2. One hypothesis test evaluates mean differences among the rows and a second test evaluates mean differences among the columns. The test for an interaction evaluates the significance of any mean differences that are not explained by row and/or column differences.
4. a. Lines are parallel with each other and the X-axis b. Lines are parallel to each other but go from lower left to upper right. c. Lines cross (disordinal) 6. a. df = 1, 36 b. df = 1, 36 c. df = 1, 36
8. a. the first factor is the type of study (massed versus distributed), and the second factor is the time of the test (immediate versus delayed). The researcher expects tht the difference between the two types of study depends on the timing of the test.
b. One factor is the type of program (violent versus non-violent) and the second factor is the type of character (human versus cartoon). The researcher is predicting that the difference between violent and nonviolent shows will depend on the type of character.
10. The null hypotheses state tht there is no difference between levels of factor A (Ho mu-quiet = mu-noisy), no difference between levels of factor B (mu-introvert = mu-extrovert), and no interaction. All F-ratios have df = 1, 16 and the critical value is F = 4.49
Source SS df MS
_______________________________________________________________________
Between Treatments 120 3
A (Distraction) 80 1 80 F(1,16) = 16
B (Personality) 20 1 20 F(1,16) = 4
A x B 20 1 10 F(1,16) = 4
Within Treatments 80 16 5
Total 200 19
Distraction has a significant effect on performance. These results do not provide sufficient evidence to conclude that personality affects performance or that personality interacts with distraction.
12. The null hypothesis states there is no difference between genders (Ho: mu-male = mu-female), that the amount of the chemical has no effect (Ho: mu-none = mu-small = mu-large), and that there is no interaction. For df = 1, 24, the critical value is F = 4.26. For df = 2, 24, the critical value is F = 3.40.
Source SS df MS
_______________________________________________________________________
Between Treatments 70 5
A 30 1 30 F(1,24) = 6
B 20 2 10 F(2,24) = 2
A x B 20 2 10 F(2,24) = 2
Within Treatments 120 24 5
Total 190 29
The results indicate that the males are significantly more active than the females. However, the data do not provide sufficient evidence to conclude that the chemical has a significant effect on activity or that the chemical has different effect on males than on females.
14. a. Parallel lines from top left to lower right
b. The lines are parallel so there does not appear to be any interaction. There is a small difference between the lines for A-1 and A-2 so there may be a small main effect for factor A. The difference between B-1 and B-2 is larger, so there probably is a main effect for Factor B.
c. The null hypotheses state that there is no difference between levels of factor A (Ho: mu-A-1 = mu-A-2), no difference between levels of factor B (Ho: mu-B-1 = mu-B-2), and no interaction. All F-ratios have df = 1,36 and the critical value is F = 4.11.
Source SS df MS
_______________________________________________________________________
Between Treatments 50 3
A 10 1 10 F(1,36) = 2
B 40 1 40 F(1,36) = 8
A x B 0 1 0 F(1,36) = 0
Within Treatments 180 36 5
Total 230 39
The main effect for Factor B is significant, but the A effect and the interaction are not.
16. a. The null hypotheses state that counseling has no effect (Ho: mu-yes = mu-no), the drug has no effect (Ho: mu-yes = mu-no), and there is no interaction. All F-ratios have df = 1,36 and the critical value is F = 4.11.
Source SS df MS
_______________________________________________________________________
Between Treatments 200 3
A (counseling) 0 1 0 F(1,36) = 0
B (drug) 160 1 160 F(1,36) = 32
A x B 40 1 40 F(1,36) = 8
Within Treatments 180 36 5
Total 380 39
b. The data indicate that overall the drug has a significant effect. The main effect for counseling is not significant. However, there is a significant interaction meaning that the effect of the drug is significantly affected by counseling. Without counseling the drug has a minimal effect but with counseling the drug has a big effect.
18. a. The treatment means are:
low medium high
easy 8.0 10.0 12.0
hard 6.0 10.0 8.0
b. The null hypotheses state that task difficulty has no effect (Ho: mu-easy = mu-hard), that arousal level has no effect (mu-low = mu-medium = mu-high), and that thee is no interaction. For df = 1,54, the critical value is F = 3.18 (using df = 50 for the denominator because 54 is not in the table).
Source SS df MS
_______________________________________________________________________
Between Treatments 220 5
A (difficulty) 60 1 60 F(1,54) = 15
B (arousal) 120 2 60 F(2,54) = 15
A x B 40 2 20 F(2,54) = 5
Within Treatments 216 54 4
Total 436 59
c. There is a significant main effect for task difficulty which simply indicates that performacne is better on easy tasks that on hard tasks.
d. For easy tasks, increased arousal increases performance until you reach a "high" level of arousal. For hard tasks, the optimum level of arousal is "medium." With higher arousal, performance on hard tasks deteriorates.
20. The null hypotheses state that self-esteem has no effect (Ho: mu-high = mu-low), the audience has no effect (Ho: mu-alone = mu-audience), and that there is no interaction. For df = 1,20, the critical value is F = 4.35.
Source SS df MS
_______________________________________________________________________
Between Treatments 216 3
A (self-esteem) 96 1 96 F(1,20) = 22.33
B (audience) 96 1 96 F(1,20) = 22.33
A x B 24 1 24 F(1,20) = 5.58
Within Treatments 86 20 4.3
Total 302 23
The significant interaction indicates that the effect of the audience was different for high self-esteem subjects that for low self-esteem subjects. Specifically, the audience produced an increase in errors for the low self-esteem and had little effect on high self-esteem.
22. The null hypotheses state that sleeping has no effect (Ho: mu-asleep - mu-awake), the test delay level has no effect (Ho: mu-2-hr = mu-8-hr), and that there is no interaction. For df = 1, 36, the critical value is F = 4.11.
Source SS df MS
_______________________________________________________________________
Between Treatments 200.48 3
A (asleep/awake) 172.23 1 172.23 F(1,36) = 73.92
B (delay time) 7.23 1 7.23 F(1,36) = 3.10
A x B 21.02 1 21.02 F(1,36) = 9.02
Within Treatments 83.90 36 2.33
Total 284.38 39
The significant interaction indicates that the amount you forget over
time (2 hours versus 8 hours) depends on whether you are asleep or awake.
For the asleep group, there was no evidence for forgetting over time and
the scores were generally high. For the awake group there was substantial
drop between 2 hours and 8 hours and the scores were generally low.