Problem Sets in ANOVA Essay

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16 -- (3 -- 1)(47.09)]/(1264.92+47.09) = 557.98/1312.01 = 0.425 = 42.5%

This finding suggests that 42.5% of the variability in performance accuracy is associated with the levels of background noise.

Question 4

In an experiment, you measure the popularity of two brands of soft drinks (factor A) and for each brand you test males and females (factor B). The following table shows the main effect and cell means from the study:

Factor A

Level A1:

Brand X

Level A2:

Brand Y

Factor B

Level B1:

Males

14

23

Level B2:

Females

25

12

A. Describe the graph of the interaction when factor A is on the X axis.

Using a line plot with factor A on the X axis, the line for males has an upward slope from brand X to brand Y, while the line representing females has a downward slope.

B. Does there appear to be an interaction effect? Why?

Yes. The independent variables are brand and gender, and the dependent variable is brand popularity. Based on the means, both brand and gender influence brand popularity.

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C. What are the main effect means and thus the main effect of changing brands?

The main effect of brand (factor A) on brand popularity was revealed by the male means 14 and 23 for brand X and Y, respectively. There was also a main effect of brand on brand popularity for women, with means of 25 and 12 for brands X and Y respectively.

D. What are the main effect means and thus the main effect of changing gender?

The main effect of gender (factor B) on brand popularity was revealed by the brand X means 14 and 25 for males and females, respectively. The main effect of gender was also revealed by the brand Y means 23 and 12 for males and females, respectively.

E. Why will a significant interaction prohibit you from making conclusions based on the main effects?

A significant interaction does not provide any information about the magnitude of the main effects, which could vary from a few percent to over 90%. Therefore, the main effect could be weak and not.....

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