Software to Simplify Statistical Practice ...

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

  1. Open the DataBook RoundingTimes.vstz
  2. Choose the menu Analyze and the command Friedman
  3. In Variables, select average.
  4. In Grouping Variables, select methods.
  5. In Blocking Variables, select players.
  6. 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

  1. Open the Script File RoundingTimes
  2. 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