Testing a hypothesis suggested by the data can very easily result in false positives (type I errors).
The negative test data that were thrown out are just as important, because they give one an idea of how common the positive results are compared to chance.
A large set of tests as described above greatly inflates the probability of type I error as all but the data most favorable to the hypothesis is discarded.
This is a risk, not only in hypothesis testing but in all statistical inference as it is often problematic to accurately describe the process that has been followed in searching and discarding data.
These include: Henry Scheffé's simultaneous test of all contrasts in multiple comparison problems is the most[citation needed] well-known remedy in the case of analysis of variance.