For a one-way ANOVA, the **Effect size** (f) is measured by:

f = \sqrt{\frac{\sum\limits_{i=1}^k p_{i} *(\mu_{i}-\mu)^{2}}{\sigma^{2}}}

where:

- n
_{i} = number of observations in group i
- N = total number of observations
- p
_{i} = n_{i} / N
- μ
_{i} = mean of group i
- μ = grand mean
- σ
^{2} = error variance within gorups

Cohen suggests that f values of 0.1, 0.25 and 0.4 represent small, medium and large effect sizes respectively.

Effect size for a between groups ANOVA

The formula is: \eta^{2} = \frac{\textrm{Treatment Sum of Squares}}{\textrm{Total Sum of Squares}}

So if we consider the output of a between groups ANOVA (output of a random example from SPSS software):

We need to have a look on the second column (Sum of Squares).

The treatment sum of squares is the first row: Between Groups (31.444)

The total sum of squares is the final row: Total (63.111)

Therefore: \eta^{2} = \frac{31.444}{63.111} = 0.498

49.8% of the variance is caused by the treatment

This would be deemed by Cohen’s guidelines as a very large effect size.