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Chapter 16:
16.9 Given the aggression scores below for Outcome A of the sleep deprivation experiment, verify that, as suggested earlier, these mean differences shouldn’t be taken seriously by testing the null hypothesis at the .05 level of significance. Use the computation formulas for the various sums of squares and summarize results with an ANOVA table.
Hours of Sleep Deprivation
Zero
Twenty-Four
Forty-Eight
3
4
2
5
8
4
7
6
6
Group Mean:
5
6
4
Grand Mean: 5
Question:
Steps:
Calculations or Logic:
Answer:
Use the computation formulas for the various sums of squares and summarize results with an ANOVA table.
What is the research hypothesis?
What is the null hypothesis?
What are the degrees of freedom?
What is the calculated ?
What is the calculated ?
What is the calculated ?
What is the calculated ?
What is the calculated ?
What is the F?
Complete the ANOVA table:
Source
SS
df
MS
F Ratio
Treatment (between)
Error (within)
Total
16.10 Another psychologist conducts a sleep deprivation experiment. For reasons beyond his control, unequal numbers of subjects occupy the different groups. (Therefore, when calculating in SS between and SS within , you must adjust the denominator term, n , to reflect the unequal numbers of subjects in the group totals.)
Hours of Sleep Deprivation
Zero
Twenty-Four
Forty-Eight
1
4
7
3
7
12
6
5
10
2
9
1
Summarize the results with an ANOVA table. You need not do a step-by-step hypothesis test procedure:
Source
SS
df
MS
F
Treatment (between)
Error (within)
Total
If hand calculating, include formulas and calculations below. If using SPSS, include a picture, screenshot, or cut/paste of the output below.
Question:
Calculations or Logic:
Answer:
Are the results statistically significant? Yes or no?
If appropriate, estimate the effect size with η2
If appropriate, use Tukey’s HSD test (with for the sample size, n) to identify pairs of means that contribute to the significant F, given that, and
What is the HSD?
Which pairs are significant at the .05 level?
If appropriate, estimate effect sizes with Cohen’s d.
Indicate how all of the above results would be reported in the literature, given sample standard deviations of s0= 2.07, s24 =1.53, and s48=2.08.
16.12 For some experiment, imagine four possible outcomes, as described in the following ANOVA table.
A.
Source
SS
df
MS
F
Between
900
3
300
3
Within
8000
80
100
Total
8900
83
B.
Source
SS
df
MS
F
Between
1500
3
500
5
Within
8000
80
100
Total
9500
83
C.
Source
SS
df
MS
F
Between
300
3
100
1
Within
8000
80
100
Total
8300
83
D.
Source
SS
df
MS
F
Between
300
3
100
1
Within
400
4
100
Total
700
7
Question:
Calculations or Logic:
Answer:
How many groups are in Outcome D?
Assuming groups of equal size, what’s the size of each group in Out-come C?
Which outcome(s) would cause the null hypothesis to be rejected at the .05 level of significance?
Which outcome provides the least information about a possible treatment effect?
Which outcome would be the least likely to stimulate additional research?
Specify the approximate p -values for each of these outcomes.
A
B
C
D
16.14 The F test describes the ratio of two sources of variability: that for subjects treated differently and that for subjects treated similarly. Is there any sense in which the t test for two independent groups can be viewed likewise?
Question:
Answer:
Is there any sense in which the t test for two independent groups can be viewed likewise?
Chapter 17:
17.6 Return to the study first described in Question 16.5 on page 336, where a psychologist tests whether shy college students initiate more eye contacts with strangers because of training sessions in assertive behavior. Use the same data, but now assume that eight subjects, coded as A, B, . . . G, H, are tested repeatedly after zero, one, two, and three training sessions. (Incidentally, since the psychologist is interested in any learning or sequential effect, it would not make sense—indeed, it’s impossible, given the sequential nature of the independent variable—to counterbalance the four sessions.) The results are expressed as the observed number of eye contacts:
WORKSHOP SESSIONS
SUBJECT
ZERO
ONE
TWO
THREE
TSUBJECT
A
1
2
4
7
14
B
0
1
2
6
9
C
0
2
3
6
11
D
2
4
6
7
19
E
3
4
7
9
23
F
4
6
8
10
28
G
2
3
5
8
18
H
1
3
5
7
16
G=138
Summarize the results with an ANOVA table. Short-circuit computational work by using the results in Question 16.5 for the SS terms, that is, SSbetween=154.12, SSwithin =132.75, and SStotal =286.87.
Source
SS
df
MS
F
Between
Within
Subject
Error
Total
If hand calculating, include formulas and calculations below. If using SPSS, include a picture, screenshot, or cut/paste of the output below.
Question:
Calculations or Logic:
Answer:
Are the results statistically significant? Yes or no?
