Chapter 10
Chapter 10
Linear Regression
Section A
1. Increasing the magnitude of Pearson's r in a regression problem (all else remaining equal),
always causes an increase in:
*
a) the variance of the estimate
b) the magnitude of the slope
c) the magnitude of the Y-intercept
d) none of the above
2. If the raw-score prediction for Y is always the same as the raw-score of X (the variable used
to make the predictions), the slope of the regression line will be:
*
a) zero
b) +1.0
c) infinity
d) it depends on the standard deviations of X and Y
3. The difference between the variance of the estimate and the total variance is:
*
a) equal to r2
b) the explained variance
c) the unexplained variance
d) equal to the coefficient of determination
4. For a sample, r2 is equal to:
*
a) the ratio of the explained variance to the unexplained variance
b) the coefficient of nondetermination
c) the proportion of the variance accounted for
d) all of the above
5. The Y-intercept is:
*
a) the value of Y when X equals zero
b) the value of Y when r equals zero
c) the value of Y when the slope equals zero
d) the value of X when Y equals zero
6. A large positive slope means that:
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a) the correlation will be large and positive
b) the Y-intercept will be large and positive
*
c) the value of Y will increase by (at least) several units when the X value increases by
one unit
d) all of the above are true
7. Suppose you draw a random sample from the population and Pearson's r is equal to +.5. If
you use your regression equation to make predictions for subjects not in your sample, some error
will be involved. The amount of error would be less if:
*
a) your correlation were higher
b) your sample were larger
c) your regression slope were larger
d) all of the above are true
8. The standard error of the estimate increases (all else remaining equal), whenever:
*
a) the sample size increases
b) the slope increases
c) the correlation increases
d) the coefficient of nondetermination increases
9. Homoscedasticity exists in the population, when for every X value:
a) the variance of the Y variable is the same
*
b) the variance around the regression line is the same
c) the slope of the regression line is the same
d) the Y-intercept is the same
10. When dealing with large sample sizes, 95% of the time the true value of Y is:
*
a) the same as the predicted value
b) within (about) one standard deviation of the mean of Y
c) within (about) two standard errors of the estimate on either side of the regression line
d) within (about) one standard error of the estimate on either side of the predicted value
Section B
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11. Suppose that there is a .45 correlation between IQ (μ = 100, σ = 15) and verbal SAT score (μ
= 500, σ = 100). What verbal SAT score would you predict for someone who has an IQ of 90?
a) 433 b) 470 c) 490 d) 510
-12. Given that μx = 57, σx = 18.5, μy = 44, σy = 16, and that the slope of the regression line for
predicting Y from X, byx, is
-.52, what must the correlation between X and Y be?
a) -.45 b) -.60 c) -.67 d) +.45
-13. If the slope for predicting Y from X, byx, is 16 and the Y-intercept, ayx, is 400, what
prediction for Y corresponds to X = 20?
a) 320 b) 420 c) 560 d) 720
-14. Suppose that there is a .6 correlation between IQ (μ = 100, σ = 15) and verbal SAT score (μ
= 500, σ = 100). What would be the variance of the estimate when predicting IQ from verbal
SAT?
a) 36 b) 64 c) 144 d) 640
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15. Given the following regression equation: Y = 16X + 5, for what value of X would 29 be
predicted?
a) 1.5 b) 1.8 c) 464 d) 469
-16. Suppose that a regression equation for predicting a midterm score from the number of
practice problems solved prior to the exam is as follows: Y' = .8X + 45. What midterm score is
predicted for someone who does not solve any practice problems?
a) .8 b) 45 c) 56.25 d) 0
-17. A professor believes that the midterm score in her class is a good prediction of the final
exam score. If the mean for the midterm () was 77, with sx = 18.5, and the mean for the final
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exam () was 84, with sy = 14, what final exam score would be predicted for someone whose
midterm was 77?
