Statistical notes for clinical researchers: assessing normal distribution (1)

Various parametric tests make assumptions of the normal distribution, including t-test, analysis of variance (ANOVA), correlation, and regression. Different from some researcher’s understanding, tests of normality are not for the normality of observed data but for normality of the population distribution of a random characteristic; e.g. assuming normality for the population distribution of the characteristic is reasonable when referring to the observed sample data. Actual distribution of the characteristic in a random sample chosen from a population with normal distribution doesn’t appear normal, especially when the sample size is small (Figure 1). Distributions of larger samples tend to resemble the distribution of the characteristic in the population better by taking on a bell-shaped curve when the values of a characteristic in the population are plotted against their frequency. Open lecture on statistics