Kruskal-Wallis Test for k=4: na= nb= nc= nd=

The logic and computational details of the Kruskal-Wallis test
are described in Subchapter 14a of Concepts and Applications.
In order to apply the Kruskal-Wallis test, the raw data from samples A, B, C, and D must first be combined into a set of N=na+nb+nc+nd elements, which are then ranked from lowest to highest, including tied rank values where appropriate. After all N items have been ranked, these rankings are then re-sorted into the three separate samples.

If your data have already been ranked, these ranks can be entered directly into the cells headed by the label "Ranks." In this case, please note that the sum of all ranks for samples A, B, and C combined must be equal to [N(N+1)]/2. If this equality is not satisfied, you will receive a message asking you to examine your data entry for errors.

If your data have not yet been rank-ordered in this fashion, they can be entered into the cells labeled "Raw Data" and the ranking will be performed automatically.

After data have been entered, click one or the other of the «Calculate» buttons according to whether you are starting out with ranks or raw data.


Data EntryT
 Ranks for Sample 
 		 Raw Data for Sample 
 count 
 		A
 		B
 		C
 		D
 		A
 		B
 		C
 		D



 Mean Ranks for Sample 
A
 		B
 		C
 		D
H =
df =
P =
*
*If the size of each of your samples is at least 5, the sampling distribution of H can be taken as a reasonably close approximation of the sampling distribution of chi-square with df = k—1. If any of your samples are of a size smaller than 5, you should regard the calculated P-value as an imperfect approximation.


















































































Disregard these cells.
They are merely place holders.