Question

Aa Aa 11. 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 wel when the environment is suppo「tive 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 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 The effect of stress on number of injuries is no different from the effect of cardiovascular reactivity X There is no interaction between stress and cardiovascular reactivity Cardiovascular reactivity has no effect on number of injuries. Stress has no effect on number of injuries. The results of your study are summarized by the corresponding sample means below. Each cell reports the average number of injuries for 5 rhesus monkeys. Factor B: Cardiovascular Reactivity Medium High Low M 2.60 T 13 SS 1.2 M- 1.80 M 2.20 T 11 SS0.8 Low TROW133 SS0.8 EX2 113 Factor A: Stress M 1.20 M 1.40 M 1.80 High ROW2 22 SS 1.2 SS 0.8 SS 0.8 TcoL1 18 TcoL2 22 TCoL3 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 Source df MS Between treatments 6.5667 4.0333 2.4667 0.0667 5.6000 12.1667 5 Factor A Factor B A X B interaction 4.0333 1.2334 0.0334 0.2333 17.29 5.29 0.14 2 24 29 Within treatments Total Work through the following steps to complete the preceding ANOVA table 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 evaluates the mean differences between the levels of factor B. Select the correct values for the sums of squares for factors A and B in the ANOVA table. 2. Select the correct value for the within-treatments sum of squares in the ANOVA table 3. Select the correct degrees of freedom for all the sums of squares in the ANOVA table. 4. Select the correct values for the mean square due to A X B interaction, the within treatments mean square, and the F-ratio for the A X B interaction 5. Use the results from the completed ANOVA table and the F distribution table (click on the following dropdown menu to access the table) to make the following conclusions The F Distribution Table entries in lightface type are critical values for the.05 level of significance. Boldface type values are for the.01 level of significance At the significance level α-.05, the main effect due to factor A is the main effect due to factor B is , and the interaction effect between the two factors is

Answer 1

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