Post Hoc Tests
Understanding post hoc analysis
Post hoc analysis, which simply refers to “after test” is a test that analyzes the results of a certain experiment. In most cases, post hoc test are conducted after other analysis hence their name. for instance, after analysis of variance (ANOVA) a post hoc test is used to determine which exact groups were different an analysis that ANOVA itself will not tell you. The most used and common types of post hoc test are;
Bonferroni procedure (Bonferroni Correction)
When doing numerous independent or dependent statistical tests at the same time, this multiple-comparison post hoc adjustment is performed. The problem with running multiple tests at the same time is that the likelihood of a significant result rises with each test run. The significance cutoff for this post-hoc test is α/n. For example, if 20 tests are done simultaneously at = 0.05, the correction is 0.0025. More information. The Bonferroni suffers from a power loss, this is attributable to a variety of factors, including the high Type II error rates for each test. In simpler words, it overcorrects for Type I mistakes.
Fisher’s least significant difference (LSD)
Fisher's Least Significant Difference is a method for determining the least significant difference between two groups (LSD). It is used for determining which pairs of means differ statistically. Essentially the same as Duncan's MRT, but instead of Q values, t-values are used.
Duncan new multiple range test (MRT)
The results of an Analysis of Variance (ANOVA) will inform you whether there is a mean difference. It will not, however, identify the groups of means that are different. Duncan's Multiple Range Test will find the pairs of means that differ (from at least three). The MRT is similar to the LSD, only it uses a Q Value instead of a t-value.
Rodger's Approach
Some consider this to be the most potent post hoc test for finding group differences. As the degrees of freedom increase, this test protects against statistical power loss.
Scheffé Method
The Scheffe method is used when you wish to look at post hoc comparisons in general (as opposed to just pairwise comparisons). Scheffe's method controls are used to determine the overall level of confidence. It's commonly utilized when the sample sizes aren't equal.
Newman-Keuls
The Newman-Keuls post hoc test, like Tukey's, identifies sample means that differ from one another. For comparing pairs of means, Newman-Keuls uses distinct critical values. As a result, significant differences are more likely to be discovered.
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