Problem Sets for Elements of Mental Tests 1
MATHEMATICAL AND
MULTIPLE CHOICE
PROBLEM SETS
for
The Elements of Mental Tests
SECOND EDITION
John D. Mayer
January 25th, 2016 Version
Problem Sets for Elements of Mental Tests 2
Table of Contents
Problem Set for Chapter 1 ______________________________________________________ 3
Problem Set For Chapter 2 ______________________________________________________ 4
Problem Set For Chapter 3 ______________________________________________________ 5
Problem Set For Chapter 4 ______________________________________________________ 7
Problem Sets For Chapter 5 _____________________________________________________ 8
Problem Sets For Chapter 6 ____________________________________________________ 11
Problem Sets For Chapter 7 ____________________________________________________ 12
Problem Sets For Chapter 8 ____________________________________________________ 17
Problem Sets For Chapter 9 ____________________________________________________ 20
Problem Sets For Chapter 10 ___________________________________________________ 22
Problem Sets For Chapter 11 ___________________________________________________ 28
Problem Sets For Chapter 12 ___________________________________________________ 29
Appendix: Hints, Intermediate Values and Answers for Selected Problems _______________ 30
Problem Sets for Elements of Mental Tests 3
PROBLEM SET FOR CHAPTER 1
Types of multiple choice questions that address the content of Chapter 1
Questions about the History of Testing
1.1. Journalists have criticized psychological tests beginning
a. in the past decade.
b. with the introduction of intelligence tests in the early 1900s.
c. only mildly at first, but with increasing intensity through the 20th century.
d. only in the last few years.
Questions about What a Test Is
1.2. Which feature is NOT a defining aspect of a mental test:
a. an integrated mental procedure
b. collects data about mental life
c. uses ratio scales
d. indicates the presence of magnitude of features
Questions about the Advantages and Drawbacks of Testing
1.3. Psychological tests have this relationship with informal interviewing (say, a job interview):
a. they have not been compared
b. psychological tests are more reliable and less biased
c. psychological tests are more biased and less valid
d. psychological tests lose or miss more information than does the interviewer
Problem Sets for Elements of Mental Tests 4
PROBLEM SET FOR CHAPTER 2
Types of multiple choice questions that address the content of Chapter 2
Questions about the History and Classification of Tests
2.1. Mental testing began by trying to distinguish those with higher versus lower
a. wealth
b. sociability
c. mental health (versus psychopathology)
d. mental abilities
Questions about Specific Widely-Used Tests
2.2. The Positive and Negative Affect Test (PANAS) measures
a. mood
b. mental ability to affect the correct answers
c. good versus bad attitude
d. none of the above
Questions about Data
2.3. Data about a person can be divided between inner and outer sources called:
a. self-report and personal report
b. observer report and informant report
c. personal-report data, external source data
d. institutional data and self-report data
Problem Sets for Elements of Mental Tests 5
PROBLEM SET FOR CHAPTER 3
Reverse-Scoring a Test
To solve problems 3.1-3.6 use the following information:
Trevor and Adrianne each took an extraversion scale. Their responses, on the actual
extraversion scale itself are shown in Tables 3.1 and 3.2. The two test-takers responded to each
test item on a scale that went from 1 (disagree) to 7 (agree). One view of extraversion, by
Costa and McCrae, includes six defining qualities: (a) warmth, (b) gregariousness, (c)
assertiveness, (d) activity, (e) excitement-seeking, and (f) positive emotions. Introversion
involves (a) coldness, (b) withdrawal, (c) passivity, (d) low activity level, (e) excitementavoidance, and (f) negative emotions.
Table 3.1
Trevor’s Data on a Measure of Extraversion
Disagree
1
2
3
1
2
3
4
I enjoy reading books
I enjoy boisterous parties
I prefer to study alone.
I think it is fun to be the center of attention at a
party
5 I like playing practical jokes
6 People often tell me I’m quiet
7 I belong to many social organizations.
8 I prefer to be alone more than I am.
9 I like to read in the evenings.
10 I like to go out with a group of people.
4
5
Agree
6
7
X
X
X
X
X
X
X
X
X
X
Problem Sets for Elements of Mental Tests 6
PROBLEM SET FOR CHAPTER 3 (CONTINUED)
Table 3.2
Adrianne’s Data on a Measure of Extraversion
1
1
2
3
4
5
6
7
8
9
10
I enjoy reading books
I enjoy boisterous parties
I prefer to study alone.
