p-Value adjustment to control type I errors in linear regression models

The paper is devoted to a new randomization method that yields unbiased adjustments of p-values for linear regression model predictors by incorporating the number of potential explanatory variables, their variance–covariance matrix and its uncertainty, based on the number of observations. This adjustment helps control type I errors in scientific studies, significantly decreasing the number of publications that report false relations to be authentic ones. Comparative analysis with such existing methods as Bonferroni correction and Shehata and White adjustments explicitly shows their imperfections, especially in case when the number of observations and the number of potential explanatory variables are approximately equal. Proposed method is easy to program and can be integrated into any statistical software package.