Testing hypotheses suggested by the dataIn statistics, hypotheses suggested by a given dataset, when tested with the same dataset that suggested them, are likely to be accepted even when they are not true. This is because circular reasoning (double dipping) would be involved: something seems true in the limited data set; therefore we hypothesize that it is true in general; therefore we wrongly test it on the same, limited data set, which seems to confirm that it is true.
Family-wise error rateIn statistics, family-wise error rate (FWER) is the probability of making one or more false discoveries, or type I errors when performing multiple hypotheses tests. John Tukey developed in 1953 the concept of a familywise error rate as the probability of making a Type I error among a specified group, or "family," of tests. Ryan (1959) proposed the related concept of an experimentwise error rate, which is the probability of making a Type I error in a given experiment.
Bonferroni correctionIn statistics, the Bonferroni correction is a method to counteract the multiple comparisons problem. The method is named for its use of the Bonferroni inequalities. An extension of the method to confidence intervals was proposed by Olive Jean Dunn. Statistical hypothesis testing is based on rejecting the null hypothesis if the likelihood of the observed data under the null hypotheses is low. If multiple hypotheses are tested, the probability of observing a rare event increases, and therefore, the likelihood of incorrectly rejecting a null hypothesis (i.
Post hoc analysisIn a scientific study, post hoc analysis (from Latin post hoc, "after this") consists of statistical analyses that were specified after the data were seen. They are usually used to uncover specific differences between three or more group means when an analysis of variance (ANOVA) test is significant. This typically creates a multiple testing problem because each potential analysis is effectively a statistical test. Multiple testing procedures are sometimes used to compensate, but that is often difficult or impossible to do precisely.
Statistical hypothesis testingA statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see .
