This might be a rather basic question, but I really want to get it right.
When doing multiple hypothesis testing, researchers typically account for the "multiple" part by controlling for the family wise error rate by means of e.g. the Bonferroni Correction procedure.
However, is it possible to make a "summarizing" inference based on the hypothesis test results of multiple tests? Say, for example, I conducted a hypothesis test repeatedly for 5 times. I controlled for the family wise error rate by adjusting each p-value by applying the Bonferroni Correction procedure. In 3 cases I reject the null hypothesis, in 2 cases I do not.
Can I reject or accept the null hypothesis "in general" based on this result? I.e. can I summarize those 5 test results in some way?