In a scientific study, post hoc analysis (from
Latin
Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
''
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
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician ...
(ANOVA) test is significant. This typically creates a
multiple testing problem because each potential analysis is effectively a
statistical test
A 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.
...
. Multiple testing procedures are sometimes used to compensate, but that is often difficult or impossible to do precisely. Post hoc analysis that is conducted and interpreted without adequate consideration of this problem is sometimes called ''
data dredging
Data dredging (also known as data snooping or ''p''-hacking) is the misuse of data analysis to find patterns in data that can be presented as statistically significant, thus dramatically increasing and understating the risk of false positives. T ...
'' by critics because the statistical associations that it finds are often spurious.
Common post hoc tests
Some common post hoc tests include:
[{{Cite web , last=Pamplona , first=Fabricio , date=2022-07-28 , title=Post Hoc Analysis: Process and types of tests , url=https://mindthegraph.com/blog/post-hoc-analysis/ , access-date=2022-12-09 , website=Mind the Graph Blog , language=en-US]
*
Holm-Bonferroni Procedure
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Newman-Keuls
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Rodger’s Method
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Scheffé’s Method
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Tukey’s Test (see also: Studentized Range Distribution)
Causes
Sometimes the temptation to engage in post hoc analysis is motivated by a desire to produce positive results or see a project as successful. In the case of pharmaceutical research, there may be significant financial consequences to a failed trial.
See also
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HARKing
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Testing hypotheses suggested by the data
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Nemenyi test
References
Data analysis
Multiple comparisons
Clinical research
Medical statistics