Common misconceptions held by health researchers when interpreting linear regression assumptions, a cross-sectional study

Abstract

BackgroundStatistical models are powerful tools that can be used to understand complex relationships in health systems. Statistical assumptions are a part of a framework for understanding analysed data, enabling valid inferences and conclusions. When poorly analysed, studies can result in misleading conclusions, which, in turn, may lead to ineffective or even harmful treatments and poorer health outcomes. This study examines researchers’ understanding of the commonly used statistical model of linear regression. It examines understanding around assumptions, identifies common misconceptions, and recommends improvements to practice.MethodsOne hundred papers were randomly sampled from the journal PLOS ONE, which used linear regression in the materials and methods section and were from the health and biomedical field in 2019. Two independent volunteer statisticians rated each paper for the reporting of linear regression assumptions. The prevalence of assumptions reported by authors was described using frequencies, percentages, and 95% confidence intervals. The agreement of statistical raters was assessed using Gwet’s statistic.ResultsOf the 95 papers that met the inclusion and exclusion criteria, only 37% reported checking any linear regression assumptions, 22% reported checking one assumption, and no authors checked all assumptions. The biggest misconception was that the Y variable should be checked for normality, with only 5 of the 28 papers correctly checking the residuals for normality.ConclusionThe prevalence of reporting linear regression assumptions remains low. When reported, they were often incorrectly checked, with very few authors showing any detail of their checks. To improve reporting of linear regression, a significant change in practice needs to occur across multiple levels of research, from teaching to journal reviewing. The focus should be on understanding results where the underlying statistical theory is viewed through the lens of “everything is a regression” rather than deploying rote-learned statistics.