Question

5. When to use a second factor Aa Aa Dr. Diane Gold and her colleagues study how rotating shift work (switching back and forth between the night shift and the day shift, for example) contributes to disrupted sleep cycles, accidents, and nodding off at work. Suppose you are studying a group of police officers to see whether different circadian types are impacted differently by working particular rotations. Circadian types include larks, who are most active in the early morning; hummingbirds, who are active in the middle of the day; and owls, who are active late into the night. You administer a sleepiness test to 72 police officers (6 in each cell) each day for a month and use an average score across the month for each person as the indication of each person's typical sleepiness. The means of the scores are shown in the following table, where a higher score indicates more sleepiness Factor A: Circadian Type Factor B: Shift Rotation Day/Evening Evening/Night Night/Day M 0.33 M = 0.50 M 1.00 ME/N 0.61 Day/Night/ Evening M- 1.33 M 0.17 M 1.67 MD/N/E 1.06 Lark Hummingbird Owl M = 0.17 M 1.50 M 1.33 MD/E 1.00 M0.50 M 0.33 M 1.17 MN/D0.67 MLark 0.58 MHumminabird 0.63 Mow 1.29 You perform a two-factor analysis of variance to test for an interaction effect between circadian type and work shifts The following ANOVA summary table describes the results.

Answer 1

Identify whether the main effect due to factor A is significant or not. From the ANOVA table, the F value corresponding with factor A is 5.74, the df for factor A is 2 and the df for within treatments is 60 From F table, the critical value is 2,60,0.01 2,600498 Rejection rule: If test statistic is greater than the critical value, then reject the null hypothesis Conclusion: The test statistic is greater than the critical value. By the rejection rule, reject the null hypothesis. Therefore, the main effect due to factor A(Circadian Type) is significant. That is, F 5.74)> F 4.98)