*
a) 77
b) 84
c) 91
d) cannot be answered without knowing Pearson's r
18. Given the following summary statistics: = 36, sx = 1.6,
= 44, sy = 2.8, r = .7, N = 10, what is the unbiased estimate for the standard error of the
estimate?
a) 1.21 b) 1.63 c) 2.0 d) 2.12
-19. Although instructions to use imagery to link items in a list can significantly improve free
recall, recall after instructions can be predicted rather well from recall performance before
instructions. Data for eight subjects are given below:
Before
After
8
14
11
15
7
9
10
16
9
9
12
13
8
7
10
12
What is the slope of the regression equation for predicting a subject's score after instruction from
his or her score before instruction?
a) .31 b) .59 c) 1.13 d) 1.91
-20. To show that the number of hours spent studying can, to some degree, predict scores on a
quiz, a professor collected the data presented below:
Study Hours Quiz Score
7
5
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6
11
5
15
11
12
11
7
10
6
4
9
10
8
9
7
What is the Y-intercept of the regression equation for predicting the quiz score from the number
of hours studied (i.e., what quiz score is predicted for someone who doesn't study)?
a) .31 b) 3.09 c) 4.58 d) 7.08
-Section C
21. Experiments A and B resulted in the same two-group t value, but experiment A involved
more subjects. Which of the following can be concluded from this information?
a) More variance is accounted for in experiment A.
*
b) More variance is accounted for in experiment B.
c) The same amount of variance is accounted for in both experiments.
d) Nothing can be concluded without knowing the separation of the sample means in each
experiment.
22. Suppose that the calculated t value for a two-group experiment with 43 subjects per group is
4.0. What is the value of the point-biserial r?
*
a) .16
b) .19
c) .4
d) .44
23. Suppose that the calculated t value for an experiment with two equal-sized groups is 2.0. If
the point-biserial r is .3, how many subjects must have been in each group?
*
a) 20
b) 21
c) 40
d) 42
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24. If the effect size (d) for a two-group experiment is 1.0, what proportion of the variance in the
population is accounted for by group membership?
*
a) .2
b) .25
c) .4
d) 1.0
25. A large two-group t value can be associated with a very small value for the point-biserial r,
if which of the following is true?
*
a) alpha is very large
b) the p value is very large
c) d is very large
d) the sample sizes are very large
Chapter 11
The Matched t-test
Section A
1. The usual null hypothesis in the matched t-test can be stated as:
a) the population mean of the difference scores is zero
b) the population means corresponding to the two sets of
scores are the same
c) the difference of the population means corresponding to
the two sets of scores is zero
*
d) all of the above
2. Compared to an independent-samples t-test on the same data, the matched t-test will always
yield:
*
a) a smaller critical t
b) a larger critical t
c) a smaller calculated t
d) none of the above
3. The matched t-test is always preferable to the independent-samples t-test, when:
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a) the correlation between the two sets of scores is positive
b) there are no carry-over effects
c) the two samples are equal in size
d) none of the above
4. The matched t will equal the independent-samples t calculated on the same data, when:
*
a) the correlation between the two sets of scores is zero
b) the correlation between the two sets of scores is 1.0
c) the variability of the difference scores is zero
d) the sample variances of the two sets of scores are equal
5. The direct-difference method:
*
a) requires that the correlation between the two sets of
scores be calculated first
b) resembles the one-sample t-test
c) only applies when the same subject has been measured
twice
d) yields the same value as an independent-groups t-test
6. When the correlation between the two sets of scores in a matched t-test is 1.0:
*
a) the matched t will be zero
b) the difference of the sample means will be zero
c) the variability of the difference scores will be zero
d) the independent-samples t will be larger than the
matched t
7. Matching subjects in pairs is usually preferable to repeated measures on the same subjects,
whenever:
*
a) there are order effects
b) there are carry-over effects
c) the correlation between the two sets of scores is low,
but positive
d) all of the above
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8. The purpose of counterbalancing is:
*
a) to average out order effects
b) to average out carry-over effects
c) to increase the correlation between the two sets of
d) none of the above
scores
9. Drawing conclusions from a before-after design can be misleading if:
*
a) the same subjects are measured twice
b) the correlation between the two sets of scores is very
high
c) the design is correlational rather than experimental
d) there is no control group
10. When the correlation between the two sets of scores in a matched t-test is high and positive,
the advantage of the matched t-test (compared to the independent-samples test) is that:
*
a) there is less chance of making a Type I error
b) there is less chance of making a Type II error
c) it is more reasonable to perform a one-tailed test
d) the results are more conclusive
Section B
11. If a study involves 12 pairs of matched subjects, what would be the appropriate critical t
value for a .01, one-tailed test?