I think it is fun to be the center of attention at a
party
I like playing practical jokes
People often tell me I’m quiet
I belong to many social organizations.
I prefer to be alone more than I am.
I like to read in the evenings.
I like to go out with a group of people.
2
3
4
5
X
6
7
X
X
X
X
X
X
X
X
X
3.1. In Tables 3.1 and 3.2, how many participants’ test data are there? That is, how many
participants took the test? (Hint: this is easy) _____
3.2. Judging from Tables 3.1 and 3.2, how many items were on the test? _______
3.3. Using the test data in Table 3.1, construct a raw data table that includes the item-level
responses for Trevor. Please create a 10 (row) by 2 (column) chart in which each row represents
an item (the items can be numbered). Column 1 should label the item numbers; column 2 should
include the response.
3.4. Using the test data shown in Table 3.2 (and the rules listed in 3.3), construct a raw data table
that includes the item-level responses for Adrianne.
3.5. Add a further column for Trevor’s scores that include the scored data (reversed where
needed)
3.6. Add a further column for Adrianne’s scores that include the scored data (reversed where
needed)
3.7. Calculate Trevor’s total score on the test.
3.8. Calculate Adrianne’s total score on the test.
Problem Sets for Elements of Mental Tests 7
PROBLEM SET FOR CHAPTER 4
Types of multiple choice questions that address the content of Chapter 4
Questions about Types of Items
4.1. Empirically-keyed data begins with responses to _______ that then are evaluated according
to ________.
a. self-judgment items; how well they distinguish between groups
b. projective stimuli; open-ended responding
c. intelligence test items; open-ended responding
d. creativity tests; divergent responding
4.2. Thematic-report data is often used in:
a. self-report tests using likert scales
b. projective tests using open-ended responding
c. intelligence tests using open-ended responding
d. creativity tests
Problem Sets for Elements of Mental Tests 8
PROBLEM SETS FOR CHAPTER 5
Basic Symbols
5.1 Write out what i means:________________________________________
5.2. Write out what X refers to: ______________________________________
5.3. Write out what x refers to: ______________________________________
5.4. Write out what σ2X refers to:____________________________________
Learn the Column-by-Column Method for Calculating Z-Scores
5.5. Calculate the mean, deviation, squared deviations, standard deviation, and z-scores using the
step-by-step method shown in the text for the following data:
X
7
3
1
5
4
5.6. Six people obtained the following scores: 1, 9, 12, 3, 7, and 4. Use the step-by-step method
you used above to calculate their z-scores.
Check Z-Scores
5.7. Use the step-by-step method to check that the z-scores you obtained in problem 5.5 are zscores.
5.8. Are these five numbers z-scores? -1.41, .71, 0, -.71, 1.41
(Problems continue on the next page.)
Problem Sets for Elements of Mental Tests 9
PROBLEM SETS FOR CHAPTER 5 (CONTINUED)
Comparing Scales with Different Response Alternatives
People took the same test items twice; their results are in Table 5.1. The first time, they used a 7point Likert scale, and the second time, a dichotomous scale.
Table 5.1
Scores for the Same Questions Using a 7-Point Scale and a 2-Point Scale
Participant
Test X
Test Y
a
7-point scale
Yes/No scaleb
Rebecca
7
2
Jonah
6
2
Caitlyn
4
1
Rylee
2
1
Ella
1
1
a
7=Agree; 1=Disagree b2=Yes; 1=No
Create a table and use the column-by-column method to answer questions 5.9 to 5.14:
5.9. What is the mean of Test X?
5.10. What are the deviations of Test X?
5.11. What are the squared deviations of Test X?
5.12. What is the variance of Test X?
5.13. What is the standard deviation of Test X?
5.14. What are the z-scores of Test X?
(Problems continue on the next page.)
Problem Sets for Elements of Mental Tests 10
PROBLEM SETS FOR CHAPTER 5 (CONTINUED)
Create a table and use the column-by-column method to answer questions 5.15 to 5.20:
5.15. What is the mean of Test Y?
5.16. What are the deviations of Test Y?
5.17. What are the squared deviations of Test Y?
5.18. What is the variance of Test Y?
5.19. What is the standard deviation of Test Y?
5.20. What are the z-scores of Test Y?
5.21. (Write out) How do the means of tests X and Y compare?
