# #StackBounty: #hypothesis-testing #post-hoc #friedman-test How must the null hypothesis be rejected for Nemenyi test to be allowed?

### Bounty: 50

Suppose we have algorithms \$A_k\$ and \$B_k\$, \$1leq kleq n\$, and \$alpha = 0.05\$.

Friedman test for the algorithms \$A_k\$ shows that the null hypothesis that all \$A_k\$s perform equally well, can be rejected. Suppose \$p_A = 10^{-5}llalpha\$.

Friedman test for the algorithms \$B_k\$ shows that the null hypothesis that all \$B_k\$s perform equally well, cannot be rejected. Suppose \$p_B = 0.4\$.

My problem is that the \$p\$-value \$p_{AB}\$ from the Friedman test for \$A_k\$s and \$B_k\$s is greater than \$alpha\$, hence I cannot apply Nemenyi post-hoc test if I blindly follow the procedure

• perform Friedman on algorithms
• if \$H_0\$ is rejected, proceed to Nemenyi on the same algorithms

Question: Are the results from Nemenyi test for all algorithms still valid?

I am not sure, but I would say yes because

• I have shown that already not all \$A_k\$s have the same performance (and the results would still be significant with \$2p_A\$, i.e., if I used Bonferroni correction for multiple-hypothesis testing)
• Nemenyi for \$A_k\$s and \$B_k\$s found two groups of algorithms, i.e., some differences.

Get this bounty!!!