a) 2.492 b) 2.508 c) 2.681 d) 2.718
-12. Twenty matched pairs of subjects were given simulated work tasks under two different sets
of working conditions. The mean number of tasks completed was 12.6 for one condition and
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14.2 for the other. If the (unbiased) standard deviation of the difference scores was 4, what is the
matched t value?
a) 1.79 b) 3.58 c) 7.16 d) 8.0
-13. Suppose you have scores taken before and after some treatment on 30 subjects. If the
standard deviation of the before scores is 7.5 and the standard deviation of the after scores is 6.1,
and the correlation between the before and after scores is .5, what is the standard error of the
difference scores (i.e., the denominator of the matched t-test)?
a) 1.26 b) 1.59 c) 1.77 d) 2.15
-14. Given the following summary statistics: 1 = 1.6, 2 =5.1,
s1= 3, s2= 4, N = 16, r = .3, what is the value of the matched t?
a) 1.66 b) 2.80 c) 3.32 d) 6.83
-15. If the matched t equals 3.33 in an experiment, in which the standard deviation of the
difference scores (sD) equals 2.7 and the difference of the two sample means equals 4.5, how
many pairs of scores must have been involved?
a) 2 b) 4 c) 8 d) 16
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16. Imagine that 36 subjects are each run in two experimental conditions and that the mean for
one condition is 7.2, while the mean for the other condition is 4.7. If the standard deviation of
the difference scores (sD) is 4.5, what is the two-tailed p level that corresponds to the matched t?
*
a) > .05
b) between .05 and .02
c) between .02 and .01
d) < .01
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17. Which of the following will produce the highest matched t value, assuming that the
numerator is the same in each case?
*
a) sD = 5, N = 12
b) sD = 6.5, N = 17
c) sD = 4, N = 9
d) sD = 9, N = 21
18. A computer company claims that their new keyboard is designed for faster typing. In a pilot
study, six subjects typed the same material on both the new and an old keyboard. Given the
scores below (in words per minute), what is the value of t that would be used to test the null
hypothesis?
Subject Old keyboard New keyboard
1
48
2
56
3
49
4
68
5
66
6
59
52
56
55
65
67
63
a) 1.37 b) 1.49 c) 2.74 d) 3.35
-19. A student would like to demonstrate that the final exam was significantly more difficult than
the midterm. The scores for four of the student's friends are shown below. What is the matched
t value for these data?
Student
1
2
3
4
Midterm
Final
88
84
86
80
91
80
79
65
a) .77 b) 1.54 c) 1.33 d) 2.66
-20. It has long been known that the use of imagery can improve recall in a memory test. The
data below represent the number of words recalled from a list before and after the subject is
given instructions to use imagery to memorize the list of words.
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Subject
1
2
3
4
5
6
7
8
Test Items
Before
8
11
7
10
9
12
8
10
After
14
15
9
16
9
13
7
12
What is the two-tailed p value that corresponds to the matched t for this experiment?
*
a) > .05
b) between .05 and .02
c) between .02 and .01
d) < .01
Section C
21. If a high value has been calculated for a matched t-test, but the sample size was small, and
the separation of the sample means was small compared to the standard deviation of the scores in
each condition, which of the following must have been true?