5.22. (Write out) How do the standard deviations of tests X and Y compare?
5.23. (Write out) What similarities and differences do you notice between the z-scores on Tests
X and Y?
Problem Sets for Elements of Mental Tests 11
PROBLEM SETS FOR CHAPTER 6
Converting from Z-Scores to Other Scales
6.1 If a person has a z-score of -1.5 on an IQ test, what is their IQ score (M = 100, S = 15)?
6.2 If a person has a z-score of .5 on the SAT, what is their SAT score (M = 500, S = 100)?
6.3 If a person has a z-score of 2.0 on the psychopathic deviancy score of the MMPI, what is
their MMPI scale score (M = 50; S = 10)?
Learning Pascal’s Triangle
Table 6.1
Rows 1 through 7 of Pascal’s Triangle
1
1
1
1
1
1
1
2
3
4
5
6
1
3
6
10
15
1
1
4
10
20
1
5
15
1
6
1
6.4. Given the rows of of Pascal’s triangle in Table 6.1, what is row 8 of Pascal’s Triangle?
6.5. Given the rows of of Pascal’s triangle in Table 6.1, what is row 9 of Pascal’s Triangle?
6.6. Find the sum of the numbers in each of the rows of Pascal’s triangle shown in Table 6.1
6.7. What happens to the sum of the rows as you move down the rows of Pascal’s Triangle—
what is the pattern of the sums?
Problem Sets for Elements of Mental Tests 12
PROBLEM SETS FOR CHAPTER 7
Calculating the Correlation Coefficient from Z-Scores
Table 7.1
Raw Data and Z-Scores for Participants on Tests T and U
T
U
ZT
ZU
1
3
3
1
1
2
3
3
1
1
3
3
3
1
1
4
3
3
1
1
5
3
3
1
1
6
1
1
-1
-1
7
1
1
-1
-1
8
1
1
-1
-1
9
1
1
-1
-1
10
1
1
-1
-1
7.1. Using the data in Table 7.1, what is the correlation between tests T and U?
Table 7.2
Raw Data and Z-Scores for Participants on Tests V and W
V
W
Zv
Zw
1
8
10
1
-1
2
8
10
1
-1
3
8
10
1
-1
4
8
10
1
-1
5
8
10
1
-1
6
10
8
-1
1
7
10
8
-1
1
8
10
8
-1
1
9
10
8
-1
1
10
10
8
-1
1
7.2. Using the data in Table 7.2, what is the correlation between tests V and W?
Problem Sets for Elements of Mental Tests 13
PROBLEM SETS FOR CHAPTER 7 (CONTINUED)
Table 7.3
Raw Data and Z-Scores for Participants on Tests X and Y
X
Y
Zx
Zy
1
2
5
-.214
.0
2
1
4
-.286
-.071
3
5
5
.0
0
4
4
10
-.071
.367
5
5
15
0
.714
6
10
7
.367
.142
7
15
0
.714
-.367
8
7
1
.142
-.286
9
0
2
-.367
-.214
10
1
1
-.286
-.286
7.3. Using the data in Table 7.3, what is the correlation between tests X and Y?
(Problems continue on the next page.)
Problem Sets for Elements of Mental Tests 14
PROBLEM SETS FOR CHAPTER 7 (CONTINUED)
Calculating the Correlation Coefficient from Observed Scores
Table 7.4
Scores for Four Participants on Test X
Index
Score on
Number
Test X
1
8
2
0
3
2
4
2
7.4. Using the data in Table 7.4, calculate the z-scores for Test X using the column-by-column
method. (There may be more columns than you need).
Table 7.5
Scores for Four Participants on Test Y
Index
Score on
Number
Test Y
1
11
2
1
3
11
4
1
7.5. Using the data in Table 7.5, calculate the z-scores for Test Y using the column-by-column
method. (There may be more columns than you need).
7.6. Calculate the correlation coefficient between Tests X and Y using the data from Tables 7.4
and 7.5.
(Problems continue on the next page.)
Problem Sets for Elements of Mental Tests 15
PROBLEM SETS FOR CHAPTER 7 (CONTINUED)
Table 7.6
Scores for Six Participants on Test L
Index
Scores on
Number
Test L
1
10
2
10
3
10
4
0
5
0
6
0
7.7. Using the data in Table 7.6, calculate the z-scores for Test L using the column-by-column
method.
