10. ___ Kolmogorov-Smirnov
11. ___ under normal circumstances are more powerful
12. ___ ANOVA
13. ___ skewed data
14. ___ Wilcoxon Rank Sum
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 18.5 True (T) or False (F).
1. ___ One of the most widely used designs in behavioral research is the ANOVA model.
2. ___ Constant variance is often called homoscedasticity in ANOVA.
3. ___ Noncontrast variance is a problem because it does not allow the researcher to focus on a
single parameter.
4. ___ Assuming away differences in distributional shape and spread allows the test to focus on a
single parameter that defines the differences between population distributions.
5. ___ Parametric assumptions concern samples not populations.
6. ___ A wide range of research designs can be analyzed with parametric linear models.
7. ___ The presence of outliers would not be reason for concluding a distribution is not normal.
8. ___ When the null hypothesis is true the dependent variable and the population are different.
9. ___ All nonnormaility is due to data entry error or nondeclared missing values.
10. ___ Data transformations are mathematical modifications to the values of a variable.
11. ___ Parametric statistical procedures assume that the variables are normally distributed.
12. ___ The values of the transformed variable are the same as the original variable.
13. ___Logarithmic transformations are a class of transformations, rather than a single
transformation.
14. ___ Ranks methods and most other nonparametric methods generalize to multiple group
experiments.
Activity 18.6 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. trimming and Winsorization
___ 2. parametric test
___ 3. robust
___ 4. skewed distributions
___ 5. ANOVA
___ 6. parameters of interest
___ 7. ladder of power transformations
___ 8. inverse transformation
___ 9. inverse of squares transformation
a. less sensitive to outliers.
b. involves obtaining data on samples from two or
more populations that differ with respect to some
characteristics.
c. Suggested when linear model assumptions are
violated.
d. 1/Y2.
e. Used to make parameter estimates sometimes at
the expense of reduced statistical efficiency.
f. A test that focuses on a single parameter.
g. 1/Y.
h. When a measure has a ceiling or floor effect.
i. Means, regression coefficients, correlation
coefficients.
© 2015. Cengage Learning. All rights reserved.
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 18.7 Determine whether the following are characteristic of parametric tests (P) or
nonparametric tests (N).
1. ___ chi square
2. ___ nominal data
3. ___ normally distributed scores
4. ___ interval scale
5. ___ ratio scale
6. ___ Mann-Whitney U
7. ___ ordinal data
8. ___ t-tests
9. ___ outliers
10. ___ under normal circumstances are more powerful
11. ___ ANOVA
12. ___ skewed data
13. ___ Kruskal-Wallis tests
Activity 18.8 Answer the following questions about data transformations.
1. What are data transformations?__________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Describe linear transformations? ________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. Describe nonlinear transformations? ______________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4. Give some examples of both linear and nonlinear transformations? ______________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 18.9 Explain the following concepts.
1. Explain the concept of trimming. _________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Explain the concept of Winsorization. _____________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. Explain the concept of square root transformations. __________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4. Explain the concept of log transformations. ________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
5. Explain the concept of inverse transformations._____________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
6. Explain the concept of inverse of squares transformation.______________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
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Student Workbook for Research and Evaluation in Counseling, 2e
CHAPTER 19 Multivariate Statistical Analysis
Activity 19.1 True (T) or False (F).
1. ___ In multivariate statistical analysis, the word “multivariate” indicates that two or more
dependent variables are simultaneously used in a single analysis.
2. ___ Correlation for multiple regression predictions always infers causation.
3. ___ In multiple regression analysis, more variables are always better.
4. ___ According to a recommended rule about 15 subjects per predictor are needed for a
multiple regression equation to predict well with future samples.
5. ___ The estimates of multiple regression parameters are sensitive to outliers.
6. ___ Data errors and observations which represent extreme magnitudes on variables are both
causes of outliers.
7. ___ The interpretation of any regression coefficient is based on the assumption that the
relationship between the criterion variable and the predictor is the same for any fixed value of the
other predictors.
8. ___ The equation of the best fit represents a surface cutting through dimensional space.
9. ___ The regression coefficients for a given predictor indicate the change in the predicted Y
value produced by a one-unit change in this predictor, while controlling for all the other
predictors.
10. ___ A multiple regression coefficient is statistically significant even if its population value is
zero.
11. ___ Two regression models are referred to as the full model and restricted model if the
restricted model includes only some of the predictors in the full model.
12. ___ The higher the multicollinearity, the smaller the standard error for the regression
coefficients.
13. ___ The coefficient of determination for the original sample is always greater than its
counterpart produced by the original regression equation when applied to any other sample.
Activity 19.2 What are the three major problems related to multicollinearity in multiple linear
regression:
1. ____________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. ____________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. ____________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 19.3 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. screening sample
___ 2. orthogonal
___ 3. multiple regression
___ 4. cross-validation
___ 5. coefficient of determination
___ 6. shrinkage
___ 7. coefficient of multiple correlation
___ 8. power
___ 9. multicollinearity
___ 10. specification errors
___ 11. a priori
a. Indicates the proportion of the variance in Y
accounted for by the predictors.
b. Occur when relevant predictors are omitted or
irrelevant predictors are included into the regression
equation.
c. The sample initially used to develop a multiple
regression equation.
d. Does not correlate with any of the remaining
predictors.
e. Before a study.
f. Two or more predictor variables are used to
predict the criterion variable, Y.
g. The probability of rejecting the null hypothesis
when it is indeed false.
h. Depends on the ratio of sample size to number of
predictors.
i. The Pearson r between the actual and predicted Y
scores.
j. Occurs when there are moderate to high
correlations among the predictors.
k. The estimation of R2 shrinkage.
Activity 19.4 What are the three most recommended procedures for detecting outliers and
influential data points when using SPSS and other major statistical packages? List each of the
three procedures and explain what the procedure does.
1. _____________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. ______________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. ______________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 19.5 List and explain five approaches to statistical selection of predictors in multiple
regression.
1. ____________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. ______________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. ______________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4. ______________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
5. ______________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 19.6 True (T) or False (F).
1. ___ Multivariate analysis of variance (MANOVA) is employed when two or more groups are
compared on a set of two or more dependent variables.
2. ___The omnibus null hypothesis in MANOVA states that the group centroids are equal for the
study population.
3. ___ A statistically significant Wilk’s lambda always means that the groups differ on separate
dependent variables.
4. ___ MANOVA and separate univariate ANOVAs address the same research questions and
provide the same information about the data and their interpretation.
5. ___The relative importance of a given dependent variable is determined by the magnitude of
its F-to-remove statistic.
6. ___ Linear discriminant functions are determined in increasing order of their contribution to
the group separation and they are correlated.
7. ___ The word “orthogonal” means correlated.
8. ___ Determining an appropriate sample size with MANOVA applications depends on the
number of groups, number of dependent variables, effect size, power of the test, and level of
statistical significance.
9. ___ Use of too many dependent variables is not recommended because the power of the test
tends to decrease when the number of dependent variables increase.
Activity 19.7 What are the two circumstances when correlated contrasts may occur?
1. ______________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. ______________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Activity 19.8 According to the rule of thumb purposed by Cohen, rate the following effect sizes
as small, medium, or large.
1. ___________
2. ___________
3. ___________
4. ___________
5. ___________
6. ___________
7. ___________
8. ___________
.50
.89
.79
.49
.23
.15
.55
.81
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 19.9 Determine whether the following are more characteristic of MANOVAs (M) or
ANOVAs (A).
