# Advice: Unpaired t or Normal Distribution Test

Interval (normal) vs. Dichotomous

A. Small to medium sized samples:

UNPAIRED (TWO SAMPLE) STUDENT t TEST FOR THE COMPARISON OF MEANS: Listed in the parametric methods section of the analysis menu. With small samples we must assume that the observations have been drawn from a normal distribution. The Shapiro-Wilk W test for non-normality can be used to test this assumption but if there is any doubt then you are advised to use the distribution free (nonparametric) method of Mann and Whitney (Wilcoxon rank sum). You can sometimes use transformations (e.g. natural logs) to "normalise" your data then apply parametric methods to them but you are advised to seek statistical advice before doing this.

B. Large samples (n > 100) that are not clearly "non-normal":

Z (NORMAL DISTRIBUTION) TEST FOR THE COMPARISON OF MEANS. This is listed in the parametric methods section of the analysis menu. With large samples that are not clearly "non-normal" we can assume that the means are normally distributed and that the variances are good estimates of their population values. The definition of a large sample is somewhat debateable but > 100 is a reasonably safe level. You will find some authors quoting > 50 and even > 30 as large samples but we favour a more conservative approach.