When a t-test hides what a sign test exposes

John Cook recently posted a case where a statistical test "confirmed" a hypothesis but failed to confirm a more general hypothesis. Along those same lines, I had a recent case where I was comparing a cheap and a more expensive way of determining the potency of an assay. If they were equivalent, the sponsor could get by with the cheaper method. A t-test was not powerful enough to show a difference, but I noticed one method showed consistency lower potency than the other. I did a sign test (compared the number with lower results against the expected number based on a binomial) and got a significant result. I could not recommend the cheaper method.

Lessons learned:

- t-test is not necessarily more powerful than a sign test
- a t-test can "throw away" information
- dichotomizing data is often good and exchanges one type of information (qualitative) for loss of quantitative information