### Ophthalmic statistics note 7: multiple hypothesis testing—to adjust or not to adjust

Valentina Cipriani, Ana Quartilho, Catey Bunce, Nick Freemantle, Caroline J Doré
2015 British Journal of Ophthalmology
on behalf of the Ophthalmic Statistics Group DEFINING THE PROBLEM Investigating multiple research questions, or hypotheses, within one study is a common scenario in biomedical research with many examples in ophthalmology. As the number of statistical tests increases, the overall chance that we draw an erroneous conclusion in our study gets higher in a predictable manner. Each statistical test conducted at the conventional 5% significance level (α) has a one in 20 chance (or 0.05 probability) of
more » ... appearing significant simply due to chance (a type I error) and a 1−0.05=0.95 probability of being nonsignificant. If we test two independent true null hypotheses, the probability that neither test will be significant is 0.95×0.95=0.90. Likewise, if we test 14 independent hypotheses, the probability that none will be significant is 0.95 14 =0.49, and the probability that at least one will be significant is 1−0.49=0.51, that is, we are more likely than not to find at least one test significant. In other words, if we go on carrying out tests of significance we are very likely to find a spurious significant result. In the field of statistics, this phenomenon is known as the problem of multiple testing or the multiplicity problem.