Post Hoc Paired Comparisons after Kruskal-Wallis

 

Groups are equal in size

 

N = the number of cases in each sample group.

 

From the SPSS output for K-W, identify the Mean Rank for each group.

Multiply each mean rank by the N for that group to get the Rank Total for each group.

 

Now, for any paired comparison of interest between two groups, calculate

d = rank total of one group rank total of the other

 

Next calculate K = d - 0.8

N x √N

 

Now look up K on this table. If K is equal to or greater than the table value, the difference is significant

 

 

 

 

Total number of groups in the analysis

When comparing any groups with each other in pairs

When comparing several groups with a control group but not with each other

If K is equal to or greater than the table value, then the difference is significant at the level indicated by p

p = 0.05

p = 0.01

p = 0.05

p = 0.01

3

2.89

3.60

2.72

3.45

4

4.22

5.12

3.86

4.80

5

5.60

6.69

5.00

6.16

6

7.01

8.30

6.17

7.53

7

8.46

9.92

7.37

8.94

8

9.94

11.58

8.55

10.33

9

11.43

13.25

9.77

11.77

10

12.97

14.95

11.01

13.19

Table adapted from R.Langley Practical Statistics Simply Explained Pan Books 1979 p220

 

Groups are not equal in size

 

One option is to run Oneway ANOVA in SPSS and use one of the Post Hoc options that caters for unequal variances, such as Tamhane.

 

Or one could use the Mann-Whitney test on each pair of groups and adjust the p value with the Bonferroni method, but that is rather overcautious and one might miss a sig result.

 

By the way, for k groups, the total number of possible paired comparisons = (k x (k-1)) / 2.