If appropriate, estimate the effect size with η2
If appropriate, use Tukey’s HSD test.
What is the HSD?
Which pairs are significant at the .05 level?
If appropriate, estimate effect sizes with Cohen’s d.
Compare these results with repeated measures with those in Question 16.5 for independent samples.
17.7 Recall the experiment described in Review Question 16.11 on page 314, where errors on a driving simulator were obtained for subjects whose orange juice had been laced with controlled amounts of vodka. Now assume that repeated measures are taken across all five conditions for each of five subjects. (Assume that no lingering effects occur because sufficient time elapses between successive tests, and no order bias appears because the orders of the fi ve conditions are equalized across the five subjects.)
DRIVING ERRORS AS A FUNCTION OF ALCOHOL CONSUMPTION (OUNCES)
SUBJECT
ZERO
ONE
TWO
FOUR
SIX
TSUBJECT
A
1
4
6
15
20
46
B
1
3
1
6
25
36
C
3
1
2
9
10
25
D
6
7
10
17
10
50
E
4
5
7
9
9
34
T 15
20
26
56
74
Summarize the results in an ANOVA table. If you did Review Question 16.11 and saved your results, you can use the known values for SSbetween , SSwithin , and SStotal to short-circuit computations.
Source
SS
df
MS
F
Between
Within
Subject
Error
Total
If hand calculating, include formulas and calculations below. If using SPSS, include a picture, screenshot, or cut/paste of the output below.
Question:
Calculations or Logic:
Answer:
Are the results statistically significant? Yes or no?
If appropriate, estimate the effect size with η2
If appropriate, use Tukey’s HSD test.
What is the HSD?
Which pairs are significant at the .05 level?
If appropriate, estimate effect sizes with Cohen’s d.
Compare these results with repeated measures with those in Question 16.5 for independent samples.
17.8 While analyzing data, an investigator treats each score as if it were contributed by a different subject even though, in fact, scores were repeated measures.
Question:
Answer:
What effect, if any, would this mistake probably have on the F test if the null hypothesis were:
True?
False?
Chapter 18:
18.8 For the two-factor experiment described in the previous question, assume that, as shown, mean bar press rates of either 4 or 8 are identified with three of the four cells in the 2 X 2 table of outcomes.
Food Deprivation (Hours)
0
24
Reward Amount (Pellets)
1
8
2
4
8
Furthermore, just for the sake of this question, ignore sampling variability and assume that effects occur whenever any numerical differences correspond to either food deprivation, reward amount, or the interaction.
Question:
Answer?
Indicate whether or not effects occur for each of these three components if the empty cell in the 2 X 2 table is occupied by a mean of :
12
Which main effects are significant?
Is the interaction significant? (yes or no)
8
Which main effects are significant?
Is the interaction significant? (yes or no)
4
Which main effects are significant?
Is the interaction significant? (yes or no)
18.11 In what sense does a two-factor ANOVA use observations more efficiently than a one-factor ANOVA does?
Question:
Answer:
In what sense does a two-factor ANOVA use observations more efficiently than a one-factor ANOVA does?
18.12 A psychologist employs a two-factor experiment to study the combined effect of sleep deprivation and alcohol consumption on the performance of automobile drivers. Before the driving test, the subjects go without sleep for various time periods and then drink a glass of orange juice laced with controlled amounts of vodka. Their performance is measured by the number of errors made on a driving simulator. Two subjects are randomly assigned to each cell, that is, each possible combination of sleep deprivation (either 0, 24, 48, or 72 hours) and alcohol consumption (either 0, 1, 2, or 3 ounces), yielding the following results:
NUMBER OF DRIVING ERRORS
ALCOHOL CONSUMPTION (OUNCES)
SLEEP DEPRIVATION (HOURS)
0
24
48
72
Trow
0
0
2
5
5
29
841
3
4
4
6
1
1
3
6
5
36
1296
3
3
7
8
2
3
2
8
7
53
2809
5
5
11
12
3
4
4
10
9
68
4624
6
7
13
15
=1466
Tcolumn
25
30
64
67
G=186
625
900
4096
4489
G2=34596
Summarize the results with an ANOVA table.
Source
SS
df
MS
F
Column
Row
Interaction
Within
Total
If hand calculating, include formulas and calculations below. If using SPSS, include a picture, screenshot, or cut/paste of the output below.
Question:
Calculations or Logic:
Answer:
Which results are statistically significant?
If appropriate, conduct additional F tests.
If appropriate, estimate the effect size with η2
Column
Row
Interaction
If appropriate, use Tukey’s HSD test.
What is the HSD?
Which pairs are significant at the .05 level?
If appropriate, estimate effect sizes with Cohen’s d.
