Section 30 F distribution

30.1 F distribution

The null hypothesis for the F-test is that all treatment means are the same.

One-way ANOVA is a technique which partitions the total variation in the dataset into two different components:

1. The variation between the means of each treatment and the overall mean

2. The variation within each treatment, between the individual sample values and the corresponding treatment mean.

The F-test is used to assess whether the ratio between these two variances is likely to have arisen by chance.

If there are no differences between the treatments, then the variation among the treatment means will also be a measure of the random variation.

If there are genuine differences between the treatments, then the ‘between treatment variation’ will be much larger than the ‘within-treatment variation’, which represents the random variation and the result of the F-test will be significant.