1. ___ Employed when two or more groups are compared on a set of two or more dependent
variables.
2. ___ Takes into account the correlations among the dependent variables.
3. ___ Correlations are ignored.
4. ___ Groups are compared on each dependent variable separately.
5. ___ Appropriate to use when the researcher wants to know the individual dependent variable
on which the compared groups differ.
6. ___ A statistically significant Wilk’s lambda indicates that there is at least one linear
combination of the dependent variables that maximally separates the groups.
7. ___ The omnibus null hypothesis states that the group centroids are equal for the study
population.
8. ___ Does not allow researchers to address broader and more insightful questions that involve
relationships between the dependent variables.
9. ___ Is used to address complex phenomena and research questions in counseling, education,
and other behavioral fields.
10. ___ Often fails to provide sufficient information to address questions involving substantively
related variables.
11. ___ Appropriate with research questions about group differences on linear composites of
dependent variables.
Activity 19.10 What five statistical assumptions in MANOVA are closely related to those in
ANOVA?
1. ______________________________________________________________________
______________________________________________________________________________
2. ______________________________________________________________________
______________________________________________________________________________
3. ______________________________________________________________________
______________________________________________________________________________
4. ______________________________________________________________________
______________________________________________________________________________
5. ______________________________________________________________________
______________________________________________________________________________
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Student Workbook for Research and Evaluation in Counseling, 2e
Activity 19.11 In general, factor analysis is used for what purposes?
1. __________________________________________________________________
2. __________________________________________________________________
3. __________________________________________________________________
4. __________________________________________________________________
5. __________________________________________________________________
Activity 19.12 Match the concepts in the left-hand column with the descriptions in the righthand column.
___ 1. orthogonal
a. Used to determine how many factors underlie the set of
variables, which variables form which factor, etc.
___ 2. structure coefficients
b. Orthogonal factors are extracted in the order of their
contribution to explaining additive parts of the total
variance of the observed variables.
___ 3. principle component analysis c. Factors are uncorrelated.
___ 4. principal factor methods
d. Refers to a principal factor method when it is assumed
that the variance in each observed variable is fully
explained by the underlying factors.
___ 5. factor analysis
e. Correlations between a factor and all observed variables.
Activity 19.13 Explain when and how exploratory factor analysis (EFA) and confirmatory
factor analysis (CFA) are used.
Exploratory Factor Analysis (EFA):
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Confirmatory Factor Analysis (CFA):
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
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Student Workbook for Research and Evaluation in Counseling, 2e
ANSWER KEY
CHAPTER 1 The Nature and Importance of Inquiry
Activity 1.1 Key: 1) e, 2) d, 3) l, 4) a, 5) h, 6) b, 7) i, 8) k, 9) c, 10) g, 11) f, 12) j.
Activity 1.2 Key: 1) A, 2) A, 3) B, 4) B, 5) A, 6) B, 7) A, 8) B, 9) B, 10) B, 11) A.
Activity 1.3 Key: 1) e, 2) d, 3) c, 4) b, 5) a, 6) g, 7) f.
Activity 1.4 Key:
Research Method
Description
 Seek to study the effects of interventions, or cause-and-effect and the differences of these
effects across groups of subjects.
 At least two groups of subjects.
Experimental
 Subjects in one group receive a treatment, the control group receives a placebo.
 Subjects assigned randomly to make the groups as equal to each other as possible.
Correlational
Survey
Observational



Seek to study the relationships among variables.
Does not seek to study cause-and-effect.
Correlations can be positive, negative, or nonexistent.

Seeks to apply numbers and percentages about what people believe, think and how they
behave.
Descriptive research using numbers.
Group of subjects are administered a questionnaire.
Limited to the time and contexts in which the data were collected.





Seek to study people’s behavior in a natural setting.
Data gathered in a systematic way using observation checklists, tallying behaviors of
interest, coding, etc.
CHAPTER 2 Characteristics of a Research Study
Activity 2.1 Key: 1) k, 2) i, 3) d, 4) j, 5) b, 6) a, 7) e, 8) f, 9) l, 10) c, 11) h, 12) g.
Activity 2.2 Key: 4, 12, 2, 7, 3, 10, 8, 5, 1, 11, 9, 6.
Activity 2.3 Key: 1) i, 2) e, 3) d, 4) f, 5) l, 6) a, 7) j, 8) b, 9) g, 10) c, 11) h, 12) k.
Activity 2.4 Key: 1) N, 2) P, 3) P, 4) N, 5) N, 6) P, 7) P, 8) P.
Activity 2.5 Key: 1) T, 2) T, 3) F, 4) F, 5) T, 6) T, 7) T, 8) T, 9) F, 10) F, 11) T, 12) T.
CHAPTER 3 Locating, Reviewing and Writing Research
Activity 3.1 Key: 4, 1, 5, 2, 3.
Activity 3.2 Key:1) T, 2) F, 3) F, 4) T, 5) F, 6) T, 7) T, 8) T, 9) T, 10) F, 11) T, 12) F, 13) F, 14) F.
Activity 3.3 Key:
1. Introduction
 Might use compelling statistics, a brief scenario, or dramatic, factual statements related to the topic.
 Clear and concise purpose of the study.
 Engage the reader.
 Briefly describe how the current study was arrived at, where one intends to go and why it is important to do so.
2. Body
 Briefly reports what others have found.
 Begin with an introductory paragraph focusing the reader on the information that will follow.
 Divided into sections and possibly subsections.
 Each paragraph should begin with a topic sentence that clearly states what the paragraph will encompass.
 Each topic section should end with an appropriate transition that links the previous and upcoming information.
 Should begin with a broad focus and end with a narrow focus.
3. Summary/Conclusion
 Include a summary of the literature largely relevant to building the rationale for the study.
 Stress how the review relates to the study.
 Ties together the main points of the review and gives the reader a succinct depiction of what is known to date.
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Student Workbook for Research and Evaluation in Counseling, 2e
 Conclusions justified based on the literature.
Activity 3.4 Key: 1) d, 2) i, 3) f, 4) b, 5) g, 6) e, 7) c, 8) a.
CHAPTER 4 Counseling Outcomes Research
Activity 4.1 Key: 1) T, 2) F, 3) T, 4) F, 5) F, 6) T, 7) F, 8) F, 9) T, 10) F.
Activity 4.2 Key: 1) b, 2) d, 3) f, 4) g, 5) c, 6) a, 7) h, 8) e.
Activity 4.3 Key: (in no particular order) Positive regard, congruence/genuineness, repairing alliance ruptures, selfdisclosure, quality of relational interpretations, management of countertransference, and feedback.
Activity 4.4 Key: 1) large, 2) medium, 3) small, 4) small, 5) small, 6) no, 7) large, 8) medium, 9) small, 10) large.
CHAPTER 5 Introduction to Qualitative Approaches to Research and
Evaluation
Activity 5.1 Key: 1) h, 2) d, 3) f, 4) a, 5) i, 6) c, 7) e, 8) j, 9) k, 10) g, 11) b.
Activity 5.2 Key:
1. Structured interview: The researcher plans all the questions in advance. Each participant is asked the same set of
questions, often in the same sequence.
