Chapters 13-15
Chapter 13
Multiple Comparisons
Section A
1. The use of MSw in Fisher's protected t-tests is based on the assumption that:
*
a) all of the populations have the same mean
b) all of the populations have the same variance
c) all of the samples have the same size
d) all of the above
2. Tukey's HSD test assumes that:
*
a) all of the samples have the same mean
b) all of the samples have the same variance
c) all of the samples have the same size
d) all of the above
3. When conducting Fisher's protected t-tests, which of the following is determined directly by
the researcher?
*
a) the alpha per comparison
b) the experiment-wise alpha
c) the Type II error rate
d) LSD
4. If two of the pairwise comparisons following an ANOVA exceed Fisher's LSD, how many
would exceed Tukey's HSD?
*
a) one or none
b) two
c) at least two
d) no more than two
5. If a one-way ANOVA is not statistically significant:
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Chapters 13-15
*
Test Items
a) none of the pairwise comparisons will be significant
b) Fisher's protected t-tests are not justified
c) LSD is preferred to HSD
d) all of the above
6. Compared to Fisher's protected t-tests, Tukey's HSD test:
*
a) involves a smaller alpha per comparison
b) leads to a lower rate of Type II errors
c) maintains less control over experiment-wise alpha
d) is more liberal
7. Which of the following leads to a larger value for the studentized range statistic (q):
*
a) larger sample sizes
b) larger number of groups
c) larger value for alpha
d) all of the above
8. Which of the following procedures is recommended when you are performing not only
pairwise comparisons, but complex comparisons, as well?
*
a) the Scheffé test
b) Dunnett's test
c) the Newman-Keuls test
d) Tukey's HSD test
9. In addition to Tukey's HSD, which of the following procedures is based on the studentized
range statistic?
*
a) the Scheffé test
b) Dunnett's test
c) the Newman-Keuls test
d) Fisher's LSD
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Chapters 13-15
Test Items
10. When performing Fisher's protected t-tests on an experiment with more than three groups,
under which of the following conditions will the experimentwise alpha be kept at the value
initially set for the one-way ANOVA?
*
a) when all of the samples are very large
b) when all of the samples are the same size
c) when all of the population variances are equal
d) when the complete null hypothesis is true
Section B
11. If you test 9 groups in an analysis of variance, how many different pairwise comparisons can
be performed?
a) 9 b) 18 c) 36 d) 81
-12. If you want to do Fisher's protected t-tests after a one-way ANOVA in which NT = 40 and k
= 5, what value would you use for degrees of freedom when looking for the critical t value?
a) 8 b) 35 c) 36 d) 39
--
13. If your experiment involves five groups of nine subjects each, what value of the studentized
range statistic (q) would you use for Tukey's HSD test at the .05 level?
a) 3.79 b) 4.04 c) 4.76 d) 4.89
--
14. If dfw = 20 for an experiment with four equal-sized groups, and MSw = 6.66, how large is
LSD if you test at the .05 level?
a) 1.70 b) 2.20 c) 3.11 d) 3.81
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Chapters 13-15
Test Items
15. If your experiment contains three groups of seven subjects each, and MSw = 15.75, how
large is HSD if you test at the .05 level?
a) 5.42 b) 6.24 c) 7.66 d) 8.12
--
16. Suppose that an experiment comparing three conditions,
A, B, and C, obtains the following means: A = 49.1, B = 52.4,
C = 54.3. If SSw from the ANOVA is equal to 270 and there are 11 subjects in each group, which
pairs of conditions differ significantly at the .01 level, according to the LSD test?
a) none b) A&C only c) A&B and A&C d) all three
--
17. Referring to the data in the previous question, which pairs of conditions differ significantly
at the .05 level, according to the HSD test?
a) none b) A&C only c) A&B and A&C d) all three
-18. A psychologist is comparing three treatments for agoraphobia with a control group. Eleven
patients are selected for each group. After five months of treatment, the mean number of anxiety
attacks during the sixth month for each group are as follows: control = 15, scon = 4; 1 = 12, s1 = 3.5;
2 = 9, s2 = 2;
3 = 5, s3 = 3. Using Fisher's LSD test, which treatments differ significantly (at the .05 level) from
the control group?
a) only 3 b) 2 & 3 c) all three d) none
-19. Fisher's LSD test is not recommended when dealing with four or more groups as in the
previous question. By calculating HSD (at the .05 level) for the data in the previous question,
determine which of the treatments differ significantly by Tukey's criterion:
a) only 3 b) 2 & 3 c) all three d) none
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Chapters 13-15
Test Items
20. Eight schizophrenics, 11 depressives, and 14 normals are being compared with respect to the
number of minutes spent in REM sleep on a night in the sleep laboratory. The means for the
three groups are as follows: schiz = 144; dep = 129; norm = 133.
