One-Way ANOVA: Comparing Means of More than Two Samples

Abstract

One-way analysis of variance is a statistical technique used for comparing means of more than two groups. It tests the null hypothesis that samples in different groups have been drawn from the same population. It is abbreviated as one-way ANOVA. This technique can be used in a situation where the data is measured either at interval scale or ratio scale. In one-way ANOVA, group means are compared by comparing the variability between groups with that of variability within the groups. This is done by computing an F-statistic. The F-value is computed by dividing the mean sum of square (MSS) calculated between the group means by the MSS within the groups. As per the central limit theorem, if the groups are drawn from the same population, the variance between the group means should be lower than the variance within the samples. Thus, a higher ratio (F-value) indicates that the samples were drawn from different populations.