2. Unstructured interview: May resemble casual conversation with a purpose. `
3. Semi-structured interview: Researchers formulate the questions in advance but may modify the format as the
interview progresses.
4. How are these three types of interviews similar? They all use open-ended questions, and the researcher is
interested in gaining a rich account of the participant’s experiences.
Activity 5.3 Key: 1) d, 2) e, 3) i, 4) h, 5) g, 6) a, 7) c, 8) f, 9) j, 10) b.
Activity 5.4 Key:
Qualitative Methods
Quantitative Methods
To describe and understand the ways that
To study relationships, cause-and-effect.
Purpose
people give meaning to their own and others’
May manipulate variables, situations, or
behavior. To understand social phenomena as
conditions to study complex phenomena.
they occur naturally.
Research Design
Designs may be selected in advance and may
Designs developed prior to the study.
evolve during the study.
Approach
Inductive; used to develop concepts and
Deductive; tests theory.
theory.
Hypotheses
Research questions, not hypotheses, guide the
Hypotheses (null and alternative) are
study.
established in advance.
Data Collection
Individual or group interviews and/or
Standardized instruments, surveys, rating
observation, archival data.
scales, checklists.
Sampling
Purposive (expert informant), small samples.
Randomization techniques, large samples.
Nature of Data and
Data primarily are words. Narrative
Data primarily are numbers. Statistical tests
Analysis
description and interpretation used for
are used for analysis.
analysis.
Use of Results
To holistically describe phenomena, generate
To generalize to a population.
theory, and increase understanding of a
particular individual or group.
Activity 5.5 Key:
1. Comprehensive sampling: Every unit is included in the study.
2. Theoretical sampling: The researcher continues to select new participants throughout the research process as the
evolving theory emerges. Sampling continues until no new information surfaces. Participants are selected based on
the concepts that have theoretical relevance to the evolving theory.
3. Purposive-iterative sampling: The process of collecting data, analyzing data, and then selecting additional
participants until the description is comprehensive.
4. Snowball sampling: The initially selected participants suggest names of other participants who would be
appropriate for the study. It produces a pool of potential participants, and these new participants can, in turn, provide
names of other potential participants.
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5. Maximum variation sampling: The researcher may choose to interview participants who vary in age, race, gender,
and other factors. The goal is to explore differences and commonalities across participants, with a particular interest
in searching for those who might think differently from other participants, thus getting a broad range of perspectives
and experiences and constantly look for cases that might dispute present findings.
6. Homogenous sampling: Refers to purposefully selecting participants from a particular subgroup whose experience
is suspected to be somewhat alike. The purpose is to describe the experience of the subgroup in depth.
7. Typical case sampling: Involves selecting participants whose experience is typical of the one under study.
8. Extreme sampling: Selecting participants whose experiences were the most positive or most negative, thereby
helping researchers discover the boundaries of differences within an experience.
9. Critical case sampling: Look for experiences that are particularly significant because of their intensity or
irregularity. The cases are selected because the researcher believes that they can be used to illustrate a point
particularly well.
10. Convenience sampling: They are chosen based on availability or ease of access.
CHAPTER 6 Qualitative Research Designs
Activity 6.1 Key: 1) g, 2) h, 3) a, 4) j, 5) i, 6) f, 7) c, 8) k, 9) e, 10) d, 11) b.
Activity 6.2 Key: Order - 2, 1, 3.
Activity 6.3 Key:
1. Open coding involves examining the initial transcribed data in order to name and categorize discrete elements in
the data. Transcribed interview statements and other forms of data are analyzed line-by-line. Important words and
phrases are labeled. These labeled phrases are compared to other labeled phrases, thereby helping the researcher
determine the concepts that are present in the data.
2. Axial coding is the second coding stage in data analysis, when concepts developed during open coding are
examined and organized into categories. Relationships among categories are examined, which may result in the
establishment of broader (key) categories and categories that are subsumed under the key categories.
3. Selective coding is the final stage of data analysis. The goal of this stage is to create a substantive theory that is
grounded in the data. The researcher looks for the main theme that is presented in the data. The researcher continues
to collect and analyze data but with more focus on developing the theory. The researcher continues to recheck
existing data to see how the theory matches what has already been collected. The researcher also compares the
developing theory with existing processes found in the literature.
Activity 6.4 Key:
1. Ethnography: The purpose is to describe the cultural characteristics of a group in its natural setting. Immersion in
the site is important. Its disciplinary roots are in anthropology.
2. Case Study: The purpose is to address research questions by describing one or more cases, or bounded systems in
depth. It uses multiple data collection techniques to examine the particular unit of study. Its multidisciplinary roots
are in medicine, law, business, education, and social sciences.
3. Phenomenology: The purpose is to determine the meaning, structure, or essence, of a particular phenomenon as
experienced by an individual or by many individuals. Researchers conduct in-depth interviews with participants so
as to understand the essence of the experience. Its disciplinary roots are in philosophy.
4. Grounded Theory: The purpose is to generate theory based on the data collected about a particular phenomenon.
Grounded theorists systematically collect data, identify categories found in the data, connect those categories, and
use the resulting information to inductively form a theory. Its disciplinary roots are in sociology.
Activity 6.5 Key:
1. Intrinsic case study: The goal of this type of case study is to increase understanding of the intrinsic aspects of a
particular client, organization, or other entity.
2. Instrumental case study: The researcher is interested in understanding more than just a single case. Instrumental
case studies are designed to help the researcher understand some external theoretical question or problem. The
particular case is still examined in depth, but the case is secondary to the external interest that is under investigation.
3. Collective case studies: Represents an extensive study of several instrumental cases. The specific cases are
selected because of their potential to increase understanding about a larger theoretical collection of cases.
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CHAPTER 7 Quantitative Approaches to Research
Activity 7.1 Key: 1) e, 2) j, 3) f, 4) g, 5) h, 6) c, 7) b, 8) l, 9) k, 10) i, 11) a, 12) d.
Activity 7.2 Key:
1. Content-related evidence asks the question of whether the instruments or sample accurately represent the variable
under study. A researcher would ask whether the questions used in the instrument adequately assess the variable
under study. To ensure content-related validity, researchers should look over the content and format of the
instrument to be used.
2. Criterion-related evidence is used to determine validity by comparing the instrument used in the study to another
instrument or form of assessment presumed to measure the same variable. Two forms of criterion-related validity are
predictive and concurrent. Predictive validity is obtained by administering the instrument and then allowing an
elapsed time interval to pass for later comparison with the criterion scores. Concurrent validity requires
administration of the instrument and criterion data at the same time. A correlation coefficient often is used to
determine if a relationship exists between the scores from the two instruments.
3. Construct-related evidence includes a variety of different types of evidence supporting the characteristic being
measured. Three common ways to measure construct-related validity includes use of a clearly defined variable, the
hypotheses based on theory explaining the variable, and logical and empirically tested hypotheses.
Activity 7.3 Key: 1) F, 2) T, 3) T, 4) F, 5) T, 6) T, 7) T, 8) F, 9) T.
Activity 7.4 Key:
1. Standardize the conditions in which the study occurs.
2. Know the characteristics of the participants in the study.
3. Know the details of the study such as where, when and the extraneous events that may occur.
4. Plan and choose a suitable design
Activity 7.5 Key:
1. Randomization: Randomization or random sampling is the process of drawing a research sample in which each
member of a population has an equal chance of being selected. Random selection reduces sampling biases and
increases generalizability of the results to the larger population.
