Yes you may proceed. there is no problem in applying Kruskal wallis for unequal size group.

For better understanding you may find this reference where they have given such example:

http://vassarstats.net/textbook/ch14a.html

I hope this will help you.

Dear Srikanth

You can use Kruskal-Wallis test with three (or more) independent groups , equal or unequal sample size in the groups.

Good Luck

Hello

Definitely Yes. The Kruskal Wallis test can be used under the circumstances:

• Sometimes you may wish to know whether the means of three or more different sets of scores are significantly different from each other but feel that the requirement that the scores on each variable are roughly normally distributed (bell-shaped) is not fulfilled. Non-parametric tests can be used in these circumstances.
• Non-parametric tests are ones which make fewer assumptions about the characteristics of the population from which the data came. This is unlike parametric tests (such as the t-test) that make fairly stringent assumptions about the distribution of the population from which the data came. The assumption of normality (bell-shaped frequency curves) is an example of the sort of assumptions incorporated into parametric statistics.
• Very few sets of data would meet the requirements of parametric testing exactly. However, some variation makes little difference. The problem is knowing just how much the assumptions of parametric tests can be violated without it having a major impact on the outcome of the study.
• Strictly speaking, non-parametric statistics do not test for differences in means. They cannot, since, for example, they use scores turned into ranks. Usually they test whether the ranks in one group are typically larger or smaller than the ranks in the other groups.
• We have included the Friedman test for related data. In other words, it is the non-parametric equivalent to the related ANOVA.
• The Kruskal–Wallis test is used for unrelated data. That is, it is the nonparametric equivalent to the unrelated ANOVA.
• For more information, please refer to:

. Landau, S. and Everitt, B. S.(2004). A Handbook of Statistical analyses using SPSS.

. Howitt, D. and Cramer, D.(2008). Introduction to SPSS.

Regards,

Zuhair

I am comparing multi-group dependent measurements, which can not be assumed to have normal distribution and equal variance. So, I chose to do friedman test. But, the sample size in different groups are not equal. Can I still use friedman test? Or I can use Kruskal–Wallis instead.

Thank you.

Baoqiang

Dear Baoqiang Li ,

In the case of dependent (paired) you should use Friedman, otherwise (independent/un-paired) then use Kruskal-Wallis.

Thank you Edgar.

Your group sizes are so big that you can assume normal distributions.

There may be serious issues with the use of KW test with unbalanced data.

See https://arxiv.org/pdf/1802.05650.pdf

and

Brunner, E., Bathke, A.C., and Konietschke, F. (2018). Rank- and Pseudo-Rank Procedures for Independent Observations in Factorial Designs - Using R and SAS. Springer

The Kruskal-Wallis H Test is the non-parametric alternative to a parametric one-way between groups analysis of variance for independent groups. As your group sizes are big you can use parametric tests.