Assuming that homogeneity of variance exists, that MSw = 150, and that the ANOVA is
significant at the .05 level, conduct Fisher's protected t-tests to answer the question: which
pair(s) of groups differ(s) significantly at the .05 level?
*
a) Schizophrenics vs. Depressives
b) Schizophrenics vs. Normals
c) Both a and b
d) All three pairs differ significantly
21. If your experiment involves six groups of 21 subjects each, what is the critical F for
Scheffé's test at the .05 level?
a) 11.45 b) 13.74 c) 19.6 d) 23.5
--
22. If you want to compare one group with the average of three other groups, which of the
following sets of coefficients would be appropriate?
*
a) +1 +1 +1 +3
b) -1/3 -1/3 -1/3 +1
c) +1 +1 +1 -4
d) -1 -1 -1 +1/3
23. Suppose that SSbetween for your four-group ANOVA equals 552. If the SS for your planned
contrast is half of that, and MSW equals 55, what is the F ratio that you would use to test the
significance of your contrast?
a) 1.25 b) 1.67 c) 2.51 d) 5.02
-24. If your planned contrast involves comparing the mean of one group to the average of three
other groups, and there are 31 subjects in each group, what would be the appropriate critical
value for F?
a) 2.45 b) 2.68 c) 3.92 d) 4.17
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Chapters 13-15
Test Items
-25. If your one-way ANOVA is not statistically significant:
a) a pairwise comparison may be significant by the LSD test, but the LSD test is not
permitted in this case.
b) Tukey's HSD test is permitted, but is not likely to yield significant results.
c) you will not be able to find a complex contrast that is significant using Scheffé's test.
*
d) all of the above
Section C
26. What is the harmonic mean of the following three numbers: 10, 20, 30?
*
a) 5.5
b) 16.4
c) 20
d) 24.4
27. In a five-group experiment, what is the largest number of comparisons you can have in a set
of mutually orthogonal comparisons?
*
a) 4
b) 5
c) 6
d) 10
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Chapters 13-15
Test Items
28. If in a five-group experiment, you plan to test six particular complex comparisons, which of
the following procedures would maximize your power and still be adequately conservative?
*
a) use Tukey's test for all comparisons
b) use Scheffé's test for all comparisons
c) use the .05 level for each comparison
d) use the .0083 level for each comparison
29. According to the Bonferroni inequality, if you perform 5 significance tests in the same
experiment, each at the .05 level, what is the largest that the experimentwise alpha can get?
*
a) .05
b) .25
c) .50
d) 1.0
30. If you are using the Bonferroni test, which of the following happens as you increase the
number of planned comparisons?
*
a) the alpha per comparison decreases
b) the experimentwise alpha increases
c) both a and b
d) neither a nor b
Chapter 14
Two-Way ANOVA
Section A
1. Under which of the following conditions will the critical F be the same for testing each of the
three F ratios in a two-way ANOVA?