2. Random assignment: Random assignment is a randomization process which is usually done after the research
participants are selected to determine which participants will have which value of the independent variable. Random
assignment is essentially the process of assigning individuals or groups to different treatment conditions in order to
maximize the probability that subject characteristics are matched between the experimental groups, thus controlling
for confounding variables.
3. Matching: Matching is the technique of equating groups on one or more variables with the result of each member
of one group having a direct counterpart in another group.
4. Participants as their own control: This often occurs in single-subject experimental design or in some pretestposttest designs. This option provides high internal validity because participants serve as their own controls;
however, the results are extremely low with respect to external validity. Single-subject studies increase external
validity through the process of replication and extension.
5. Analysis of covariance: This tests the main and interaction effects of categorical variables on a continuous
dependent variable, controlling for the effects of selected other continuous variables which co-vary with the
dependent variable. The control variable is called the covariate. The main purpose of the analysis of covariance is
statistical control of variability when experimental control cannot be used. It is a statistical method for reducing
experimental error or for removing the effect of an extraneous variable.
Activity 7.6 Key:
1. Selection is the manner in which participants are chosen to participate in a study and the manner in which they are
assigned to groups. Subject characteristics are those individual factors that may account for an observed effect.
Differences that may be present between the groups prior to the study will continue throughout the study and may
result in a treatment effect when no true experimental effect is present.
2. History refers to confounding events outside of the research study that can alter or affect participants’
performance, such as experimental environmental events. Control of history can be addressed through subject
matching or randomization.
3. Maturation refers to the natural process of aging over time. Maturation can play a major role in longitudinal
studies and when studying children. Control of maturation can be addressed through subject matching or
randomization.
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4. Mortality refers to the possibility of a differential effect due to those participants who drop out during the study,
versus if the participants had stayed in the study. Since participants must have the right to withdraw from the study
at any point without penalty, it is difficult for researchers to control mortality.
5. Instrumentation refers to the changes in the measurement devices or procedures used during the course of the
study. As a result of instrumentation, changes in scores may be related to the instrument differences rather than the
independent variable. Thus, reliability of instrument scores is important.
6. Testing refers to the practice effect of participants exposed to the intervention or test. Chances are that
participants will perform better the second time merely due to practice. Some instruments have alternate forms to
control for this effect.
7. Location may affect the accuracy of scores if differences exist for the place of testing and the data collection
process. It is important to ensure that the environment is the same across conditions.
8. Implementation refers to variations in the way that the intervention is introduced or conducted, which may affect
the results of the study.
Activity 7.7 Key:
1. Selection: Random selection, random assignment.
2. History: Random selection, random assignment.
3. Maturation: Subject matching, randomization.
4. Mortality: Subject matching and omission.
5. Testing: Control group.
6. Instrumentation: Consistency and reliability.
7. Experimenter bias: Double blind study.
8. Statistical regression: Omit extreme scores, randomization.
Activity 7.8 Key
1. Placebo effects are those occasions when participants in a study act according to expectations derived from
inadvertent cues to the anticipated results of the study. Conducting a blind study reduces the possibility of this threat
by ensuring that participants are not aware of anticipated outcomes.
2. Hawthorne effect refers to changes in performance by the mere presence of others watching. Having a control
group can be one method of controlling for the Hawthorne effect.
3. Order effects are treatment effects derived from the order in which treatment is administered rather than from the
treatment itself.
4. Treatment interaction effects refer to the potential for a treatment protocol to have an effect based on the
characteristics of the participant rather than on the group as a whole.
Activity 7.9 Key: 1) d, 2) h, 3) b, 4) g, 5) j, 6) a, 7) i, 8) e, 9) k, 10) c, 11) f.
CHAPTER 8 Action Research and Using Single Subject Research
Designs
Activity 8.1 Key: 1) k, 2) c, 3) a, 4) f, 5) d, 6) j, 7) e, 8) i, 9) b, 10) g, 11) h, 12) l.
Activity 8.2 Key: in the order 2, 4, 3, 1; that is, PI, PA, PS, PE.
Activity 8.3 Key: 1) c, 2) e, 3) h, 4) d, 5) g, 6) b, 7) a, 8) f, 9) i, 10) l, 11) j, 12) k.
Activity 8.4 Key: 1) G, 2) S, 3) G, 4) S, 5) G, 6) S.
Activity 8.5 Key: 1) S, 2) S, 3) N, 4) S, 5) S, 6) S, 7) S, 8) S, 9) S.
Activity 8.6 Key:
Phase
Traditional Research
Clinical Practice
Phase I – Problem Identification
1. Research question
1. Referral problem
Phase II – Problem Analysis
1. Pilot studies
1. Assessment
2. Defining the research question
2. Defining a problem
3. Formulating a hypothesis
3. Formation of goals
4. Objectives
Phase III – Problem Solving
1. Methodology of research
1. Development of an
intervention
Phase IV – Problem Evaluation
1. Empirical evaluation
1. Empirical evaluation
2. Data-based conclusions
2. Data-based conclusions
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Activity 8.7 Key:
1. Single subject research designs: Inferences are made about the type of intervention by comparing different
treatment conditions presented to the same participants of a group over time. This also reduces the number of errors
a professional counselor makes.
2. Within-series designs: Enable professional counselors to draw causal inferences between intervention and
changes in behavioral data. They can even provide evidence of the effectiveness of an intervention with minimal
changes in a treatment phase.
3. A-B-C design: Provides a method for evaluating the benefits of one component of treatment in interaction with
another. The two components in an A/B/C design are measured against the data in the baseline phase.
4. Changing-criterion design: Emulates an A/B simple phase change; in that there is a baseline and only one
treatment implemented. It allows the professional counselor to evaluate the level of intervention necessary to
achieve the therapeutic goals.
5. Reversal design: A/B/A/B. The baseline data is collected in the initial phase, followed by the treatment phase.
Then in the second initial phase treatment is removed and changes relative to the removal of the treatment are
recorded. Then the treatment phase is re-introduced as the second phase. This design can increase internal validity
by demonstrating an opposite pattern in trend and variability between the A and B phases.
6. Parametric design: Similar to changing-criterion designs but the treatment results are compared to other phase
designs rather than a specific criterion. Each phase progresses along the lines of a continuum.
7. Between-series design: Allows professional counselors to group target behaviors by condition and allows
professional counselors to evaluate the results of treatment across settings.
CHAPTER 9 Needs Assessment
Activity 9.1 Key: 1) P, 2) D, 3) P, 4) D, 5) D, 6) P, 7) P, 8) D, 9) D, 10) P.
Activity 9.2 Key: 1) G, 2) O, 3) G, 4) O, 5) G, 6) G, 7) O, 8) O, 9) O, 10) G, 11) G, 12) O.
Activity 9.3 Key:
1. Professional counselors should assess important stakeholders, whether other professional counselors, clients,
students, parents, local business people, educators, local agencies, funding sources, etc.
2. In agencies, clinics or other non-school venues needs assessments should be conducted about every three to six
years or when the professional counselor is considering major programmatic changes and wants or needs data to
guide the program. The ASCA standards lends itself to a six-year continuous needs assessment and
accountability cycle in which professional school counselors divide the academic, career, and personal-social
standards. Thus, every six years the entire comprehensive developmental school counseling program will be
assessed for need and accountability.
