3. Two-factor analysis of variance Emphasis on calculations Aa Aa W. Thomas Boyc

Question

3. Two-factor analysis of variance Emphasis on calculations Aa Aa W. Thomas Boyce, a professor and pediatridan at the University of British Columbia, Vancouver, has studied interactions between individual differences in physiology and differences in experience in determining health and well-being. Dr. Boyce fou that some children are more sensitive to their environments. They do exceptionally well when the environment is supportive b are much more likely to have mental and physical health problems when the environment has challenges. You decide to do a similar study, conducting a factorial experiment to test the effectiveness of one environmental factor and om physiological factor on a physical health outcome. As the environmental factor, you choose two levels of stress. As the physiological factor, you choose three levels of cardiovascular reactivity. The outcome is number of injuries in the previous 12 months, and the research participants are rhesus monkeys. You conduct a two-factor ANOVA on the data. The two-factor ANovA involves several hypothesis tests. Which of the following are null hypotheses that you could use this ANOvA to test? Check all that apply. D Stress has no effect on number of injuries. Cardiovascular reactivity has no effect on number of injuries. The effect of stress on number of injuries is no different from the enect of cardiovasoular reactivity. There is no interaction between stress and cardiovascular reactivity. The results of your study are summarized by the corresponding sample means below. Each cell reports the average number of injuries for 9 rhesus monkeys. Factor B: Cardiovascular Reactivity High M as 3.22 2.44 M 2.22 T 29 20 71 SS 1.5556 2.2222 1.5556 Factor A1 a 415 Mai 2.89 M 2,78 High T 26 T 25 Teow2 76 SS 1.5556 1.5556 Too is 55 Tou 47 Toou3 45 You perform an ANovA to test that there are no main effects of factor A, no main effects of factor B, and no interaction between factors A and B. Some of the results are presented in the following ANOVA table.

Explanation / Answer

Result:

ANOVA table

Source

SS

df

MS

F

Between treatments

5.5000

5

FactorA

0.4630

1

0.4630

2.38

Factor B

3.1112

2

1.5556

8.00

Interaction

1.9257

2

0.9629

4.95

within

9.3333

48

0.1944

Total

14.8333

53

Critical F(1,48) =7.19

Critical F(2,48) =5.077

The main effect due to factor A is not significant, the main effect due to factor B is significant. the interaction between the two factors is not significant.

ANOVA table

Source

SS

df

MS

F

Between treatments

5.5000

5

FactorA

0.4630

1

0.4630

2.38

Factor B

3.1112

2

1.5556

8.00

Interaction

1.9257

2

0.9629

4.95

within

9.3333

48

0.1944

Total

14.8333

53

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