obg.cuhk.edu.hk 1 October 2016
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Kruskall-Wallis One Way Analysis of Variance

How: Place the number of rows (groups) in the contingency table in the first text box, the number of columns (ordinal values) in the next.   Place the frequency table into the large text box.   Each columns must be separated by a white space (blank or tab).  The data can be typed in, or the cells from an excel file may be copied and pasted into the box.  Click the Do Kruskall Wallis button, and the results will show.
Number of rows
Number of columns
Data must be in the correct number of columns separated by white spaces (space or tab) and all element of the matrix must be filled, otherwise the calculation will be in error.

If the row count differs from the stated number of rows then the lower number will be used.

Numbers can be typed in, but a convenient way is to use excel and paste the data into the text box.

Reference: Siegal S, Castellan Jr. N.J. (1988) Nonparametric statistics for the Behavioral Sciences 2nd. Ed. ISBN 0-07-057357-3 0. McGraw Hill Book Company New york P206-212. Minimum mean Rank differences: ditto p. 213-215

Dunn's Test:Description: Zar Z.H. (1974) Biostatistical analysis (3rd.Ed) Prentice Hall, New Jersey. ISBN 0-13-084542-6. p227,228. Table for Q values App. 106

Dunn O.J. (1964) Multiple contrasts using rank sums. Technometrics 6:241:252

Explanation: This performs the nonparametric Kruskall Wallis One Way Analysis of variance, comparing multiple groups with ordinal data, using a frequency table as the input.   The data is a matrix, where each row represents the data in a group, and each column an ordinal value.   The number in the cell therefore represents the number of cases in that group with that value.

Example: Let say we compare children from 3 schools (3 rows) in their liking for their teachers in a scale of 0 to 3 (4 cols).   From school A 10 children scored 0, 15 scored 1, 20 scored 2, and 20 scored 3.   From school B 20 each scored for each value.   From school C 20 scored 0, 10 scored 1, 10 scored 2, and 10 scored 3.   The data are in the following 3 rows: 10 15 20 20, 20 20 20 20, and 20 10 10 10.  From this the following results are generated.  


Grp1 n=65 Mean Rank=110.3077
Grp2 n=80 Mean Rank=97.3750
Grp3 n=50 Mean Rank=83.0000

Kruskal-Wallis H=7.0782 df=2 p=0.0290

Minimum significant diff in rank (Siegal and Castellan)

grp grp Diff Dif(0.05) Dif(0.01) Dif(0.001)
0 1 12.93 15.55 21.96 29.31
0 2 27.31 17.52 24.74 33.02
1 2 14.38 16.79 23.71 31.64

Minimum Significant diff in rank (minimum Q by Dunn)

grp grp Q Q(0.05) Q(0.01) Q(0.001)
0 1 2.12 2.39 2.94 3.59
0 2 3.53 2.39 2.94 3.59
1 2 1.46 2.39 2.94 3.59

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