*
a) when there is no interaction
b) when the design is balanced
c) when there are two levels of each factor
d) when the two factors have the same number of levels
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2. Suppose that you are conducting an experiment in which gender is one factor, and the other
factor involves three degrees of competitiveness in a simulated industrial task. This
experimental arrangement could be described as:
*
a) a six-way design
b) a 2 by 3 design
c) an interaction design
d) a balanced design
3. Suppose that in the experiment described in the previous question, the marginal means for the
two genders are the same. This implies that:
*
a) the main effect of gender will not be significant
b) the interaction will not be significant
c) the F ratio for the main effect of competitiveness will be zero
d) none of the above
4. When there is no interaction in the population, the numerator of the F ratio for the interaction
effect:
*
a) is an estimate of the population variance
b) is expected to be zero
c) should equal the sum of the numerators of the F ratios for the two main effects
d) is an estimate of between-group variance
5. When the lines on a graph of cell means are not perfectly parallel, you know that:
*
a) the interaction is disordinal
b) there must be some interaction among the population
c) the F ratio for the interaction will be greater than 1.0
d) the F ratio for the interaction will not be zero
means
6. In a balanced two-way independent-groups ANOVA, the error term (i.e., the denominator) for
each of the three F ratios:
*
a) is the mean of all the cell variances
b) is the variance of the cell means
c) tends to get smaller as the sample size increases
d) may differ depending on the degrees of freedom associated with each effect (i.e., all
three error terms can be different)
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7. If the interaction in a two-way ANOVA is disordinal and statistically significant, the main
effects will probably:
*
a) be statistically significant
b) not be statistically significant
c) result in a Type I error
d) be misleading
8. In a particular two-way ANOVA, comparing low self esteem subjects with high self esteem
subjects performing a cognitive task for either a small or large reward, a significant interaction
was found. This implies that:
a) the different levels of reward affected performance in both groups of subjects
b) the different levels of reward affected performance for one group of subjects but not
the other
c) the different levels of reward affected performance in opposite directions for the two
groups of subjects
*
d) none of the above
Section B
9. In a 3 X 4 ANOVA with 7 subjects in each cell, what will be the value of dfw (i.e., the degrees
of freedom for the error term of each F ratio)?
a) 11 b) 72 c) 77 d) 84
-10. If dfw for a 2 X 3 ANOVA is 90, how many subjects were in each cell?
a) 5 b) 15 c) 16 d) 17
-11. In a 4 X 4 ANOVA with 10 subjects in each cell, the total SS is 550. If SSR = 50, SSC = 70,
and SSW = 370, how large is the F ratio you would use to test the significance of the interaction
of the two factors?
a) 2.59 b) 2.86 c) 3.59 d) 3.89
--
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Chapter 15
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12. Native speakers of five different languages are tested for reading speed with passages
involving one of three grammatical structures: either all active voice, all passive, or mixed.
Assume that 75 subjects are divided equally among the cells of a completely-crossed design, and
that the total SS is 3100; the sum of squares for the grammar effect equals 800, the sum of
squares for the interaction equals 600, and SSW = 1500. How large is the numerator of the F
ratio you would use to test the main effect of languages?
a) 25 b) 50 c) 75 d) 100
-13. Native speakers of five different languages are tested for reading speed with passages
involving one of three grammatical structures: either all active voice, all passive, or mixed.
Assume that 75 subjects are divided equally among the cells of a completely-crossed design, and
that the total SS is 3100; the sum of squares for the grammar effect equals 800, the sum of
squares for the interaction equals 600, and SSW = 1500. What is the p value associated with the
F ratio you would use to test the main effect of languages?
*
a) > .05
b) between .05 and .025
c) between .025 and .01
d) < .01
14. The cell means and (unbiased) standard deviations are given below for an experiment in
which coffee drinkers and coffee abstainers (nondrinkers) are compared on a motor learning task
after either a caffeine pill or placebo.
Caffeine
Placebo
Coffee
Drinker
= 27
s = 2.6
= 13
s = 2.2
NonDrinker
= 23
s = 2.1
= 17
s = 2.4
Which of the following effects cannot be statistically significant?
*
a) main effect of coffee drinker vs. nondrinker
b) main effect of caffeine vs. placebo
c) the interaction of the two factors
d) none of the above (i.e., any or all of the effects can be significant)
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Chapter 15
Test Items
15. The cell means and (unbiased) standard deviations are given below for an experiment in
which coffee drinkers and coffee abstainers (nondrinkers) are compared on a motor learning task
after either a caffeine pill or placebo.
Caffeine
Placebo
Coffee
Drinker
= 27
s = 2.6
= 13
s = 2.2
NonDrinker
= 23
s = 2.1
= 17
s = 2.4
How large is the error term (i.e., MSW) for this experiment?
a) 2.33 b) 5.44 c) 8.8 d) 9.3
-16. The cell means and (unbiased) standard deviations are given below for an experiment in
which coffee drinkers and coffee abstainers (nondrinkers) are compared on a motor learning task
after either a caffeine pill or placebo.
