Why is there a 12 in the Kruskal-Wallis Formula?

Answer 1

The 12 in the Kruskal-Wallis formula arises from the need to scale the test statistic appropriately for the sample sizes involved. Specifically, it helps to normalize the sum of ranks used in the calculation, ensuring that the resulting test statistic follows a chi-squared distribution under the null hypothesis. This scaling factor accounts for the expected variance in the ranks, making the test more robust and allowing for proper statistical inference.