# What does independence between comparisons in multiple comparisons mean?

From Wikipedia's Multiple Comparison

For hypothesis testing, the problem of multiple comparisons (also known as the multiple testing problem) results from the increase in type I error that occurs when statistical tests are used repeatedly. If n independent comparisons are performed, the experiment-wide significance level $\bar{\alpha}$, also termed FWER for familywise error rate, is given by $$\bar{\alpha} = 1-\left( 1-\alpha_\mathrm{\{per\ comparison\}} \right)^n$$

I don't understand how the comparisons can be independent? Let the multiple tests be $\{H_i, K_i, T_i, c_i), i \in I\}$, where the $i$-th test is $H_i$ versus $K_i$, with testing statistic $T_i$ and critical value $c_i$. Now given a sample $X$, the test statistics $T_i(X), i\in I$ can't be independent, and therefore the testing rules $I_{T_i(X) \geq c_i}$ can't be independent either. Am I wrong? Thanks!