*
a) the correlation between the two sets of scores must have been low
b) the correlation between the two sets of scores must have been high
c) alpha must have been small
d) a calculation error must have been made
22. As the correlation between the two sets of scores in a matched t-test increases (all else
remaining the same):
*
a) the denominator of the t-test decreases
b) the numerator of the t-test increases
c) the variance within each set of scores decreases
d) all of the above
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23. If the expected t value (delta) for a t-test of two independent groups is 2.0, what value for t
would be expected if the experiment could be changed to a matched t-test with an expected
correlation between the two sets of scores of .36?
*
a) 1.67
b) 2.0
c) 2.5
d) 3.33
24. If two population means are expected to differ by .5 standard deviations, and a matched ttest is performed with 18 matched pairs and an expected correlation between the two sets of
scores of .19, what is the expected value for the matched t?
*
a) 1.67
b) 2.4
c) 3.33
d) 4.8
25. Which of the following tends to increase the power of a matched t-test?
*
a) larger samples
b) larger alpha
c) better matching between the two sets of scores
d) all of the above
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Chapter 12
One-Way Independent ANOVA
Section A
1. In the two-group case, the F ratio for the one-way ANOVA equals:
*
a) the square-root of the t value
b) the square of the t value
c) one-half of the t value
d) twice the t value
2. The weighted average of all the sample variances is:
*
a) MSw
b) MSbet
c) SStotal
d) the F ratio
3. If the null hypothesis is true, MSbet is expected to be approximately equal to:
a) 0
b) 1
c) MSw d) F
--
4. Suppose that the F ratio calculated for a particular experiment is equal to .04. Which
of the following can be concluded?
*
a) A calculation error must have been made.
b) The null hypothesis cannot be rejected.
c) The null hypothesis can be rejected at the .05 level.
d) Nothing can be concluded without knowing the degrees of freedom.
5. When the null hypothesis is rejected in a one-way ANOVA, which of the following is
implied?
*
a) Each population mean is different from all of the other population means.
b) Each population variance is different from all of the other population variances.
c) The population means are not all equal to each other.
d) All of the above.
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6. If all of the scores in the same group are the same, but the scores in one group are
different from the scores in any other group, which of the following will be true?
*
a) MSbet will equal zero.
b) MSw will equal zero.
c) F will equal zero.
d) F will equal 1.0.
7. Which of the following will lead to a larger calculated F ratio (all else remaining
constant)?
*
a) larger variances within each of the samples
b) reduced separation of the population means
c) larger sample sizes
d) a larger alpha level
8. Which of the following leads to a smaller critical F in a typical one-way ANOVA?
*
a) an increase in dfbet
b) an increase in dfw
c) an increase in the size of alpha
d) all of the above
9. Which of the following is assumed when performing the ordinary one-way ANOVA?
*
a) All of the population means are the same.
b) All of the population variances are the same.
c) All of the sample sizes are the same.
d) All of the sample variances are the same.
10. If the levels of your independent variable represent values on an interval or ratio
scale, which of the following may give you more power than the ordinary one-way
ANOVA?
*
a) linear regression
b) random effects ANOVA
c) the raw-score formula
d) a weighted-means analysis
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Section B
11. If dfw = 50 and dfbet = 4, how many subjects were in each sample?
a) 4 b) 5 c) 10 d) 11
-12. If your experiment consists of five groups with seven subjects in each, what is the
critical value for F at the .01 level?
a) 2.69 b) 3.70 c) 4.02 d) 9.15
-13. If your study consists of 100 subjects divided equally among five groups, and you
have calculated that SStot = 11,101 and
SSbet = 8,916, what is the value for MSw?
a) 23 b) 109.25 c) 115 d) 210.7
-14. If your study consists of four groups, each with 15 subjects, and SSbet = 42 and SSw =
35, what does your F ratio equal?
a) 4.2 b) 5.6 c) 16.8 d) 22.4
-15. If you have four equal-sized groups in your study, and the standard deviation for
each group is as shown below, how large is MSw?
