Stat 461 Homework #5 | Complete Solution

Stat 461 Spring 2015 Homework #5

In this homework, we will use statistical software to perform one-way ANOVA and residual analysis for two data sets. The data is provided in Angel.
1. 40 points There are six treatments, each with n = 15 observations, and the runs were performed in completely random order.
(a) Produce side-by-side box plots of the original data. Do the treatments appear to have equal variances?
(b) Perform a formal test for equality of variances.
(c) Do you think a transformation is necessary?
(d) Perform a one way ANOVA using the original data. Comment on the residual plots. Are the one-way ANOVA assumptions met?
(e) Apply a Box-Cox transformation to the data. What is the optimal returned by software? Provide an interpretation of this .
2. 60 points There are four treatments, each with n = 10 observations, and the runs were performed in completely random order.
(a) Produce side-by-side box plots of the original data. Do the treatments
appear to have equal variances?
(b) Perform a formal test for equality of variances.
(c) Perform a one way ANOVA using the original data. Comment on the residual plots. Are the one-way ANOVA assumptions met?
(d) Apply a square root transformation to the response. Produce side-by-side box plots of the transformed data. Do the groups appear to have equal variances? Run a formal test for equality of variances.
(e) Now, run a one way ANOVA using the transformed data. Comment on the residual plots. Are the one-way ANOVA assumptions met?
(f) Finally, go back to the original data and perform a Box-Cox transforma- tion. What is the optimal returned by software?