Table 7.7
Scores for Six Participants on Test M
Index
Scores on
Number
Text M
1
11
2
7
3
7
4
5
5
5
6
1
7.8. Using the data in Table 7.7, calculate the z-scores for Test M using the column-by-column
method. (There may be more columns than you need).
7.9. Calculate the correlation coefficient between Tests L and M using the data from Tables 7.6
and 7.7. (There may be more columns than you need).
(Problems continue on the next page.)
Problem Sets for Elements of Mental Tests 16
PROBLEM SETS FOR CHAPTER 7 (CONTINUED)
Working With the Binomial Effect Size Display (BESD) Table
Table 7.8
A Binomial Effect Size Display for r = .00
Degree to Which Liked by CoWorkers
Lo Liking
Hi Liking
Scores on a test of
High
Conscientiousness
Low
Total
7.10. Fill in the values for a BESD where r = .00 in Table 7.8
Table 7.9
A Binomial Effect Size Display for r = .25
Degree to Which Liked by CoWorkers
Lo Liking
Hi Liking
Scores on the
High
MSCEIT
Low
Total
Total
Total
7.11. Fill in the values for a BESD where r = .25 in Table 7.9
Table 7.10
A Binomial Effect Size Display for r = .15
Longevity
Lifespan < 70
Lifespan > 70
Years
Years
Scores on a test of
Conscientiousness
High
Low
Total
7.12. Fill in the values for a BESD where r = .15 in Table 7.10
Total
Problem Sets for Elements of Mental Tests 17
PROBLEM SETS FOR CHAPTER 8
Learn Psychometric Symbols
8.1. Define X
8.2. Define T
8.3. Define E.
8.4. Define σT.
8.5. Define σX.
8.6. Define σ2E.
8.7. Define ρ2XT.
8.8. Define ρXX.
8.9 Define ρXX'.
Work With Psychometric Assumptions and Derivations in Equation
Form
8.10. Given: X = 10, E = 2. Solve for T.
8.11. Given: T = 12, X = 10. Solve for E.
8.12. Given: T = 8, E = -3. Solve for X.
8.13. Given σ2T = 10, σ2X = 15. Solve for σ2E
8.14. Given σT = 3, σX = 4. Solve for σ2E
8.15. Given σT = 3, σ2X = 20. Solve for ρ2XT
8.16. Given: ρ2XT = .89. Solve for ρxx
Problem Sets for Elements of Mental Tests 18
PROBLEM SET FOR CHAPTER 8 (CONTINUED)
Work With Psychometric Assumptions and Derivations: Combined
Word and Numerical Problems
To solve problems 8.17-8.23 use the following information:
Given ρ2XT = .56,
σ2X = 4.
8.17. What is the variance of the true scores?
8.18. What is the variance of the error scores?
8.19. Solve for σT.
8.20. What is the standard deviation of the error scores?
8.21. What is ρ2XX' equal to?
8.22. What is σ2X' equal to?
8.23. For a given participant, X = 10 and E = 3, Solve for T
To solve problems 8.24-8.31 refer to the following information where needed:
Given: A test, X, has a reliability of .75 and an observed standard deviation of 4.0. In
addition, there exists a test, X', that is parallel to X, and another test, Y, that intercorrelates
both with X and X' = .65.
8.24. Solve for the true-score variance of test X.
8.25. Solve for the obtained-score variance of test X.
8.26. What is the error variance of test X?
8.27. What is the value of ρET?
8.28. Calculate the correlation between error and obtained scores on test X.
8.29. Find the correlation between the test and its parallel form.
Problem Sets for Elements of Mental Tests 19
PROBLEM SET FOR CHAPTER 8 (CONTINUED)
8.30. Solve for the reliability of the test that is parallel to test X.
8.31. For a given participant, X = 12 and T = 2, Solve for E.
Problem Sets for Elements of Mental Tests 20
PROBLEM SETS FOR CHAPTER 9
Convert Probabilities to Odds Ratios
9.1. Convert 0 to an odds ratio
9.2. Convert .20 to an odds ratio
9.3. Convert .40 to an odds ratio
9.4. Convert .60 to an odds ratio
9.5. Convert .80 to an odds ratio
9.6. Convert 1.00 to an odds ratio
Convert Odds Ratios to Log Odds Units (Logits)
9.7 Convert 0 to logits
9.8 Convert .25 to logits
9.9. Convert .66 to logits
9.10. Convert 1.33 to logits
9.11. Convert 4.0 to logits
9.12. Convert ∞ to logits
(Problems continue on the next page.)
