I estimate a linear model consisting of one dependent and four independent variables. I want to test wether each of the independent variables has a significant impact on the dependent variable, i.e. I want to test four hypotheses. I repeat this test ten times with ten different variations of the dependent variable (the qualitative definition of the dependent variable stays the same). If at least one of ten of the respective p-values indicates significance, I infer that there seems to be a relation between the respective coefficient and the dependent variable.

How do I adjust p-values in this case?

Do I have to adjust them twice? One time given the fact that I test four hypotheses with one model and one time given the fact that I repeat the test ten times? If the former is true, wouldn't I always have to adjust any p-value in any multiple regression model?

I estimate a linear model consisting of one dependent and four independent variables. I want to test wether each of the independent variables has a significant impact on the dependent variable, i.e. I want to test four hypotheses. The dependent variable is some sort of "quality" indicating variable. As quality is a highly subjective term, researchers have brought forward 10 different ways of quantifying the quality variable I am interested in. I consider each one of these valid and thus want to repeat the estimation 10 times for each of the different dependent variables (that are all assumed to measure the same concept, i.e. some quality notion). If at least one of ten of the respective p-values indicates significance, I infer that there seems to be a relation between the respective coefficient and the quality notion I am interested in.

How do I adjust p-values in this case?

Do I have to adjust them twice? One time given the fact that I test four hypotheses with one model and one time given the fact that I repeat the test ten times? If the former is true, wouldn't I always have to adjust any p-value in any multiple regression model?

I estimate a linear model consisting of one dependent and four independent variables. I want to test wether each of the independent variables has a significant impact on the dependent variable, i.e. I want to test four hypotheses.

  I repeat this test ten times with ten different variations of the dependent variable. How do I adjust p-values in this case?

Do I have to adjust them twice? One time given the fact that I test four hypotheses with one model and one time given the fact that I repeat the test ten times? If the former is true, wouldn't I always have to adjust any p-value in any multiple regression model?

I estimate a linear model consisting of one dependent and four independent variables. I want to test wether each of the independent variables has a significant impact on the dependent variable, i.e. I want to test four hypotheses. I repeat this test ten times with ten different variations of the dependent variable (the qualitative definition of the dependent variable stays the same). If at least one of ten of the respective p-values indicates significance, I infer that there seems to be a relation between the respective coefficient and the dependent variable.

How do I adjust p-values in this case?

Do I have to adjust them twice? One time given the fact that I test four hypotheses with one model and one time given the fact that I repeat the test ten times? If the former is true, wouldn't I always have to adjust any p-value in any multiple regression model?

I want to test a set of four hypotheses. I estimate a single model to test all of them (each hypothesis pertains to one coefficient in the model). I repeat this estimation 10 times with 10 slightly different definitions of the dependent variable. I want to reject each null hypothesis if at least one of the 10 repeated tests indicates significance for the respective coefficient.

How do I correctly adjust the p-values in this case? Do I have to adjust them twice? My two concerns are the following: First, do I have to adjust them based on the fact that I test four hypothesis with one model? If this is the case, wouldn´t I always have to adjust any p-value in a multiple regression model then? Because in a multiple regression model, one always implicitly tests wether multiple coefficients are different than zero, i.e. tests multiple hypotheses. And second, do I have to adjust them to account for the fact that I repeat this test 10 times?

My assumption would be that I would have to adjust them once to account for the 10 repeated tests, is this correct?

I estimate a linear model consisting of one dependent and four independent variables. I want to test wether each of the independent variables has a significant impact on the dependent variable, i.e. I want to test four hypotheses.

I repeat this test ten times with ten different variations of the dependent variable. How do I adjust p-values in this case?

Do I have to adjust them twice? One time given the fact that I test four hypotheses with one model and one time given the fact that I repeat the test ten times? If the former is true, wouldn't I always have to adjust any p-value in any multiple regression model?