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I am searching for correlations between various dependent variables and various factors as well as interactions between them, using linear mixed effects models.

I am wondering how to calculate the correct alpha value, taking into account the number of the comparisons that I perform. Is there a formula to correct the alpha value and see if the p-values are actually significant?

I have been suggested to read the answer to this post: Permutation testing in multiply adjusted analyses where the an answer to my question should be included in the document http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.469.4226&rep=rep1&type=pdf

However, I do not really find the solution to my problem there. I find the document difficult for my skills and I do not see a simple formula to calculate the p-value for my case.

Let's make an example of the analysis I want to conduct and of the significant value of p I am searching: there are 2 dependent variables (let's call them dv_1, dv_2) that result from an experiment where participants had to adjust two parameters of a sound. I want to assess whether such variables are related to the participants' actual or perceived anthropometric features of body size (let's call them Height, Weight, Perceived Height and Perceived Weight). So I build some models for regression where I have various cases, e.g.

  1. dv1 predicted by Height
  2. dv1 predicted by Weight
  3. dv1 predicted by Weight*Height
  4. dv1 predicted by Perceived_Height
  5. dv1 predicted by Perceived_Weight
  6. dv1 predicted by Perceived_Weight*Perceived_Height
  7. dv2 predicted by Height
  8. dv2 predicted by Weight
  9. dv2 predicted by Weight*Height
  10. dv2 predicted by Perceived_Height
  11. dv2 predicted by Perceived_Weight
  12. dv2 predicted by Perceived_Weight*Perceived_Height

so I have 12 regressions, each of them will produce a p-value. Then I need to correct such p-value because of the number of comparisons. What I am interest is: 1. Which is the correct p-value for my case? (12 regressions, with 2 predicted variables, 4 variables as predictors plus the 2 interactions between some of them) 2. Which is the general formula for calculating the p-value?

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L_T
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    Possible duplicate of [Permutation testing in multiply adjusted analyses](http://stats.stackexchange.com/questions/178428/permutation-testing-in-multiply-adjusted-analyses). – AdamO Nov 17 '15 at 18:09
  • @AdamO Thank you. I have modified my question taking into account your comment. Any idea about an answer to this modified question? – L_T Nov 20 '15 at 09:00
  • I found the answer on this post: http://stats.stackexchange.com/questions/3200/is-adjusting-p-values-in-a-multiple-regression-for-multiple-comparisons-a-good-i – L_T Nov 21 '15 at 17:00

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