Problem Sets for Elements of Mental Tests 21
PROBLEM SET FOR CHAPTER 9 (CONTINUED)
Graph a Logistic Curve
9.13. A test item has a difficulty level of β = 0. A group of people of varied abilities (θ) took the
item as part of a longer test. Graph their likelihood of passing the item on the Y axis as a
function of their ability level θ (theta), measured in log odds units, on the X axis.
Likelihood of
passing the
item
Near zero
.20
.40
.60
.80
Near 1.0
θ (theta), on a
logit scale
-3.00
-1.39
-.41
.41
1.39
+3.00
Table 9.1
Correlations Among the Four Items of Test X
A
B
A
B
.62
C
.64
.58
D
.54
.54
C
D
.46
9.14. How many factors might there be in Test X. What items make up the factor or factors?
Table 9.2
Correlations Among the Four Items of Test Y
A
B
A
B
.15
C
.64
-.14
D
.06
.54
C
D
.20
9.15. How many factors might there be in Test Y. What items make up the factor or factors?
Problem Sets for Elements of Mental Tests 22
PROBLEM SETS FOR CHAPTER 10
Review of Symbols
10.1. What does ρxx' stand for?
10.2. What does ρXT stand for?
10.3. What does ρXE stand for?
10.4. What does σT stand for?
10.5. What does σ2X’ stand for?
General Problems in Classical Test Theory and Reliability
To solve problems 10.6-10.9 refer to and use the following information where needed:
Given: ρxx' = .8, and σ2X = 25.
10.6. Find the value of ρXT.
10.7. What is ρXE?
10.8. What is σ2T?
10.9. Find the value of σ2E?
(Problems continue on the next page.)
Problem Sets for Elements of Mental Tests 23
PROBLEM SETS FOR CHAPTER 10 (CONTINUED)
Mixed Word and Symbol Problems in Classical Test Theory and
Reliability
To solve problems 10.10-10.15 refer to the following information where needed:
Given: ρ2XT = .60,
σ2 X = 9
10.10. Solve for the variance of the true scores.
10.11. Solve for the variance of the error scores.
10.12. What is σT?
10.13. What is the standard deviation of the error scores?
10.14. Solve for ρXX'.
10.15. Solve for σ2X'.
10.16. When does X = T?
10.17. When does X = E?
To solve problems 10.18-10.22 refer to the following information where needed:
Given: ρ2XT = .49, σ2X = 7
10.18. What is the variance of the true scores?
10.19. Solve for the variance of the error scores.
10.20. Solve for the parallel test’s reliability.
10.21. What is the standard deviation of the observed scores?
10.22. What is the expected value of the error scores?
Problem Sets for Elements of Mental Tests 24
PROBLEM SETS FOR CHAPTER 10 (CONTINUED)
Word Problems: Basic Computation of Test Reliability
10.23. You split a test in half and observe a correlation of r = .8 between the halves. What is the
test reliability of the first half of the test?
10.24. You split a test in half and observe a correlation of r = .65. What is the test reliability?
10.25. You calculate a split-half reliability estimate and observe a correlation of .3 between the
two halves. What is the estimated reliability of the test?
10.26. What is the estimated reliability of a test if the variance of the scores on the first half of
the test is 20, the variance of scores on the second half of the test is 25, and the variance of total
test scores is 60?
10.27. What is the estimated reliability of a test if the variance of scores on the first half of the
test is 20, the variance of scores on the second half of the test is 30, and the variance of total test
scores is 70?
10.28. You calculate a split-half reliability estimate and observe a correlation of .4 between the
two halves. What is the estimated reliability of the test?
10.29. What is the estimated reliability of a test if the variance of the scores on the first half of
the test is 10, the variance of scores on the second half of the test is 25, and the variance of total
test scores is 60?
To solve problems 10.30-10.32 refer to the following information where needed:
Given: A test is split in half. The scores on the first half of the test have a variance of 10, and
the scores on the second half of the test have a variance of 15. The correlation between the
scores on the two halves is .50. The variance of the total test score is 37.2.
