Multiple Comparisons Using R

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The Bonferroni adjustment simply divides the Type I error rate. Hence, this method is often considered overly conservative. The Bonferroni adjustment can be made using p.

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Multiple Comparisons

Using the Bonferroni adjustment, only the mental-medical comparison is statistically significant. This suggests that the mental treatment is superior to the medical treatment, but that there is insufficient statistical support to distinguish between the mental and physical treatments and the physical and medical treatments.

Notice that these results are more conservative than with no adjustment. The Holm adjustment sequentially compares the lowest p-value with a Type I error rate that is reduced for each consecutive test.

(PDF) Multiple Comparisons Using R by Frank Bretz, Torsten Hothorn, Peter Westfall

In our case, this means that our first p-value is tested at the. This method is generally considered superior to the Bonferroni adjustment and can be employed using p.

Adjust P-values for Multiple Comparisons

Using the Holm procedure, our results are practically but not mathematically identical to using no adjustment. The Fisher Least Significant Difference LSD method essentially does not correct for the Type I error rate for multiple comparisons and is generally not recommended relative to other options.

R Tutorial Series: ANOVA Pairwise Comparison Methods

However, should the need arise to employ this method, one should seek out the LSD. Using the LSD method, our results are practically but not mathematically identical to using no adjustment or the Holm procedure. This method can be executed using the TukeyHSD x function, where x is a linear model object created using the aov formula, data function.

Note that in this application, the aov formula, data function is identical to the lm formula, data that we are already familiar with from linear regression. To see a complete example of how various pairwise comparison techniques can be applied in R, please download the ANOVA pairwise comparisons example.

ANOVA, Multiple Comparisons & Kurskal Wallis in R - R Tutorial 4.6 - MarinStatsLectures

A numeric vector of corrected p-values of the same length as p , with names copied from p. Controlling the false discovery rate: The control of the false discovery rate in multiple testing under dependency. Annals of Statistics , 29 , — A simple sequentially rejective multiple test procedure.


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Scandinavian Journal of Statistics , 6 , 65— A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika , 75 , — A sharper Bonferroni procedure for multiple tests of significance. It also introduces the multcomp package in R, which offers a convenient interface to perform multiple comparisons in a general context. Following this theoretical framework, the book explores applications involving the Dunnett test, Tukey's all pairwise comparisons, and general multiple contrast tests for standard regression models, mixed-effects models, and parametric survival models.

1st Edition

The last chapter reviews other multiple comparison procedures, such as resampling-based procedures, methods for group sequential or adaptive designs, and the combination of multiple comparison procedures with modeling techniques. Controlling multiplicity in experiments ensures better decision making and safeguards against false claims. A self-contained introduction to multiple comparison procedures, this book offers strategies for constructing the procedures and illustrates the framework for multiple hypotheses testing in general parametric models.