## Friedman Rank Sum Test

#### Data

Hollander & Wolfe (1973), p. 140ff.

Comparison of three methods ("round out", "narrow angle", and

"wide angle") for rounding first base. For each of 18 players

and the three method, the average time of two runs from a point on

the first base line 35ft from home plate to a point 15ft short of

second base is recorded.

#### Analysis

- Open the DataBook
*RoundingTimes.vstz* - Choose the menu
**Analyze**and the command**Friedman** - In
**Variables**, select*average*. - In
**Grouping Variables**, select*methods*. - In
**Blocking Variables**, select*players*. - Click
**OK**

#### Output

By default, R code is printed after parsing and before
evaluation.

You can avoid this in **File / Option / Advanced**
menu.

DataSheet is converted to DataFrame, in the form *
DataBook.DataSheet*

> friedman.test(RoundingTimes.RoundingTimes$average, RoundingTimes.RoundingTimes$methods, RoundingTimes.RoundingTimes$players) Friedman rank sum test data: RoundingTimes.RoundingTimes$average, RoundingTimes.RoundingTimes$methods and RoundingTimes.RoundingTimes$players Friedman chi-squared = 11.1429, df = 2, p-value = 0.003805

#### Using Script

- Open the Script File RoundingTimes
- Choose the menu
**Standard**and the command**Run**

#### Output

> ## Hollander & Wolfe (1973), p. 140ff.

> ## Comparison of three methods ("round out", "narrow angle", and

> ## "wide angle") for rounding first bas .... [TRUNCATED]

> friedman.test(RoundingTimes)

Friedman rank sum test

data: RoundingTimes

Friedman chi-squared = 11.1429, df = 2, p-value = 0.003805

> ## => strong evidence against the null that the methods are
equivalent

> ## with respect to speed

>

> wb <- aggregate(warpbreaks$breaks,

+ .... [TRUNCATED]

> wb

w t x

1 A L 44.55556

2 B L 28.22222

3 A M 24.00000

4 B M 28.77778

5 A H 24.55556

6 B H 18.77778

> friedman.test(wb$x, wb$w, wb$t)

Friedman rank sum test

data: wb$x, wb$w and wb$t

Friedman chi-squared = 0.3333, df = 1, p-value = 0.5637

> friedman.test(x ~ w | t, data = wb)

Friedman rank sum test

data: x and w and t

Friedman chi-squared = 0.3333, df = 1, p-value = 0.5637