## 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.

### Summary

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

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

### Comments

**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`

.

If R were consistent, these two analyses would have similar syntax, but it isn't and they don't.

**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.

### More Exact Computation

The contributed package `SuppDists`

contains a better
approximation to the distribution of the Friedman test statistic
under the null hypothesis. Here's how that works.

The `P`-value hardly changes, and in this example is so small
that the better calculation makes no difference. Either way the treatment
is highly statistically significant. But on different data,
the better calculation might be important.