## Power calculation for One-way independent ANOVA

Enter a value for and two varaibles:

• Number of Groups
• Sample Size
• Power

The remaining empty field will be calculated. You can perform multiple power/sample size calculations.

The number of groups in your study.

per group

Sample size is the number of observations in a sample.

Power is the probability of accepting the alternative hyptothesis when it is in fact true.

Effect Size is the measure of strength of a phenomenon (effect). See the definition box on the right-hand-size.

Significance Level is the α value

### Results

The highlighted field denotes which variable is calculated.

Effect Size

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:
• ni = number of observations in group i
• N = total number of observations
• pi = ni / N
• μi = mean of group i
• μ = grand mean
• σ2 = 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.

Not sure if you are running the right test? Try the