Hi,

I would refer you to the below paper:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.490.7640&rep=rep1&type=pdf

I copied their conclusion for short:

- They began to say that: "It is not common practice among applied researchers

to use adjusted t-tests for variable selection in regression analysis. Rather, it is much more common to see each individual test conducted at the nominal level, usually using α= 0.05".

- Based on their simulation study, they have shown that: "This research indicates that when unadjusted t-tests are used for individual variable selection, the associated overall Type-I error rate may be inflated by as much as 2 to 6 times the

nominal α-level depending upon the number of predictors in the model and the number of predictors that have a non-zero correlation with the response. Consequently, one or more variables are identified as “significant” predictors of the response that are not actually needed in the model, i.e., the amount of unique variance in the response explained by these variables is negligible. "

So, it depends on the purpose of your regression model. If you would look for a set of covariates to predict the values of the response as accurate as possible, then I personally think that the adjusted t-tests are not necessary. That is also what I have done for many analysis.

In case you prefer to have variable selection, using other approach, for example, the Lasso or the elastic net.

Hope it help.

Hello, you can use this correction for your studies. Go through the article which may help you to understand the Bonferroni correction.

Hi Suleiman,

That should be the simplest way to go about it. Yes, Bonferroni correction is applicable to multiple linear regression analysis, as it is to other multiple analysis. Simply divide your alpha by the number of simultaneous multiple comparison. If your predictor variables are five, then divide your P-Value by 5 to give you a more realistic threshold of significance. Otherwise, you could also use more accurate Sidak correction.

I hope this helps.

Thanks all. I found your contributions helpful.

I find use of Bonferroni correction advocated for in statistics texts. However, it is seldom used in research articles apart from cases of mean comparisons (such as ANOVA). It seems researchers are more comfortable risking type I than type II error (at least in this case). I will apply the Bonferroni correction to control for familywise errors. 

Mustafa Ojonuba Jibrin I wanted to ask you a practical question: when using the Bonferroni correction, do you use it only for the overall regression model or for each correlations within the model? For example, if I have 2 multiple regression models, with the same outcome variable and some similar predictor variables, do I need to adjust the ANOVA p value by the number of multiple regression models I have (in my case 2) in order to see if I can accept it as significant due to running or do I accept the ANOVA as it is and I adjust for the values within the model? Thank you very much!

Sorry for late reply. Yes, you have to adjust the ANOVA p value by the number of multiple regression models.

Some explanations here: https://www.researchgate.net/post/Bonferroni_correction_for_multiple_regression_models

I don't think you really have to adjust the p values, but this depends on the nature of your analysis - explanatory or comfirmatory. In a nutshell, we need to correct for multiple comparisons when testing for a family of multiple hypotheses simultaneously. If your regression analysis is comfirmatory by nature, and you want to test for a prior H, then you don't need to correct the p value as these is only one hypothesis. For example, among the five predictors x1-x5, the predictor of interest is x1 based on your H, and x2-x5 are covariates, then there is no need to adjust the P value (e.g., divide it by 5 or use other methods for correcting family wise error rate or false discovery rate). However, if your analysis is explanatory (there is no a prior H and all five predictors are of interest) you need to adjust the p values. In addtion, if you have more than one a prior Hs, you should also use the adjusted p values depending on the number of your Hs. Therefore, whether or not using adjusted p values depends on the number of Hs that are tested simultaneously.

Each approach has been used in previous literature and I personally prefer the second approach - adjusting p value at the comparison level instead of the overall level. Christodouli Lagogianni

sorry for the typo in my original post - the "explnanatory" should be "exploratory".