# Statistics 5601 (Geyer, Spring 2006) Examples: Two-Way Layout

## General Instructions

To do each example, just click the "Submit" button. You do not have to type in any R instructions or specify a dataset. That's already done for you.

## Friedman

### Example 7.1 in Hollander and Wolfe.

External Data Entry

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### Summary

• Friedman test for randomized complete block data
• P = 0.0038

• two-way ANOVA test for randomized complete block data
• P = 0.0041

Note: In the `friedman.test` function call the "groups" variable goes in front of the vertical bar and the "blocks" variable goes behind the vertical bar. We are looking for a "method" effect here so `method` goes in front of the bar.
The second analysis done by the `aov` function is the usual parametric procedure: two-way ANOVA. It produces P = 0.004084 for comparison with the Friedman P-value.
The first line tells R that `player` is to be treated as a factor, that is, as a non-numerical variable. If it were omitted, the ANOVA would be nonsense. For some reason `friedman.test` comes out the same if it is omitted.
We don't also have to tell R that `method` is a factor, because it automatically treats any non-numerical variable as a factor. If method had been designated by numerical codes, we would also need a statement like the first line for `method`.
Warning: Do not omit the lines converting the categorical variables to R `factor` objects. At least don't omit them unless you are sure it won't make a difference.