One method of analyzing the difference between group means is analysis of variance. The ANOVA procedure follows the classical, statistical hypothesis, inference-testing format. First, state the null and alternative hypotheses. The ANOVA procedure creates a table that tests the null hypothesis of equal means against the alternative hypothesis that at least two groups have different means. Next you choose the level of significance for the ANOVA, which is a type 1 error of 0.05 by default.

ANOVA uses the f-statistic. This is a ratio comparing the variation between groups to the variation due to random error. You compare this f-ratio to a critical f-value. The critical f is determined by your chosen error rate, and the sample sizes used to calculate the between group and error variances. If the computed f value is greater than the critical f, you will reject the null hypothesis and conclude that there is a difference. Otherwise you will fail to reject the null, and conclude that the means might not be different.

## One-way ANOVA with MS-Excel

In the video tutorial below you will learn how to create a One-way ANOVA with MS-Excel.