One-Way ANOVA Calculator

A one-way ANOVA, short for analysis of variance, tests whether the means of several groups differ by more than you would expect from chance alone. This calculator compares up to three groups: you paste a comma separated list of values for each group, and it works out the F statistic, the degrees of freedom, and the sums of squares that drive the test. The idea is to split the total variation in the data into two parts, the variation between the group means and the variation within each group. Dividing each sum of squares by its degrees of freedom gives a mean square, and the F statistic is the between groups mean square divided by the within groups mean square. A large F means the gaps between group means are large relative to the scatter inside the groups, which points to a genuine difference. New Zealand students, researchers, and analysts use one-way ANOVA to compare, for example, sales across three regions, yields from three methods, or scores from three teaching approaches, all in one test rather than many separate t-tests that would inflate the error rate. To read the result, compare the F statistic against a critical value from an F table using the between and within degrees of freedom; a larger F suggests at least one group mean differs. For sound results, use roughly equal group sizes where you can, check that the groups have similar spread, and follow a significant ANOVA with a post hoc test to find which specific groups differ. Always report the group sizes and means alongside the F value so the comparison can be judged fairly.

F = MS between / MS within, where MS = SS / df. df between = groups - 1, df within = total values - groups.