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I wanna make t-test for effect of gender, another t-test for effect of age, one-way ANOVA for effect of education and MIXED ANOVA (3x8) for another effect? Should I use Bonferroni corection? All is on same dependent variable.

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The key point about the multiple testing problem is that every time you have a p-value you have to pay -- like rolling the dice in a casino. A table of p-values needs to be adjusted by the number of tests. Bonferroni is very conservative (i.e., will really lower the adjusted p-values) so you may want to invoke the false discovery rate (FDR) instead -- look up the 1995 paper by Benjamini & Hochberg. But yes, for 2-way and multiway ANOVA, most labs apply a Bonferroni correction.

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  • $\begingroup$ There is also bootstrap and permutation p-value adjustment methods. This is covered in the book by Westfall and Young. "Resampling-Based Multiple Testing Examples and Methods for p-value Adjustment" Peter H. Westfall and S. Stanley Young, Wiley 1993. $\endgroup$ – Michael R. Chernick Dec 18 '16 at 1:31
  • $\begingroup$ Here is a URL for it. www.wiley.com/WileyCDA/WileyTitle/productCd-0471557617.html $\endgroup$ – Michael R. Chernick Dec 18 '16 at 1:34
  • $\begingroup$ The Westfall & Young procedure is also a good option. $\endgroup$ – JoleT Dec 18 '16 at 1:46
  • $\begingroup$ I noticed that Peter Westfall is also a member on CV. The advantage of the bootstrap approach is that it is not nearly as conservative as Bonferroni. I am pretty sure it deals with family-wise error rate and not False Discovery Rate. $\endgroup$ – Michael R. Chernick Dec 18 '16 at 2:10

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