3. Either comprehensive assessments should be used which collect demographic information and evaluate multiple
facets of a counseling program, including services offered, topics of interest addressed, and goals/objectives
pursued, or focused assessments which assess a specific concern like academic skills, career development or
awareness, a specific mental health issue, etc.
4. Needs should be assessed either informally, which use available sources of information familiar to the
professional counselor and can be completed very quickly, or formally, using standardized and objective
measures, which results in greater ability to replicate the evidence.
CHAPTER 10 Program Evaluation and Accountability
Activity 10.1 Key: 1) e, 2) a, 3) d, 4) b, 5) f, 6) c, 7) g, 8) j, 9) i, 10) h.
Activity 10.2 Key: 1. T, 2. T, 3. F, 4. T, 5. T, 6. T, 7. T, 8. F.
Activity 10.3 Key: Order - 4, 2, 5, 3, 1
Activity 10.4 Key: 1) f, 2) j, 3) d, 4) k, 5) i, 6) a, 7) g, 8) b, 9) e, 10) h, 11) c.
Activity 10.5 Key:
1. The primary goal of program evaluation is to provide useful information to the practitioner about the
effectiveness and impact of counseling services.
2. Program evaluation can help professional counselors determine the extent to which clients are being helped by
interventions.
3. Program evaluation can help identify the most effective interventions for client populations served.
4. Program evaluation may be used as an advocacy tool in counseling with practitioners using findings to
determine program impact on larger socio-political concerns of clients.
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Student Workbook for Research and Evaluation in Counseling, 2e
5.
Program evaluations can provide essential feedback for consideration in the development or modification of
counseling programs and services.
Activity 10.6 Key:
1. Program planning: Professional counselors identify appropriate counseling interventions and programs that can
be implemented in order to meet the needs of their client populations. They consider additional factors that may
influence the provision of counseling services including staff and facility resources and any special program
materials or requests. Professional counselors also identify methods for measuring program outcomes.
2. Program implementation: Counseling services are implemented. Professional counselors consider if the planned
programs and interventions are functional and if changes need to be made before programs are fully implemented.
Feedback from clients can help professional counselors improve the outcomes of their interventions.
3. Program monitoring and refinement: Professional counselors monitor the progress of interventions and programs
and make modifications based on client feedback and improvement, the professional counselor’s own assessments
and observations, and the administrator’s observations and feedback. The professional counselor determines if
program objectives are being addressed through counseling services.
4. Outcomes assessment: The professional counselor uses outcomes assessments to determine if counseling
objectives have been met and if treatments and programs have been successful. Professional counselors collect final
data identified during the program’s planning stage, analyze data sources and draw conclusions about intervention
and program effectiveness.
5. Communicate results: The professional counselor communicates the outcome data and program results to
stakeholders by providing presentations or evaluation reports to stakeholders.
Activity 10.7 Key:
1. Feedback from stakeholders
2. Strategic planning
3. Needs assessment
4. Program objectives
CHAPTER 11 Collecting Data
Activity 11.1 Key: 1) h, 2) c, 3) k, 4) f, 5) b, 6) a, 7) d, 8) j, 9) e, 10) g, 11) i, 12) l.
Activity 11.2 Key: 1. T, 2. F, 3. T, 4. F, 5. F, 6. F, 7. T, 8. T, 9. T.
Activity 11.3 Key:
1. Nominal scales are the simplest type of scale to understand and use, although their usefulness is quite limited.
Nominal scales use numbers to name categories without imposing any requirement of order or assuming any equal
intervals of measurement between the various categories. Nominal variables are discrete and qualitative, meaning
that the numbers simply label a participant’s membership in one exclusive category. Ordinarily, nominal data is
analyzed using nonparametric statistical tests, and through frequency counts. Because nominal scales have no
magnitudes, equivalent intervals, or absolute zero point, few mathematical operations can be performed on the
results.
2. Ordinal scales use numbers not only to categorize, but also to rank or order the responses according to some
ascending degree of magnitude. However, the various numbers do not possess the characteristic of equal distance
between given points. Places in a race or a Likert scale are examples of ordinal scales. Descriptive and
nonparametric statistics can be used with ordinal data.
3. Interval scales use numbers to not only categorize and order, but also to indicate equal distances between points
on a scale. A researcher can add and subtract interval data, but cannot multiply and divide (no zero point).
Inferential statistics are usually applied to interval data.
4. Ratio scales use numbers not only to categorize, order and represent equal distances, but these scales also have a
true zero point; that is, zero means the complete absence of some characteristic. Ratio scales are commonly used in
the natural sciences, but rarely in the social sciences. They have the advantage of providing ratio comparisons. All
mathematical operations can be used with ratio data. Inferential statistics are usually applied to ratio data.
Activity 11.4 Key: 1) N, 2) I, 3) I/R, 4) N, 5) R, 6) R, 7) O, 8) O, 9) N, 10) I, 11) N, 12) R, 13) O, 14) N, 15) I, 16)
R.
Activity 11.5 Key
1. Interviews of the professional counselor, key personnel, or members of stakeholder groups can provide valuable
data. Structured interviews provide no variation in administration, thus generating clear evidence of strengths and
weaknesses. Unstructured formats allow for follow-up and deeper exploration, and are commonly used in qualitative
studies. Usually, multiple respondents are required for patterns and conclusions to emerge. Face-to-face interviews
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Student Workbook for Research and Evaluation in Counseling, 2e
are generally better than phone interviews, although usually more costly and inconvenient. Careful consideration
must be given to question development and interviewers must guard against introducing bias.
2. Observations can be classified as informal or formal. Informal observations tend to yield anecdotal data through a
“look-and-see” approach. Formal or structured observations usually involve a protocol and predetermined
procedures for collecting specific types of data during a specified time period. Structured procedures tend to
minimize bias.
3. Written questionnaires, surveys and rating scales are usually paper-and-pencil instruments asking a broad range of
open and closed-ended questions. Questionnaires and rating scales typically ask for factual responses while surveys
generally solicit participants’ perceptions. By far the greatest weakness of this data collection method is that many
participants do not complete or return the instrument. It also requires a certain level of literacy. Few respondents
take the time to write lengthy responses so usually it is best to keep the questions simple and close-ended with the
opportunity for participants to expand upon a response if needed. Multi-scaled response formats often provide more
helpful results than yes-no questions.
4. Program records and schedules are naturally occurring and helpful sources of evaluation data. If stored on a
computer in a database format, this kind of data is particularly accessible and a professional counselor is welladvised to consider this ahead or time when determining how best to maintain electronic records and schedules.
Archives should also be kept in good order to facilitate record searches. In particular, professional counselors should
keep previous program improvement documents and outcome study reports.
5. Standardized and educator-made tests provide objective sources of measurable student performance and progress
in the academic, career, and personal-social domains. Individual, classroom, and school-wide tests can be extremely
helpful and powerful measures. Professional counselors can design and develop tests to measure behaviors and
characteristics, much like teachers design tests to measure academic achievement.
6. Performance indicators may include a students’ grade point average or classroom grade, but also includes daily
work behaviors/habits and attitudes.
7. Products and portfolios are real-life examples of performance. A product is anything created by a participant that
stemmed from a program standard. A portfolio is a collection of exemplar products which can be evaluated to
determine the quality of an individual’s performance.