10.30. Calculate the reliability of the entire test using coefficient alpha.
10.31. Calculate the reliability using the Spearman-Brown formula.
10.32. How do the coefficient alpha and Spearman-Brown estimates of reliability compare?
Problem Sets for Elements of Mental Tests 25
PROBLEM SETS FOR CHAPTER 10 (CONTINUED)
To solve problems 10.33-10.34 refer to and the following information where needed:
Given: A test is split in half. The scores on the first half of the test have a variance of 10, and
scores on the second half of the test have a variance of 25. The correlation between the scores
on the two halves is .57. The variance of the total test score is 50.
10.33. Calculate the reliability of the entire test using coefficient alpha.
10.34. Calculate the reliability using the Spearman-Brown formula.
Further Problems in the Computation of Test Reliability
To solve problems 10.35-10.36 refer to the following information where needed:
Given: A test is divided into three parts. The parts correlate with one another at an average of r
= .4. The variances of the three parts are 10, 10, and 10, and the variance of the total test is 60.
10.35. What is the Spearman-Brown estimate of the test’s reliability?
10.36. What is the Coefficient Alpha estimate of the test’s reliability?
10.37. You have a 100-item test with an estimated reliability of r = .9. What would be the
reliability of the test if you cut it in half? (Please note, students often find this problem more
difficult than the others).
(Problems continues on the next page.)
Problem Sets for Elements of Mental Tests 26
PROBLEM SETS FOR CHAPTER 10 (CONTINUED)
To solve problems 10.38-10.41 refer to and use the following information where needed:
Given: Five people took a test. Table 10.1 displays information about their performance on the
odd-numbered items, half-test 1 (H1); Table 10.2 displays information about their performance
on the even-numbered items, half-test 2 (H2), and Table 10.3 indicates the calculations that led
to the correlation between them.
Table 10.1
Scores for a 5-person Sample on the Odd Items of a Test (Half-test 1 or H1)
i
H1
M
x
x2
S
Z
1
1
2
-1
1
1.67
-.60
2
4
2
2
4
1.67
1.20
3
0
2
-2
4
1.67
-1.20
4
1
2
-1
1
1.67
-.60
5
4
2
2
4
1.67
1.20
14/5=2.8
Table 10.2
Scores for a 5-person Sample on the Even Items of a Test (Half-test 2 or H2)
i
H2
M
x
x2
S
1
0
1
-1
1
1.1
2
1
1
0
0
1.1
3
1
1
0
0
1.1
4
0
1
-1
1
1.1
5
3
1
2
4
1.1
6/5=1.2
Table 10.3
Calculation of the Correlation Between H1 and H2
I
Z1
1
-.60
2
1.20
3
-1.20
4
-.60
5
1.20
(Problem continues on the next page.)
Z2
-.91
0
0
-.91
1.82
Z1Z2
.54
0
0
.54
2.18
3.26/5 = .652 = r
Z
-.91
0
0
-.91
1.82
Problem Sets for Elements of Mental Tests 27
PROBLEM SETS FOR CHAPTER 10 (CONTINUED)
10.38. What is the correlation between the two tests?
10.39. What is the variance of the total test?
10.40. What is the coefficient alpha reliability of the test?
10.41. What is the split half reliability of the test?
Problem Sets for Elements of Mental Tests 28
PROBLEM SETS FOR CHAPTER 11
Types of multiple choice questions that address the content of Chapter 11
Questions about Validity in General
11.1. Which statement is most true?
a. The name of a test is a good index of what it measures.
b. A single test can NOT have high validity if it also has high reliability.
c. validity concerns how well a test measures what it is supposed to measure.
d. test validity is best reported in general terms.
11.2. The current validity standards define validity as centered on the interpretation and
understanding of
a. tests and test manuals.
b. test manuals only.
c. test scores.
d. administrators of tests and the way they work.
11.3. The standards for educational and psychological testing are actually developed by a joint
committee of the…..? (short answer)
Questions about Specific Types of Validity
11.4. A test-maker of an arithmetic test claims the test measures whether students have learned to
“carry” numbers when they add such figures as 14 + 19 or 23 + 28 (where, in the ones columns,
the sum exceeds 10). To establish process evidence for the measure’s validity, the test-maker
might
a. correlate the test with a pre-existing test known to measure the ability to carry numbers.
b. record students who have been instructed to speak aloud as they answer the questions to see if
carrying numbers comes up as they are solving problems.
c. correlate the test with tests in which carrying is not necessary.
d. factor analyze the test.