Caffeine
Placebo
Coffee
Drinker
= 27
s = 2.6
= 13
s = 2.2
NonDrinker
= 23
s = 2.1 s
= 17
= 2.4
If there are eight subjects per cell, how large is the F ratio for testing the main effect of caffeine
vs. placebo?
a) 0 b) 7.35 c) 73.5 d) 147
--
17. A social psychologist is studying helping behavior as a function of the gender of the helper,
and the age of the person in need (a confederate of the experimenter who apparently trips and
drops some packages). The dependent variable is the number of seconds that elapse before the
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Chapter 15
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subject begins to help in some way. The means and standard deviations are given for each cell
of the design in the table below; there are four subjects per cell:
Child
Young Adult Elderly
Men = 8.75
= 11.5
= 6.0
s = 2.99
s = 2.89
s = 1.83
Women
s = 2.75
= 7.25
s = 2.5
= 15.25
s = 1.83
= 7.0
How large is the F ratio for testing the main effect of age?
a) 1.12 b) 4.4 c) 16.6 d) 32.2
-18. A social psychologist is studying helping behavior as a function of the gender of the helper,
and the age of the person in need (a confederate of the experimenter who apparently trips and
drops some packages). The dependent variable is the number of seconds that elapse before the
subject begins to help in some way. The means and standard deviations are given for each cell
of the design in the table below; there are four subjects per cell:
Child
Young Adult Elderly
Men = 8.75
= 11.5
= 6.0
s = 2.99
s = 2.89
s = 1.83
Women
s = 2.75
= 7.25
s = 2.5
= 15.25
s = 1.83
= 7.0
What is the p value associated with the F ratio you would use to test the significance of the
interaction?
*
a) > .05
b) between .05 and .025
c) between .025 and .01
d) < .01
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19. In a study of environmental effects on mood, subjects fill out a depression questionnaire in
either a brightly colored room, an ordinary room, or a darkly colored room. In each of the three
rooms, different subjects are exposed to an experimenter who is either cheerful, neutral, or
depressed. The depression scores are shown in the table below:
Cheerful
Bright
Ordinary
Dark
14 18 22
17 20 21
14 15 25
Neutral 17 18 26
Depressed
17 21 22
13 19 20
22 23 25
22 24 25
26 29 30
How large is the error term (i.e., MSW) for this experiment?
a) 3.52 b) 9.33 c) 12.4 d) 19.3
-20. In a study of environmental effects on mood, subjects fill out a depression questionnaire in
either a brightly colored room, an ordinary room, or a darkly colored room. In each of the three
rooms, different subjects are exposed to an experimenter who is either cheerful, neutral, or
depressed. The depression scores are shown in the table below:
Cheerful
Bright
Ordinary
Dark
14 18 22
17 20 21
14 15 25
Neutral 17 18 26
Depressed
13 19 20
17 21 22
22 23 25
22 24 25
26 29 30
Perform a two-way ANOVA on the above data. Which of the F ratios are statistically significant
at the .05 level?
*
a) both main effects, but not the interaction
b) the interaction, but neither of the main effects
c) both main effects and the interaction
d) none of the above
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Chapter 15
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Section C
21. Post hoc comparisons among the different levels of a main effect are not likely to be
performed when:
*
a) that main effect has more than two levels
b) that main effect is not significant
c) the other main effect is not significant
d) the interaction is not significant
22. Averaging simple effects together to form a main effect is likely to be somewhat misleading
when:
*
a) that main effect has more than two levels
b) that main effect is significant
c) the other main effect is significant
d) the interaction is significant
23. Given the cell means below, what is the value of L that you would use to calculate the
interaction as a contrast?
Caffeine
Coffee Drinker
= 27
= 13
Non-Drinker
= 23
= 17
c) 4
--
d) 8
a) 0
b) 2
Placebo
24. Suppose that you are following up a significant interaction in a 3 X 4 ANOVA by
computing various interaction contrasts. How does the critical F from Scheffé's test compare to
the critical F that you would have used to test the entire 3 X 4 interaction?
*
a) it is six times larger
b) it is eleven times larger
c) it is twelve times larger
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d) it is somewhat smaller
25. The analysis of unweighted means is most appropriate when the differences in cell sizes are:
*
a) zero
b) related to the experimental treatments
c) proportional to the differences in population size
d) accidental
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Chapter 15
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Chapter 15
Repeated Measures ANOVA
Section A
1. Imagine a study in which there are two repeated conditions, and both the matched t
and repeated measures ANOVA are calculated. Which of the following will be true?
a) The critical F will be the same as the critical t.
