W. Thomas Boyce, a professor and pediatrician 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 found that some children are more sensitive to their environments. They do exceptionally well when the environment is supportive but 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 one physiological factor on a physical health outcome. As the environmental factor, you choose two levels of oral hygiene. As the physiological factor, you choose three levels of cortisol value. The outcome is number of cavities, and the research participants are kindergartners. 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. Cortisol value has no effect on number of cavities.

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2. Two-factor ANOVA - Emphasis on calculations
W. Thomas Boyce, a professor and pediatrician 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 found that some children are more sensitive to their
environments. They do exceptionally well when the environment is supportive but 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 one physiological factor
on a physical health outcome. As the environmental factor, you choose two levels of oral hygiene. As the physiological factor, you choose three levels
of cortisol value. The outcome is number of cavities, and the research participants are kindergartners.
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.
O Cortisol value has no effect on number of cavities.
There is no interaction between oral hygiene and cortisol value.
O The effect of oral hygiene on number of cavities is no different from the effect of cortisol value.
O Oral hygiene has no effect on number of cavities.
The results of your study are summarized by the corresponding sample means below. Each cell reports the average number of cavities for 5
kindergartners.
Transcribed Image Text:2. Two-factor ANOVA - Emphasis on calculations W. Thomas Boyce, a professor and pediatrician 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 found that some children are more sensitive to their environments. They do exceptionally well when the environment is supportive but 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 one physiological factor on a physical health outcome. As the environmental factor, you choose two levels of oral hygiene. As the physiological factor, you choose three levels of cortisol value. The outcome is number of cavities, and the research participants are kindergartners. 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. O Cortisol value has no effect on number of cavities. There is no interaction between oral hygiene and cortisol value. O The effect of oral hygiene on number of cavities is no different from the effect of cortisol value. O Oral hygiene has no effect on number of cavities. The results of your study are summarized by the corresponding sample means below. Each cell reports the average number of cavities for 5 kindergartners.
The results of your study are summarized by the corresponding sample means below. Each cell reports the average number of cavities for 5
kindergartners.
Factor A: Oral Hygiene
Low
High
Factor B: Cortisol Value
Low
Medium
M = 2.20
M = 2.60
T = 11
T = 13
SS = 0.8
SS = 1.2
M = 1.40
T = 7
SS = 1.2
TCOL1 = 18
M = 1.80
T = 9
SS = 0.8
TCOL2 = 22
High
M = 1.80
T = 9
SS = 0.8
M = 1.20
T = 6
SS = 0.8
TCOL3 = 15
TROW1 = 33
TROW2 = 22
ΣΧ2 = 113
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.
Transcribed Image Text:The results of your study are summarized by the corresponding sample means below. Each cell reports the average number of cavities for 5 kindergartners. Factor A: Oral Hygiene Low High Factor B: Cortisol Value Low Medium M = 2.20 M = 2.60 T = 11 T = 13 SS = 0.8 SS = 1.2 M = 1.40 T = 7 SS = 1.2 TCOL1 = 18 M = 1.80 T = 9 SS = 0.8 TCOL2 = 22 High M = 1.80 T = 9 SS = 0.8 M = 1.20 T = 6 SS = 0.8 TCOL3 = 15 TROW1 = 33 TROW2 = 22 ΣΧ2 = 113 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.
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