Abstract
Misconceptions about the assumptions behind the standard linear regression model are widespread and dangerous. These lead to using linear regression when inappropriate, and to employing alternative procedures with less statistical power when unnecessary. Our systematic literature review investigated employment and reporting of assumption checks in twelve clinical psychology journals. Findings indicate that normality of the variables themselves, rather than of the errors, was wrongfully held for a necessary assumption in 4% of papers that use regression. Furthermore, 92% of all papers using linear regression were unclear about their assumption checks, violating APA-recommendations. This paper appeals for a heightened awareness for and increased transparency in the reporting of statistical assumption checking.
Highlights
IntroductionOne of the most frequently employed models to express the influence of several predictors on a continuous outcome variable is the linear regression model: Yi = β0 + β1X1i + β2X2i + ··· + βpXpi + εi
One of the most frequently employed models to express the influence of several predictors on a continuous outcome variable is the linear regression model: Yi = β0 + β1X1i + β2X2i + ··· + βpXpi + εi.This equation predicts the value of a case Yi with values Xji on the independent variables Xj (j = 1,...,p)
We investigate how statistical assumptions were covered in various journals of clinical psychology and what types of misconceptions and mistakes are occurring most often
Summary
One of the most frequently employed models to express the influence of several predictors on a continuous outcome variable is the linear regression model: Yi = β0 + β1X1i + β2X2i + ··· + βpXpi + εi. This equation predicts the value of a case Yi with values Xji on the independent variables Xj (j = 1,...,p). The error for the given Yi, the difference between the observed value and value predicted by the population regression model, is denoted by εi and is supposed to be unrelated to the values of Xp. Here, β0 denotes the intercept, the expected Y value when all predictors are equal to zero.
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