# Joint NC BERD Seminar: Breaking Free from the Myth of Normality

It is widely and incorrectly believed that t-tests and linear regression are only valid for "Normal" data or data that follow a bell-shaped curve. In manuscript submissions, for example, investigators are often asked by referees to defend their analyses when their outcomes are skewed or non-normal. Popular standard statistical approaches used for continuous or quantitative outcomes are Student's t-test (comparing two groups) and classical linear regression for more general comparisons of means of an outcome variable. It is true that tests from these methods are valid and optimal (e.g., most efficient) in small samples, provided the outcome is Normal and other distributional assumptions are met (e.g., common variances). However, their major usefulness is because in large samples these tests - robust versions of them (e.g., Welch's t-test) - are still valid for most distributions.

We will demonstrate this validity by evaluating extremely non-Normal data using Monte Carlo simulation. We examine the appropriateness, or lack thereof, of other commonly used methods mistakenly believed to be "robust" substitutes to the t-test (which models the mean as the scientific summary of interest), such as the Wilcoxon rank sum test, which is believed to model medians.

We assert that the t-test and linear regression are often the most straightforward and practical alternatives. The key limitation of the t-test and linear regression for making statistical inference is not a distributional one, but whether using means as one's summary statistic best addresses the scientific question at hand.

Zoom: https://duke.zoom.us/j/99193151349?pwd=a0RaQzdJWEtpcmhZTGQrdmdubWlBUT09

This event is being cross-promoted by the NC BERD Consortium, a collaboration of the CTSA-funded BERD cores at UNC-Chapel Hill, Wake Forest University School of Medicine, and Duke University School of Medicine.