In a clinical study, after applying the clustering method, several classes are identified. We perform ANOVA or Kruskal Wallis for between-class comparison. The class has a different sample size (unequal). I hope that is fine. For a post hoc test, it has been suggested that effect sizes are better than the p-value. Can you please suggest what type of effect size is expected? If there is any other method, please let us know.
Effect sizes and hypothesis tests (p-values) convey entirely different information.
You should be reporting both p-values and effect size statistics, all the time, for both omnibus and post-hoc tests.
For Kruskal-Wallis, standardized effect size statistics include Freeman's theta and the epsilon-squared that is used for the K-W test.
For the post-hoc test, standardized effect size statistics include Glass rank biserial correlation coefficient and Vargha and Delaney's A.
There are also non-standardized effect size statistics. You can simply report e.g. the medians, and looking at the differences in medians counts as a non-standardized effect size statistic.
If you are opting for ANOVA, you need to calculate eta square. In case you have opted for the Kruskal-Wallis test, then you need to calculate Epislon's measure. I have a YouTube video on how to do this.
https://www.youtube.com/watch?v=_tuU5dU3oDc&t=25s
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