The importance of the normality assumption in large public health data sets.
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.
Lumley
Thomas
T
Department of Biostatistics, University of Washington, Box 357232, Seattle, Washington 98195, USA. tlumley@u.washington.edu
Diehr
Paula
P
Emerson
Scott
S
Chen
Lu
L
D003625:Data Collection; D003627:Data Interpretation, Statistical; D006801:Humans; D016014:Linear Models; D015233:Models, Statistical; D017063:Outcome Assessment, Health Care / Q000706:statistics & numerical data; D011634:Public Health / Q000706:statistics & numerical data*; D014481:United States