Family-wise C.I. and Multiple Hypothesis Testing

Relationship between Family-wise Confidence Intervals and Hypothesis Testing

With multiple hypothesis testing:

\(H_{0}\) says that all of our individual null hypotheses \(H_{0i}\) are true.

Then if atleast one of the \(H_{0i}\) are false, then \(H_{0}\) is rejected.

The larger our individual \(\alpha_i\) level is, that family-wise \(\alpha\) level can be depending on how we control it (e.g. Bonferroni, \(\alpha\) = \(\alpha_i/ k\) where k is the number of hypothesis tests.)

Then, in order to control how easy it is to reject \(H_0\), we need to control \(\alpha_i\)