Problem Sets for Elements of Mental Tests 29
PROBLEM SETS FOR CHAPTER 12
Types of multiple choice questions that address the content of Chapter 12
Questions about How Tests Cause Discomfort
12.1. What is not a source of discomfort about tests described in Chapter 12?
a. They are used for selection and therefore influence people’s lives.
b. They can provide painful feedback.
c. They are less valid that other people’s observations.
d. They are sometimes misused.
Questions about Improving the Test Experience
12.2. Several recommendations in Chapter 12 to improve testing experience include attempts to
a. raise test literacy.
b. discourage informed skepticism about tests.
c. tell people they should usually score well on tests.
d. improve test reliability.
Questions about Collaborative Testing
12.3. The collaborative testing movement involves collaboration between
a. test makers and test administrators.
b. professionals who provide test feedback and test takers.
c. test makers and test takers.
d. the government and test makers.
Problem Sets for Elements of Mental Tests 30
APPENDIX: HINTS, INTERMEDIATE
VALUES AND ANSWERS FOR SELECTED
PROBLEMS
Chapter 1
1.1. B
1.2. C
1.3. B
Chapter 2
2.1 D
2.2. A
2.3. C
Chapter 3
3.3.
Item
Trevor’s
Response
1
2
3
4
5
6
7
8
9
10
Chapter 4
4.1. A
4.2. B
6
2
6
1
1
6
4
6
6
1
Problem Sets for Elements of Mental Tests 31
Chapter 5
5.1. index number
5.3. a deviation on Test X
5.10.
X
7
6
4
2
1
M
4
4
4
4
4
x
3
2
0
-2
-3
Chapter 6
6.1. 100-22.5 = 78.5
6.6. (partial answer): 1, 2, 4, 8,…
Chapter 7
7.4. Partial check: Note that standard deviation for Test X is 3.
7.5. Partial check: Note that the variance for Test Y is 25.
7.7. Partial check: Note that the standard deviation for Test L is 5.
7.8. Partial check: Note that the variance for Test M is 9.
Chapter 8
Hint for Chapter 8 Problem Sets: Matters will go more easily—especially for the later
problems—if you first create a reference sheet on which you copy down the following from
Chapter 8:



The key assumptions of psychometric theory
The definition of a parallel test
The remaining equations of the chapter
8.7. The squared population correlation between obtained and true scores on a test
8.13. 5
Problem Sets for Elements of Mental Tests 32
Chapter 9
Convert Probabilities to Odds Ratios
9.1. 0:1
9.3. 2:3
9.5. 4:1
Convert Odds Ratios to Log Odds Units (Logits)
9.7. -∞
9.9. -.415
9.11. 1.39
Chapter 10
Review of Symbols
10.1. The reliability of a test, and the correlation between a test and its parallel form
10.4. The standard deviation of the true score
10.5. The variance of the obtained scores on a parallel test
Mixed Word and Symbol Problems in Classical Test Theory and Reliability
10.10. Answer: 5.4
10.11. Answer: 3.6
10.12. Answer: 2.32
10.13. Answer: 1.90
10.14. Answer: .60
10.15. Answer: 9
10.18. Answer: 3.43
10.19. Answer: 3.57
10.20. Answer: .49
10.21. Answer: 2.65
10.22. Answer: 0
Word Problems: Basic Computation of Test Reliability
10.28. Answer: .57
10.29. Answer: .83
10.30 Answer: 66
10.31. Answer: .67
10.33. Answer: .60
Problem Sets for Elements of Mental Tests 33
10.34. Answer: .73
10.35. Answer: .67 Calculation: [3(.4)] / [1+(3-1).4] = 1.2 / 1.8 = .67
10.36. Answer: .75 Calculation: [3/(3-1)] * [(60-(10+10+10))/60] = 3/2 * [30/60] = 3/2* .5 =
.75
Chapter 11
Multiple Choice/Short Answer
11.1. C
11.2. C
11.3. AERA, APA, NCRE
11.4. B
Chapter 12
12.1. C
12.2. B
12.3. B