Activity 11.6 Key
1. Open-ended items do not provide choices for the participant to respond, to, just a stem or question that cannot be
answered with a yes or no, or single word. The purpose of the open-ended item is to generate an extended response
without biasing the participant with preconceived notions of what their response should be. Each of these questions
requires the participant to think and construct a response that has meaning to her as an individual. Open-ended
questions are frequently used in qualitative research and program evaluation studies. The responses yield thick, rich
descriptive data, but are difficult to code and analyze quantitatively. Participants frequently skip open-ended
questions because these questions require participants to think and put effort into a response.
2. Forced-choice items are popular in testing. Multiple-choice items provide a stem or question along with several
possible answers. The respondent is instructed to choose the correct or best answer from among the given responses
choices.
3. Ranking items requires participants to rank or place in order a number of choices. Usually three or four choices
are optimal. Ranking items is easy for participants to respond to but difficult to analyze statistically. Sometimes
participants do not rank all of the choices. Also, because the data are ranked, nonparametric or descriptive statistics
are used, not parametric statistics.
4. Checklist items list words so the participant can mark the choices that apply. Sometimes participants are asked to
check their favorite, or the best choices; other times participants may check all that apply. The more items that are
checked, the more difficult the data is to analyze.
5. Binary option items provide two mutually exclusive answer choices for each item. The disadvantage of binary
items is that on items of preference or attitude, the participant’s choice may not be all or none, thus contributing to
response error. On the other hand, statistical analysis is simplified because of the forced-choice format.
6. Likert items assess a participant’s attitude or preference by presenting a question along with an order of response
choices. The classic Likert scale did not include a middle choice, but researchers frequently add a middle choice.
Researchers also need to decide whether or not to present a numerical scale along with the answer choices. Usually
the researcher will not provide the numbers, but will assign these numbers during the coding procedures so that
quantitative analysis is facilitated. There is some disagreement over the optimal number of response choices to offer,
but reliability tends to be enhanced when scales provide four or five response choices. It is also essential that every
point on the response continuum be labeled.
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7. Guttman-type items provide a series of items, usually with binary response choices, and on a continuum such that
a participant’s response to one item in the series indicates they would also approve of all choices below the level
indicated. In order to be analyzed, these data must be coded as a sequence. Often times, Guttman scales are more
simply represented as a single item with a multiple-choice format.
8. Semantic differential items use bipolar adjectives comprising activity pairs, evaluative pairs, or potency pairs. The
evaluative type is used most frequency in quantitative research. When using semantic differential scales it is
considered good practice to periodically switch the poles from right to left to avoid a response set bias and keep the
participants from simply circling all one number. Researchers usually use between 5-9 choices, and usually only the
bipolar ends are labeled.
CHAPTER 12 Describing Data
Activity 12.1 Key:
1. Bar graphs: Used to visually display discrete variables (nominal data).
2. Histograms: Used to visually display continuous variables (ordinal, interval or ratio data).
3. Frequency polygon: Used to visually display continuous variables (ordinal, interval or ratio data).
4. Stem-and-leaf plots: You would use stem-and-leaf plots when you wanted to visually display continuous
variables but you wanted to provide the actual numerical values.
5. Box-and-whisker plot: You would use a box-and-whisker plot when you wanted to display trends in data and to
visually display potential skewing.
Activity 12.2 Key:
1. Mean: The mean is 78.5. The mean is the arithmetic average of a set of scores. M = ∑X/n = 1570/20 = 78.5.
2. Median: The median is 82. When lining up the scores from lowest to highest (21, 53, 64, 71, 73, 76, 77, 77, 81,
82, 82, 82, 84, 88, 89, 91, 92, 93, 95, 99) the 10th score from each end is 82.
3. Mode: The mode is 82. In this distribution of scores, 82 occurs three times.
Activity 12.3 Key:
1. Range: The range is 79. Range = XH – XL + 1 where XH = the highest score and XL = the lowest score. So, 99 –
21 + 1 = 79.
2. Semi-interquartile range: The semi-interquartile range is 8.375. The semi-interquartile range is the difference
between the three points within a distribution which divide the distribution into four equal parts. Q = (Q 3 – Q1)/2.
Rank:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 53 64 71 73 76 77 77 81 82 82 82 84 88 89 91 92 93 95 99
↑
↑
↑
25%ile
50%ile
75%ile
Place # 5.25
Place#10.5
Place#15.75
Q1 = 73.75
Median (Q2) = 82
Q3 = 90.50
Thus, Q = (90.50 – 73.75)/2; Q = 16.75/2; Q = 8.375.
Activity 12.4 Key: 1. bar graph, 2. frequency polygon, 3. histogram, 4. box-and-whisker plot, 5. stem-and-leaf plot.
Activity 12.5 Key:
Positively skewed
82
Negatively skewed
Normal curve
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Platykurtic
Leptokurtic
Mesokurtic
Activity 12.6 Key: 1) g, 2) l, 3) e, 4) f, 5) a, 6) c, 7) n, 8) k, 9) o, 10) d, 11) h, 12) m, 13) b, 14) i, 15) j.
CHAPTER 13 Deriving Standardized Scores
Activity 13.1 Key: 1) h, 2) d, 3) k, 4) a, 5) l, 6) g, 7) j, 8) b, 9) f, 10) i, 11) e,
12) c.
Activity 13.2 Key: 1. About 68% (68.26%). 2. About 95% (95.44%). 3. About 99% (99.74%). 4. 50% or half of the
scores. 5. 50% or half of the scores.
Activity 13.3 Key:
1. z = X - Mx
SD
Where X = the participant’s raw score; Mx = the sample mean; and SD = the sample standard deviation
2. X = 35; Mx = 40; SD = 15;
z = X - Mx
SD
z = 35 – 40
15
z = -.33
3. SS = 15(z) + 100
4. SS = 15(z) + 100 = 15(-.33) + 100 = 95
Activity 13.4 Key:
Test
Standard Score
Percentile Rank
Interpretative Ranges
IQ
123
94
Superior
Oral Reading
111
77
High Average
Reading Comprehension
93
32
Average
Math Computation
99
47
Average
Math Problem Solving
130
98
Very Superior
Written Expression
72
3
Borderline
Spelling
62
1
Very Deficient
Science
95
37
Average
Social Studies
101
53
Average
Activity 13.5 Key:
1. The scores I am about to discuss with you are percentile ranks. Percentile ranks can best be understood by
imagining a line of 100 children with the 1st child being the lowest performer and the 100th child being the highest
performer. For example, if he received a percentile rank of 65, he would have exceeded 65% of children his age.
Caleb’s score is his place on that line.
2. The scores I am about to discuss with you are interpretative ranges. Interpretative ranges are verbal descriptions
of scores. For example, Average means normal performance, High Average means higher than normal and Low
Average means below normal performance.
3. Caleb’s IQ ability exceeded that of 94% of children his age. His performance was Superior. Caleb’s oral reading
ability exceeded that of 77% of children his age. His performance was High Average.
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CHAPTER 14 Statistical Hypothesis Testing
Activity 14.1 Key: 1) d, 2) b, 3) f, 4) a, 5) g, 6) e, 7) a, 8) i, 9) h, 10) c.
Activity 14.2 Key: 1) T. 2) T, 3) T, 4) F, 5) F, 6) T, 7) F, 8) F, 9) T, 10) T, 11) F, 12) F.
Activity 14.3 Key: 4, 7, 3, 1, 5, 2, 6.
