The Treatment Effects Performing a One Way ANOVA Table Analysis

You have to use R 1) Write down the model equation of the one-way ANOVA model that is described by this set-up.  Be sure to clearly identify each parameter and variable in terms of the problem.  Also identify the ni and t.

2) To the extent possible from the data given and the experimental set-up, check that the four assumptions for performing a one-way ANOVA hold, including using Levene’s test.

For 3-6 you may assume the assumptions you checked in two were found to hold.

3) What hypothesis is being tested by the F-statistic in the ANOVA table?  Carefully state your conclusion in terms of the problem at the ?=0.05 level.

4) The output using the summary function gives baseline mean (calling it the Intercept) and then estimates for five of the treatment effects relative to that.  Which of the facial expressions has its mean being used as the baseline?

5) Consider the five p-values for testing that the treatment effects are equal to zero, and testing them at the family-wise alpha=0.05 level using the Bonferroni inequality. Which of the expressions would be found to have a significant treatment effect?

6) Consider the five p-values for testing that the treatment effects are equal to zero, and testing them at the family-wise alpha=0.05 level using the Holm procedure. Which of the expressions would be found to have a significant treatment effect?

The simulated data set at:

https://people.stat.sc.edu/habing/courses/data/personality.txt

is based on an experiment reported in the Journal of Nonverbal Behavior (Fall 1996). A sample of 36 introductory psychology students was randomly divided into six groups. Each was asked to view one of six slides showing a person making either an angry, disgusted, fearful, happy, sad, or neutral face. After viewing the slides the students rated the degree of dominance that they inferred from the facial expression (a higher score indicating more dominance).