Group
s
1
4.9
2
3.6
3
4.1
4
5.4
a) 4.5 b) 6.0 c) 20.74 d) 27.65
-16. Imagine a study in which a different teaching method is assigned to each of three
equal-sized groups, all of which take the same final test. The mean test score and
standard deviation for each group is as follows: 1 = 80, s1 = 9; 2 = 81, s2 = 11;
3 = 84, s3 = 12. If the F ratio for this experiment is 1.88, what must have been the size of
each group?
a) 50 b) 100 c) 125 d) 150
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17. A neuropsychologist is studying patients with five types of brain damage on a maze
learning task. The mean number of trials to complete the task, the standard deviation,
and the size of each group are as follows: 1 = 8, s1= 2.5, N1 = 8; 2 = 4, s2= 2, N2 = 14; 3 =
6, s3= 1.8, N3 = 10; 4 = 9, s4= 2.5, N4 = 16; 5 = 8, s5= 2.2, N5 = 12. What is the F ratio for
this study?
a) 2.5 b) 5.6 c) 8.8 d) 11.1
-18. A psychophysiologist is investigating the hypothesis that vividly imagining physical
exercise will cause an increase in the respiratory rate. Three groups are tested: one that
vividly imagines relaxing in a beach chair, one that imagines walking briskly down the
street, and one that imagines sprinting around a racetrack. The respiration rates for four
subjects in each group are shown below:
Relaxing
22
21
19
19
Walking
24
23
19
23
Running
25
28
22
25
What is the p value that corresponds to the F ratio for these data?
a) > .05
*
b) between .05 and .025
c) between .025 and .01
d) < .01
19. A clinical psychologist is comparing (bipolar) manic-depressives with both unipolar
manics and unipolar depressives on their clinical response to a new type of psychoactive
drug. Clinical improvement scores for subjects in all three groups are given below:
Bipolar
3
4
3
2
Manics
4
4
5
3
4
3
Depressives
3
4
2
5
4
What is the F ratio for this study?
a) 1.02 b) 2.04 c) 3.06 d) 4.08
-20. Both gender and handedness seem to be important factors associated with the degree
to which various cognitive functions are "lateralized" (performed better or more quickly
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with one cerebral hemisphere than the other). Lateralization scores (on a scale from 0 to
10) were determined for subjects in the four combinations of gender and handedness as
shown below:
Left-Men
5
4
5
Left-Women
7
6
8
Right-Men
8
9
7
7
9
What is the p value that corresponds to the F ratio for these data?
a) > .05
b) between .05 and .025
c) between .025 and .01
*
d) < .01
18
Right-Women
8
7
8
5
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Section C
21. A group of 30 schizophrenics is compared to 30 neurotics on a vigilance task. The
standard deviation of the vigilance measure is 6 for the schizophrenics and 3 for the
neurotics. What is the value of the F ratio that you might use to test whether the two
populations have equal variances?
*
a) .5
b) 1.0
c) 2.0
d) 4.0
22. In a one-way ANOVA, eta-squared is:
*
a) an unbiased estimate of omega-squared
b) the proportion of variance in your samples accounted for by group membership
c) SSbet divided by SSw
d) all of the above
23. Which of the following would result in an increase in omega-squared (the variance
accounted for in the population)?
*
a) increasing the separation of the population means
b) increasing the sample sizes
c) increasing alpha
d) all of the above
24. For a particular one-way ANOVA, SSbet was 23 and SSw was 69. What is the value
for eta-squared?
*
a) .25
b) .33
c) .5
d) cannot be determined without knowing the df components
25. If you expect a medium-sized effect (f = .25), and your experiment consists of four
groups of 16 subjects each, what can you expect for your Type II error rate when testing
your F ratio at the .05 level?
a) .29 b) .34 c) .64 d) .66
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