Activity 14.3 Key:
1. Increasing alpha: A null hypothesis (true or false) is more likely to be rejected when alpha is .05 than when it is
.01.
2. Increasing sample size: A correct decision is more likely to be made when the sample size is 50 than when it is
25. Adding participants to samples with smaller numbers will increase the power more than adding participants to
samples that are already larger.
3. Increasing the effect size: Maximizing the effects of the independent variable increases the likelihood that effects
will be detected. Effects are maximized by administering the treatment over a long period of time or in sufficient
intensity.
4. Minimizing error: When potential sources of systematic error and random error are controlled, it is easier to detect
the effects of the independent variable. Thus, using reliable dependent variables minimizes error. Likewise,
controlling extraneous variables or within-subjects designs minimizes within-group variability.
5. Using a one-tailed test when appropriate: When used appropriately, a one-tailed test is more powerful than a twotailed test.
6. Using a parametric test: Parametric tests are more powerful than nonparametric tests.
Activity 14.5 Key: Type I error occurs when the null hypothesis is rejected, but should have been retained. It is
when the researcher determined that statistically significant differences existed between the groups when they
actually did not exist. The amount of type I error is identified as alpha. The researcher always establishes the
amount of type I error allowed in the study. Meanwhile, type II error occurs when the null hypothesis is retained, but
should have been rejected. It is when the researcher determined that statistically significant differences did not exist
between the groups when they actually did exist. The amount of type II error is identified as beta. Type II error is
conversely related to statistical power.
CHAPTER 15 Using SPSS to Analyze Data
Activity 15.1 Key: 1. T, 2. F, 3. T, 4. T, 5. T, 6. T, 7. F, 8. T, 9. T, 10. T, 11. F, 12. F, 13. T, 14. T.
Activity 15.2 Key: 1) f, 2) a, 3) g, 4) h, 5) b, 6) d, 7) e, 8) c.
Activity 15.3 Key: 1) ric = .29, 2) r = -.264, 3) r = -.254, 4) r = .02, 5) t = -2.229; p = .034.
CHAPTER 16 Univariate Inferential Statistics
Activity 16.1 Key: 1) i, 2) e, 3) b, 4) g, 5) c, 6) k, 7) d, 8) j, 9) f, 10) a, 11) h.
Activity 16.2 Key:
Type of Test
Purpose
Answers the Question
z-test
Tests hypotheses between a sample mean and a
Is there a difference between the
population mean.
sample and population mean?
t-test
Tests hypotheses between two sample means.
Is there a difference between two
means?
ANOVA
Tests hypotheses between two or more sample means.
Is there a difference among the means?
Tests hypotheses between two or more sample means
Is there a difference among the means,
ANCOVA
while controlling for another variable that affects the
when controlling for a mediating
outcome of the dependent variable.
variable?
Activity 16.3 Key: 1. T, 2. F, 3. F, 4. F, 5. T, 6. T, 7. T, 8. T, 9. F, 10. T, 11. T.
Activity 16.4 Key:
1. They are all parametric statistics.
2. They are all univariate, meaning they are all focused on the measurement of one dependent variable.
3. They all test hypotheses between two or more means.
4. Each test statistic is computed from a fraction.
5. The numerator represents a computation for mean differences, such as by comparing two groups and subtracting
one mean from another.
6. The denominator is an error term, computed by taking into account the standard deviation or variance, and
sample size.
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CHAPTER 17 Correlation and Regression
Activity 17.1 Key: 1) d, 2) h, 3) f, 4) a, 5) k, 6) b, 7) j, 8) c, 9) e, 10) i, 11) g.
Activity 17.2 Key: 1. moderate, 2. high, 3. very high, 4. low, 5. moderate, 6. moderate, 7. very high, 8. very low, 9.
low, 10. high.
Activity 17.3 Key:
1. Positive slope
2. Negative slope
3. Negative correlation
5. Perfect Positive Correlation
4. Positive correlation
6. Perfect Negative Correlation
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Activity 17.4 Key:
1. T, 2. T, 3. F, 4. F, 5. F, 6. T, 7. T, 8. F, 9. T, 10. T, 11. T.
Activity 17.5 Key: 1) T, 2) T, 3) T, 4) F, 5) T, 6) T, 7) T.
Activity 17.6 Key: 1) b, 2) a, 3) c.
Activity 17.7 Key: 1) P, 2) P, 3) S, 4) P, 5) S, 6) P, 7) P.
CHAPTER 18 Nonparametric Statistical Analysis
Activity 18.1 Key:
1. What are nonparametric tests?
Nonparametric tests are useful in analyzing nominal, ordinal and even skewed data sets when the assumptions
required for parametric tests have been violated.
2. Nonparametric tests are applied under what two kinds of conditions?
First, nonparametric tests are applied when the data are categorical or count variables and thus are known not to
follow a normal curve. Second, nonparametric procedures are applied when the data, although measured as
continuous variables, are suspected to violate the normality assumption.
3. Why are parametric tests more powerful than nonparametric test?
When error distributions (the distribution of Y for each value of X) are normal or at least symmetric, then parametric
tests are more powerful than nonparametric tests.
4. When do nonparametric tests begin to show advantages in statistical power over their parametric counterparts?
When error distributions are identically skewed, then nonparametric tests begin to show advantages in statistical
power over their parametric counterparts.
Activity 18.2 Key: 1) e, 2) f, 3) d, 4) a, 5) c, 6) g, 7) b.
Activity 18.3 Key: 1. T, 2. T, 3. F, 4. F, 5. F, 6. T, 7. T, 8. T, 9. F, 10. F, 11. T, 12. T, 13. T, 14, T.
Activity 18.4 Key: 1) N, 2) N, 3) P, 4) P, 5) N, 6) N, 7) N, 8) N, 9) P, 10) N, 11) P, 12) P, 13) N, 14) N.
Activity 18.5 Key: 1. T, 2. F, 3. T, 4. T, 5. F, 6. T, 7. F, 8. F, 9. F, 10. T, 11. T, 12. F, 13. T, 14. T
Activity 18.6 Key: 1) e, 2) f, 3) a, 4) h, 5) b, 6) i, 7) c, 8) g, 9) d.
Activity 18.7 Key: 1) N, 2) N, 3) P, 4) P, 5) P, 6) N, 7) N, 8) P, 9) N, 10) P, 11) P, 12) N, 13) N.
Activity 18.8 Key
1. What are data transformations?
Data transformations are mathematical modifications to the values of a variable.
2. Describe linear transformations?
Linear transformations will change scaled statistics such as the mean, variance, and regression coefficients.
However, linear transformations will not affect scale-free statistics such as correlation coefficients and t-tests. Linear
transformations will not help normalize a distribution of scores or residuals.
3. Describe nonlinear transformations?
Nonlinear transformations will affect the value and hopefully reduce bias of test statistics as well as scaled statistics.
If a nonlinear transformation changes the value of a regression coefficient, researchers must change their
interpretation accordingly. If a nonlinear transformation changes the value of a test statistic then it may also affect
whether the test results are statistically significant.
4. Give some examples of both linear and nonlinear transformations?
Examples of linear transformations are adding constants and/or multiplying. Examples of nonlinear transformations
are squaring or raising to a power, taking the square root of the values, inverting and reflecting, converting to
logarithmic scales, and applying trigonometric transformations such as sine wave transformations.
