# Two factor ANOVA, mean difference, F ratio, sample variances

Please do the 4 questions that are circled. Please show each calculation step and give a conclusion.

16. The structure of a two-factor study can be presented as matrix with the levels of one factor determining the rows and the levels of the second factor determining the columns. With this structure in mind, describe the mean differences that are evaluated by each of the three hypothesis tests that make up a two-factor ANOVA.

18. For the data in the following matrix:

no treatment treatment overall m=4

male m=5 m=3

female m=9 m=13 overall m=11

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overall m=7 overall m=8

a) describe the mean difference that is the main effect for the treatment.

b) describe the mean difference that is the main effect for gender.

c) Is there an interaction between gender and treatment?

10. For the preceding problem, you should find that there are significant differences among the three treatments. One reason for the significance is that ...

8. For the preceding problem, you should find that there are significant differences among the three treatments. The primary reason ...

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#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided in the attached file.