Kruskal-Wallis Test for k=3
With na= With nb= nc=

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, and C must first be combined into a set of N=na+nb+nc 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.

Option for Importing Raw Data via Copy & Paste:T
Within the spreadsheet application or other source of your data, select and copy the column of data for sample A. Then return to your web browser, click the cursor into the text area for sample A and perform the 'Paste' operation from the 'Edit' menu. Perform the same procedure for samples B and C. When importing raw data into the Kruskal-Wallis test, it is essential that the numbers of data items for samples A, B, and C are precisely the same as the values of na, nb, and nc that you have specified in setting up this page. For each sample, make sure that the final entry in the list is not followed by a carriage return. To perform this check, click the cursor immediately to the right of the final entry in the list, then press the down-arrow key. If an extra line is present, the cursor will move downward. Extra lines can be removed by pressing the down-arrow key until the cursor no longer moves, and then pressing the 'Backspace' key (on a Mac platform, 'delete') until the cursor stands immediately to the right of the final entry.T

Import Raw DataT
Sample A Sample B Sample C Import data
to data cells

Clear All

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

 Mean Ranks for Sample 
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 = k1. If any of your samples are of a size smaller than 5, you should regard the calculated P-value as an imperfect approximation.

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©Richard Lowry 2001-
All rights reserved.

Disregard these cells.
They are merely place holders.