Activity 18.9 Key:
1. Explain the concept of trimming.
Trimming is used to make parameter estimates sometimes at the expense of reduced statistical efficiency.
Symmetrically trimming a data set involves removing the k cases with the k/2 largest values and the k/2 smallest
values. The trimmed mean is the mean value for the data ignoring the k extreme values. The even positive integer k
determines the amount of trimming. Trimming can be an effective way to deal with outliers and obtain a robust
estimate of location. Trimming is not recommended for computing variances.
2. Explain the concept of Winsorization.
Winsorizing is used to down-weight the influence of outliers. It is a procedure similar to trimming but instead of
throwing away the k extreme values, the k extreme values are replaced by the remaining extreme values. This moves
the extreme values toward the center of the distribution. This technique is sensitive to the number of outliers, but not
to their actual values. To Winsorize the data, tail values are often set equal to some specified percentile of the data.
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Student Workbook for Research and Evaluation in Counseling, 2e
3. Explain the concept of square root transformations.
When one applies a square root transformation, the square root of every value is taken. However, one cannot take
the square root of a negative number, so if there are negative values for a variable a constant must be added to move
the minimum value of the distribution above 0, preferably to 1.
4. Explain the concept of log transformations.
Logarithmic transformations are a class of transformations, not just a single transformation. Basically a logarithm is
the power a base number must be raised to in order to get the original number.
5. Explain the concept of inverse transformations.
To take the inverse of a variable is to compute 1/Y. This makes very small numbers become very large, and very
large numbers become very small. This transformation has the effect of reversing the order of the scores.
6. Explain the concept of inverse of squares transformation.
To make this transformation is to compute 1/Y2. This makes very small numbers become very large and very large
numbers become very small. This transformation has the effect of reversing the order of your scores, and one may
choose to reflect, or reverse, the distribution prior to applying an inverse transformation. More importantly, if there
are scores below 0, the ordering of the variable will not be preserved.
CHAPTER 19 Multivariate Statistical Analysis
Activity 19.1 Key: 1. T, 2. F, 3. F, 4. T, 5. T, 6. T, 7. T, 8. T, 9. T, 10. F, 11. T, 12. F, 13. T.
Activity 19.2 Key:
1. First, when the correlation between predictors increases, the proportion of the variance in the criterion variable (Y)
uniquely accounted for by these predictors decreases. Thus, it is difficult to determine the relative importance of
individual predictors in the presence of multicollinearity, as the effects of the predictors are confounded due to the
correlations among the predictors.
2. Second, when the predictors are highly correlated, changes in one predictor are naturally associated with changes
in the other predictors. Therefore, when multicollinearity exists, it is not quite realistic to interpret the regression
coefficient for a predictor as representing its effect while holding the other predictors constant.
3. Third, the higher the multicollinearity, the larger the standard errors of the regression coefficients and therefore,
the lower the accuracy of the prediction with future samples.
Activity 19.3 Key: 1) c, 2) d, 3) f, 4) k, 5) a, 6) h, 7) i, 8) g, 9) j, 10) b, 11) e.
Activity 19.4 Key:
1. One recommended procedure is the studentized deleted residual. This index is used to detect outliers on Y. For
any observation, the studentized deleted residual is calculated for the sample, with this observation excluded. As the
index follows a Student t distribution, there should be a red flag for an outlier on Y when the studentized deleted
residual for an observation is greater than 3.00 in absolute value.
2. Another recommended procedure is the leverage value. This index is used to detect outliers on X; that is,
observations with extreme values on some predictors. A leverage size is considered large when it exceeds 3(k+1)/n,
where k is the number of predictors and n is the sample size.
3. A third recommended procedure is Cook’s distance. This index is used to detect influential data points. The
Cook’s distance considers the effect of deleting an observation on the residual of all observations. It measures the
impact of a specific observation on the estimates of regression parameters. All Cook’s distance values are positive,
but a Cook’s distance value greater than 1.00 is considered large.
Activity 19.5 Key:
1. One approach is forward selection. The first step consists of selecting the predictor that has the highest zero-order
correlation with the criterion variable, Y. At any following step, the predictor producing the greatest increment in R2
enters the equation if it meets the criterion of inclusion, otherwise the procedure terminates. A major drawback of
this approach is that once a predictor enters the equation, it stays in the equation although it might have lost its initial
importance when new predictors are added to the equation.
2. A second approach is backward selection. This approach begins with all predictors in the equation and removes
them one at a time until the final equation is obtained. At each step, the predictor that produces the smallest
increment in R2 is selected and tested for removal.
3. A third approach is stepwise selection. This approach combines the methods of forward selection and backward
elimination. It works as a forward selection, but at each step the predictors which are in the equation are reexamined
for possible backward elimination. This allows predictors that were suitable to enter the equation at previous steps,
but lost much of their predictive power when additional predictors were added, to be removed from the regression
equation. This is an important advantage of the stepwise approach over the forward selection.
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Student Workbook for Research and Evaluation in Counseling, 2e
4. A fourth approach is blockwise selection. In this approach predictors are grouped in blocks. The assignment of
variables to blocks and the order of the blocks is based on some theoretical and/or empirical consideration. First, a
stepwise selection is conducted for the predictors in each block and the predictors that have survived the
immediately preceding stepwise selection.
5. A fifth approach is hierarchical regression. In this approach, intact blocks of predictors are forced into the
regression equation, one at a time, to determine their unique contribution to the prediction of the criterion variable,
Y. Also, forcing some blocks into the equation and conducting blockwise selection on others is a very useful
combination in many research applications of multiple regression.
Activity 19.6 Key: 1. T, 2. T , 3. F, 4. F, 5. T, 6. F, 7. F, 8. T, 9. T.
Activity 19.7 Key:
1. Correlated contrasts may occur when the sum of coefficient products is not equal to zero.
2. Correlated contrasts may also occur when the compared groups do not have equal sample sizes.
Activity 19.7 Key: 1. Medium, 2. Large, 3. Large, 4. Medium, 5. Small, 6. Small, 7. Medium, 8. Large
Activity 19.8 Key: 1) M, 2) M, 3) A, 4) A, 5) A, 6) M, 7) M, 8) A, 9) M, 10) A, 11) M.
Activity 19.9 Key:
1. The subjects are randomly sampled from the target population.
2. The observations are statistically independent of one another.
3. The dependent variables have a multivariate normal distribution within each group.
4. All groups have the same variance on each dependent variable.
5. The correlation between any two dependent variables must be the same in all groups.
Activity 19.10 Key:
Factor analysis is used to determine: 1) how many factors underlie the set of variables; 2) which variables form
which factor; 3) the correlation between each variable and each factor; 4) the scores of each individual on the
factors; and 5) the correlations among factors.
Activity 19.11 Key: 1) c, 2) e, 3) d, 4) b, 5) a.
Activity 19.12 Key:
Exploratory Factor Analysis (EFA): Typically used when researchers do not have enough theoretical and/or
empirical information to hypothesize how many factors underlie the set of observable variables and which variables
form which factor. It defines factor through a mathematical procedure that usually maximizes the total variance in
the observed variables accounted for by the factors. The factors are extracted mathematically and then the
researchers interpret them.
Confirmatory Factor Analysis (CFA): Factors are defined directly through their hypothesized relations with
observed variables. It forces researchers to think about the reasons for selecting observed variables and the
organization of the data ahead of time. The process is more theory-driven.
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