Question

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, The effect of oral hygiene on number of cavities is no different from the effect of cortisol value. Oral hygiene has no effect on number of cavities. There is no interaction between oral hygiene and cortisol value. The results of your study are summarized by the corresponding sample means below. Each cell reports the aver cavities for 8 kindergartners. number of Factor B: Cortisol Value Medium High Low Low M = 4.13 T-33 SS 0.875 M-3.25 T = 26 SS - 1.500 M3.13 T = 25 SS - 0.875 TROW - 84 2X2 = 630 Factor A: Oral Hygiene High M = 3.50 T= 28 SS = 2.000 M = 3.63 T-29 SS = 1.875 M = 3.88 T-31 SS - 0.875 Trow = 88 Tcou - 61 Tcou - 55 Trou - 56 ction between You perform an ANOVA to test that there are no main effects of factor A, no main effects of factor B, and no inte factors A and B. Some of the results are presented in the following ANOVA table. ANOVA Table SS 5.6667 MS F df 5 Source Between treatments Factor A Factor AXB interaction Within treatments Total 0.3333 0.6459 1.75 3.39 4.0417 13.6667 47 Work through the following steps to complete the preceding ANOVA table. 1. The main effect for factor A evaluates the mean differences between the levels of factor A. The main effect for factor B Rest of the Question is on next page

Answer 1

Option A, C and D

Source	SS	df	MS	F	p-value
Between treatments	5.666667	5
Factor A	0.333333	1	0.333333	1.75	0.193034
Factor B	1.291667	2	0.645833	3.390625	0.043144
A-B	4.041667	2	2.020833	10.60937	0.000186
Within treatments	8	42	0.190476
Total	13.66667	47

not significant, significant, significant