The importance of the normality assumption in large public health data sets

• Published in: Annual review of public health Vol. 23; no. 1; pp. 151 - 169
• Main Authors: Lumley, Thomas, Diehr, Paula, Emerson, Scott, Chen, Lu
• Format: Journal Article
• Language: English
• Published: United States Annual Reviews, Inc 01.01.2002
• Subjects: Data Collection; Data Interpretation, Statistical; Health Research; Humans; Inference; Linear Analysis; Linear Models; Models, Statistical; Outcome Assessment (Health Care) - statistics & numerical data; Public Health; Public Health - statistics & numerical data; Regression Analysis; United States; Validity; Variables; United States
• ISSN: 0163-7525; 1545-2093
• DOI: 10.1146/annurev.publhealth.23.100901.140546

It is widely but incorrectly believed that the t-test and linear regression are valid only for Normally distributed outcomes. The t-test and linear regression compare the mean of an outcome variable for different subjects. While these are valid even in very small samples if the outcome variable is Normally distributed, their major usefulness comes from the fact that in large samples they are valid for any distribution. We demonstrate this validity by simulation in extremely non-Normal data. We discuss situations in which in other methods such as the Wilcoxon rank sum test and ordinal logistic regression (proportional odds model) have been recommended, and conclude that the t-test and linear regression often provide a convenient and practical alternative. The major limitation on the t-test and linear regression for inference about associations is not a distributional one, but whether detecting and estimating a difference in the mean of the outcome answers the scientific question at hand.