5. When to use a second factor Aa Aa Dr. Diane Gold and her colleagues study how
ID: 3230565 • Letter: 5
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 moming; 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 cel) 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 B: Shift Rotation Factor A: Day/Night/ Circadian Evening Day/Evening Evening/Night Night/Day Type M- 1.67 Mark 0.71 M 0,33 M 0.50 M 0.33 Lark M 1.17 M,summingbird 0.50 M 0.50 Hummingbird M 0.17 M 0.50 Mowl 0.63 Owl M 1.33 M 0,50 M m 0.17 MEN 0.39 Mrvo 0.33 MONE 1.11 Move 0.61 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. MS SS Source Between treatments 16.4471 11 0.5278 2 0.2639 0.70 Factor A 3 2.2592 5.98 Factor B A x B interaction 9.1416 6 1.5236 4.03 Within treatments 22.6640 60 0.3777Explanation / Answer
p-value for main effect of A= FDIST(0.70,2,60)= 0.5006
p-value for main effect of B= FDIST(5.98,3,60)= 0.0012
p-value for interaction effect of AXB= FDIST(4.03,6,60)= 0.0019
So main effect of B and interaction effect are significant while main effect of A is not significant at 5% level of significance.
. The main effect due to factor A (Circadian Type) is not significant
. The main effect due to factor B (Shift rotation ) is significant
The interaction effect due to two factors is significant.
As interaction effect is significant, so we should include factor A also in the ANOVA and hence answer is as follows:
No, you should include circadian type as a second factor, because there is main effect for A (circadian type) and/or an interaction effect, meaning thereby that including the circadian type will reduce variance caused by individual differences.
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