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In the design and analysis of experiments, post hoc analysis (from Latin ''post hoc'', "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 by critics ''data dredging'' 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. Post hoc analysis is an important procedure without which multivariate hypothesis testing would greatly suffer, rendering the chances of discovering false positives unacceptably high. Ultimately, post hoc testing creates better informed scientists who can therefore formulate better, more efficient ''a priori'' hypotheses and research designs. == Relationship with the multiple comparisons problem == In its most literal and narrow sense, post hoc analysis simply refers to unplanned data analysis performed after the data is collected in order to reach further conclusions. In this sense, even a test that does not provide Type I Error Rate〔 protection, using multiple comparisons methods, is considered as post hoc analysis. A good example is performing initially unplanned multiple ''t''-tests at level , following an level anova test. Such post hoc analysis does not include multiple testing procedures, which are sometimes difficult to perform precisely. Unfortunately, analyses such as the above are still commonly conducted and their results reported with unadjusted p-values. Results of post hoc analyses which do not address the multiple comparisons problem should be explicitly labeled as such to avoid misleading readers. In the wider and more useful sense, post hoc analysis tests enable protection from the multiple comparisons problem, whether the inferences made are selective or simultaneous. The type of inference is related directly to the hypotheses family of interest. Simultaneous inference indicates that all inferences, in the family of all hypotheses, are jointly corrected up to a specified type I error rate. 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 . Therefore, simultaneous inference may be too conservative for certain large scale problems that are currently being addressed by science. For such problems, a selective inference approach might be more suitable, since it assumes that sub-groups of hypotheses from the large scale group can be viewed as a family. Selective post hoc examination strengthens induction by limiting the probability that significant differences will seem to have been discovered between sub-groups of a population when none actually exist. Accordingly, p-values of such sub-groups must be interpreted in light of the fact that they are a small and selected subset of a potentially large group of p-values. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Post hoc analysis」の詳細全文を読む スポンサード リンク
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