*
b) The p values will be the same for both tests.
c) The RM ANOVA will have a greater chance of statistical significance than the
matched t.
d) The matched t will have a greater chance of statistical significance than the RM
ANOVA.
2. One disadvantage of a repeated-measures ANOVA (as compared to an independentgroups ANOVA on the same data) is:
*
a) the reduction of degrees of freedom in the error term
b) the reduction in the numerator of the F ratio
c) the reduction in the size of the error term
d) the reduction in alpha
3. If the one-way RM ANOVA is looked at as a two-way ANOVA with subjects as one
of the factors, which of the following two-way ANOVA components will equal zero?
a) SScols
b) SSsubs
c) SSinter
d) SSw
--
4. In a repeated measures ANOVA, as SSsub (the variability of the marginal means of the
subjects) increases (and SStotal stays the same):
*
a) SSinter (or SSresidual) decreases
b) F decreases
c) the numerator of the F ratio decreases
d) all of the above
5. If an independent-groups ANOVA and a repeated-measures ANOVA are performed
on the same data, which of the following will be the same for both analyses?
*
a) the numerator of the F ratio
b) the denominator of the F ratio
c) the critical F
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Chapter 15
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d) none of the above
6. If the F ratio for the repeated-measures ANOVA turns out to be smaller than the F
ratio for an independent-groups ANOVA calculated on the same data, this means that:
*
a) a calculation error has been made
b) the RM ANOVA should probably not be performed
c) the subject by treatment interaction is even smaller than can be expected from
chance factors
d) the null hypothesis cannot be rejected
7. Counterbalancing is most likely to be used with which of the following experimental
designs?
*
a) simultaneous repeated measures
b) successive repeated measures
c) randomized blocks
d) a correlational design
8. Which of the following is likely to cause a simple order effect?
*
a) carry-over from one treatment to the next
b) fatigue
c) the use of randomized blocks
d) all of the above
9. Differential carry-over effects can be eliminated by:
*
a) counterbalancing
b) using a Latin-Square design
c) matching subjects in blocks
d) using only two repeated conditions
10. When compound symmetry exists in the population, you can be sure that:
a) your calculated F ratio will not be positively biased
b) sphericity (or circularity) also exists in the population
c) the population correlation between one pair of conditions will be the same as
for any other pair
*
d) all of the above
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Section B
11. If 55 subjects are matched into blocks of five, what is the critical value of F for the
one-way randomized blocks ANOVA?
a) 2.37 b) 2.45 c) 2.53 d) 2.61
-12. Thirty subjects are measured before and after some treatment, and again at followup. The total sum of squares is found to be 1108, the SS for the RM treatment equals
118, and the SS for the subjects factor equals 538. What is the F ratio for the one-way
RM ANOVA?
a) 3.18 b) 6.36 c) 7.57 d) 7.79
-13. Twenty subjects memorize similar lists of words under four different conditions.
The total sum of squares is found to be 395. If the SS for subjects equals 59, and the
SSresidual equals 285, what is the F ratio for the one-way RM ANOVA?
a) .18 b) 2.82 c) 3.40 d) 3.76
-14. Twenty subjects memorize similar lists of words under four different conditions.
The total sum of squares is found to be 395, the SS for subjects equals 59, and the
SSresidual equals 285. What would be the F ratio if the one-way independent-groups
ANOVA were calculated, in spite of the fact that this is a repeated-measures design?
a) .18 b) 2.82 c) 3.40 d) 3.76
-15. Fifteen ninth-graders are matched in blocks of three, based on academic
performance, and then randomly assigned to one of three methods for teaching history:
traditional, self-paced, and computer-assisted. The final exam scores for each student are
shown in the table below, along with the row and column means:
Block #
1
2
3
4
5
Mean
Traditional
85
84
90
81
77
83.4
Self-Paced
80
92
85
84
87
85.6
18
Computer Mean
93
86
95
90.33
83
86
96
87
88
84
91
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Chapter 15
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What is the sum of squares for the teaching method (RM) factor?
a) 153 b) 224 c) 377 d) 441
-16. Fifteen ninth-graders are matched in blocks of three, based on academic
performance, and then randomly assigned to one of three methods for teaching history:
traditional, self-paced, and computer-assisted. The final exam scores for each student are
shown in the table below, along with the row and column sums:
Block #
1
2
3
4
5
Mean
Traditional Self-Paced Computer Mean
85
80
93
84
92
95
90
85
83
81
84
96
77
87
88
83.4
85.6
91
86
90.33
86
87
84
86.67
If the sum of all the squared scores is 113,108, what is the p value associated with the F
ratio for the teaching method (RM) factor?
