EDUC 5504 Midterm—Open Book Section
Name ________________________________________________
1. Calculate the three measures of central tendency for the following information.
Scores on a statistics test (but not ours!!!):
98, 77, 56, 89, 78, 65, 45, 89, 66, 99, 100, 69, 86, 89, 84, 79, 54, 68, 92, 91, 89, 83
a. Mean________79.36_____________
b. Median ________83.5___________
c. Mode __________89________________
2. Using the same set of data as noted in question #1, calculate the three measures of
variability (or dispersion) that we learned about:
a. Range _________55_________
b. Standard deviation __________15.28______________
c. Variance _______233.48______________
3. One of the suggestions for replacing the OGT (Ohio Graduation Test) is to have all high
school students take the SAT (Scholastic Aptitude Test). If this were carried out, would
you expect the new standard deviation for test-takers in your high school to be larger or
smaller than the standard deviation for the group of students who currently take the SAT in
your high school? Explain your answer.
Larger because more varied sample. Current persons are college bound, but would
include all students.
4. A high school math teacher was interested in finding out if there were any relationships
between her students’ scores on a math computation assessment (done without a
calculator), their scores on a math problem solving assessment (using a calculator) and
their scores on an assessment of math anxiety. Following is the correlation matrix she
obtained. Look it over and answer the questions that follow it.
Math Computation
(without a
calculator)
Math Problem
Solving (with a
calculator)
Math Anxiety Score
(High score indicates
high anxiety)
Math Computation
(without a
calculator)
Math Problem
Solving (with a
calculator)
Math Anxiety Score
(High score indicates
high anxiety)
1.0
.85
-.93
.85
1.0
-.75
-.93
-.75
1.0
a. Explain why there are three perfect correlations in the matrix.
Because the same variable equals the same variable (x=x; y=y; z=z)
b. Identify the correlation coefficient that describes the relationship between scores on
an assessment of math computation done without a calculator and scores on a math
problem solving assessment done with a calculator. _____.85____________
What is the strength of the correlation? ______very strong__________
What is the direction of the correlation? _____direct________
In your own words, what does this correlation suggest about the relationship
between the two variables?
Students who performed well without the calculator, also performed well with!
c. Identify the correlation coefficient that describes the relationship between scores on
an assessment of math computation without a calculator and scores on an
assessment of math anxiety. ______-.93_________
What is the strength of the correlation? ____very strong_________
What is the direction of the correlation? _____ indirect_______
d. Identify the correlation coefficient that describes the relationship between scores on
an assessment of math problem solving with a calculator and scores on an
assessment of math anxiety. ______-.75___________
What is the strength of the correlation? ____strong_________
What is the direction of the correlation? ______indirect________
e. In your own words, describe what the correlations in c and d suggest about the
relationship of math anxiety to the other two math assessments.
With or without a calculator, students with high math anxiety were less likely to do
well.
4. A reading teacher wants to see what the correlation is between her students’ scores on a
reading recognition assessment that uses graded word lists and an assessment of reading
fluency. She obtains the following scores on the two assessments:
Readrec
Mary
99
Billy
98
Sarah
94
Matt
88
Susan
85
Carl
83
James
81
Kathy
78
Luke
75
Robert
72
ReadFluency
95
89
96
86
89
85
88
70
79
80
Enter the scores into the David M. Lane Analysis Lab (www.davidmlane.com/hyperstat),
then answer the following questions:
a. Is there a direct or indirect correlation between the variables? ___direct__________
b. What is the correlation coefficient? ______.78_________
c. What is the strength of the relationship? _________strong________________________
d. What can the teacher say about the relationship between the two variables she
measured?
Students who scored well on one tended to score well on the other.
5. I am hypothesizing that there is a relationship between success in college classes and
whether a student is a traditional or nontraditional student. I obtain a random sample of
both types of students. I rank order them based on their GPAs; then I correlate their status
as traditional vs. nontraditional with their ranks.
a. What level of measurement is the traditional vs. nontraditional variable? ___nominal___
b. What level of measurement is the GPA variable? __________ordinal____________(drop)
c. What type of correlation coefficient would I use? _________rank biserial_______(drop)
Identify the type of reliability or validity being established in each of the following examples:
6. The Ohio Department of Education is introducing end-of-course exams. They decide
that they must establish that the exams measure what they are designed to measure, so
they assemble a team of teacher experts from across the state to analyze the tests that
match they teach. The teachers scrupulously analyze every question.
a. Is this an attempt to establish reliability or validity? ________validity_______
b. What type? ________content validity__________________
7. Before implementing the end-of-course exams, the ODE decides to obtain a random
sample of students to take the test. They wait two weeks then administer the same test
to the same set of students.
a. Is this an attempt to establish reliability or validity? _______reliability________
b. What type? _________test-retest______________
8. ODE wants further exploration of reliability and validity issues. This time they give a
pilot version of the test to a random sample of students who have completed one of the
courses. They also have these students take the New York State end-of-course exams
(which have well-established reliability and validity). They then compare students’
performances on the new Ohio exams and the New York State exams.
a. Is this an attempt to establish reliability or validity? _______validity________
b. What type? (be specific) __________concurrent-criterion related__________________
9. ODE wants to have more than one version of each test. They begin by developing a Test
A and Test B for each course. They obtain another sample of students and give them
both tests then compare their performance on Test A with their performance on Test B.
a. Is this an attempt to establish reliability or validity? ______reliability_________
b. What type? ________parallel forms_______________________