5% MINDTAP From Cengage Week 11 Homework Due on Nov 20 at 3 AM BRST 11. Two-fact

Question

5% MINDTAP From Cengage Week 11 Homework Due on Nov 20 at 3 AM BRST 11. Two-factor analysis of varlance-Emphasis on calculations W. Thomas Boyce, a professer 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 sensitve 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 envirenment has challenges. You decide to do a simlar 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 cutcome 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 hypotheses that you could use this ANOVA to test? Oeck all that apply Cortisol value has no effect on mmber of cavities. There is no interaction between oral hygiene and cortisol value. Oral hyglene has no effect on number of cavit es. The emect or oral hygiene on number ofcrites is no dfferent from the effect or cortisol value. The results of your study are summarized by the corresponding sample means below. Each cell reports the average number of cavites for 5 kindergartners Factor B: Cortisol Value Low MediumHigh M-2.20M 2.60 M -1.80 T-13 SS-0.8SS 12 S5-0.8 Low T-11 T-9 Tows-33 Ex 113 Factor A Oral Hyglene M-1.40 M 1.80 M-1.20 T-9 SS- 1.2SS Q8 SS-0.8 High T- COLs-18 Tco-22 Tc-15 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. ANOVA Table sS 6.5667 Between treatments 6 Factor A 4.0333 17.29 1.2334 5.29 Within treatments 12.1667 Work through the folowing steps to complete the preceding ANOVA table. . The main efflect for factor A evalustes the mean differences between the levels of factor A. The main effect for factor B evaluates the mean differences betvween the levels of factor B. Select the correct values for the sums of squares for factors A and 8 in the ANOVA table

Explanation / Answer

NULL HYPOTHESIS: THE EFFECT OF ORAL HYGIENE IS NO DIIFERENT FROM THE EFFECT OF CORTISOL VALUE.

p=2, q=3 and m=5

SOURCE S.S D.F M.S F Factor A 4.0333 1 4.0333 17.29 Factor B 2.4668 2 1.2334 5.29 AB interaction 0.0667 2 0.03335 0.1429 Within treatment 5.5999 24 0.2333 Total 12.1667 29

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