One-Way ANOVA

A one-way ANOVA test compares the means of three or more samples defined by one factor.

Consider the average fuel consumption of cars from three companies. Here, the samples are defined by one factor—the company.

For cars from different companies driven in summer and winter, a one-way ANOVA cannot simultaneously test for two factors—company and season.

In general, begin by stating the null hypothesis that the sample means are equal, and the alternative hypothesis that the sample means are unequal.

Next, compute the variance between the samples and the variance within the samples, and calculate the F statistic.

F statistic values far from 1 lead to smaller P-values. This occurs when the variance within samples is small or the variance between samples is high. Thereby, we infer inequality of sample means, rejecting the null hypothesis.

Alternatively, F statistic values closer to 1 lead to larger P-values. This occurs when the variance between samples is close to the variance within samples. Thereby, we infer equality of sample means, failing to reject the null hypothesis.