*
a) > .05
b) between .05 and .025
c) between .025 and .01
d) < .01
17. Five subjects rate the persuasiveness on a scale from 0 to 10 of three different
arguments. One argument is labelled as having been written by a "government expert",
one by a "local professor", and one by a "fellow student." The ratings for each subject for
each argument are shown in the table below:
Subject
1
2
3
4
5
Student Professor
0
1
2
5
1
2
5
4
2
8
Expert
2
5
6
9
8
What is the F ratio for testing the repeated-measures factor?
a) 2.0 b) 4.0 c) 8.0 d) 16.0
--
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18. Four subjects perform the same clerical task under four different levels of distraction:
none, mild, moderate, and strong. The number of errors committed by each subject under
each condition are shown in the table below:
Subject #
1
2
3
4
None
2
0
7
3
Mild
5
8
9
12
Moderate
11
4
13
10
Strong
14
11
20
15
If SStotal = 428, what is the sum of squares for the subject by treatment interaction?
a) 45.5 b) 92.5 c) 190 d) 290
-19. Four subjects perform the same clerical task under four different levels of distraction:
none, mild, moderate, and strong. The number of errors committed by each subject under
each condition are shown in the table below:
Subject #
1
2
3
4
None
2
0
7
3
Mild
5
8
9
12
Moderate
11
4
13
10
Strong
14
11
20
15
If SStotal = 428, what is the F ratio for testing the distraction factor?
a) 3.14 b) 6.28 c) 8.41 d) 19.1
-20. Suppose that you have calculated an F ratio of 4.9 for a study involving four
conditions repeated on each of 12 subjects. If you are concerned about the sphericity
assumption, which of the following can be concluded, assuming that alpha is set to .05?
a) The F does not surpass the ordinary critical F, so the null hypothesis cannot be
rejected.
b) The F surpasses the ordinary critical F, so the null hypothesis can be rejected
without further testing.
c) The F surpasses the ordinary critical F, but not the Geisser-Greenhouse
conservative F, so further testing is necessary.
*
d) The F surpasses the Geisser-Greenhouse conservative F, so the null hypothesis
can be rejected without further testing.
Section C
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21. If a repeated-measures ANOVA with four conditions is statistically significant, but
sphericity cannot be assumed, which of the following is recommended as the error term
for follow-up pairwise comparisons (assuming the numerator of each test is the difference
of the means for the two conditions involved)?
*
a) the error term from the RM ANOVA
b) one-sixth of the error term from the RM ANOVA
c) six times the error term from the RM ANOVA
d) the standard error of the difference scores for the two conditions
22. Assuming that compound symmetry is true in the population, the power of the RM
ANOVA increases (all else remaining the same) as:
a) the subject-to-subject variability within each condition decreases
*
b) the population correlation between pairs of conditions increases
c) the amount of subject by treatment interaction increases
d) alpha decreases
23. Even when an experiment is fully counterbalanced, simple order effects can reduce
the power of the ANOVA by:
*
a) increasing the size of the error term
b) decreasing the separation of the means for the different conditions
c) leading to a violation of sphericity
d) all of the above
24. If you have seven different conditions to present successively in a repeated-measures
design, how many orders would be required for a digram-balanced Latin Square Design?
a) 7
--
b) 14
c) 28
d) 56
25. Suppose that three judges, a student, a professor, and an expert in the field, rate the
persuasiveness (on a scale from 0 to 10) of five different essays. The ratings for each
essay are shown in the table below:
Essay
1
Student
0
Professor
1
Expert
2
21
Chapter 15
Test Items
2
3
4
5
2
1
5
2
5
2
4
8
5
6
9
8
How well do these raters agree, as measured by the intraclass correlation (ICC)?
a) .38 b) .57
c) .76
d) .95
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