Post hoc analysis

In the design and analysis of experiments, post hoc analysis (from Latin , "after this") consists of looking at the data—after the experiment has concluded—for patterns that were not specified a priori. It is sometimes called data dredging by critics to evoke the sense that the more one looks the more likely something will be found. More subtly, each time a pattern in the data is considered, a statistical test is effectively performed. This greatly inflates the total number of statistical tests and necessitates the use of multiple testing procedures to compensate. However, this is difficult to do precisely and in fact most results of post hoc analyses are reported as they are with unadjusted p-values. These p-values must be interpreted in light of the fact that they are a small and selected subset of a potentially large group of p-values. Results of post hoc analyses should be explicitly labeled as such in reports and publications to avoid misleading readers.

In practice, post hoc analyses are usually concerned with finding patterns and/or relationships between subgroups of sampled populations that would otherwise remain undetected and undiscovered were a scientific community to rely strictly upon a priori statistical methods. Post hoc tests—also known as a posteriori tests—greatly expand the range and capability of methods that can be applied in exploratory research. Post hoc examination strengthens induction by limiting the probability that significant effects will seem to have been discovered between subgroups of a population when none actually exist. As it is, many scientific papers are published without adequate, preventative post hoc control of the type I error rate.

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