Provide the input parameters required for the analysis

In Step 3, you specify the power analysis input parameters in the lower left of the main window.

Example

An a priori power analysis for a two groups t test would require a decision between a one-tailed and a two-tailed test, a specification of Cohen's (1988) effect size measure d under H₁, the significance level α, the required power (1-β) of the test, and the preferred group size allocation ratio n2/n1.

Let us specify input parameters for

• a one-tailed t test,
• a medium effect size of d = .5,
• α = .05,
• (1-β) = .95, and
• an allocation ratio of n2/n1 = 1

This would result in a total sample size of N = 176 (i.e., 88 observation units in each group). The noncentrality parameter δ defining the t distribution under H₁, the decision criterion to be used (i.e., the critical value of the t statistic), the degrees of freedom of the t test and the actual power value are also displayed.

Note that the actual power will often be slightly larger than the pre-specified power in a priori power analyses. The reason is that non-integer sample sizes are always rounded up by G*Power to obtain integer values consistent with a power level not less than the pre-specified one.

Because Cohen's (1988) book on power analysis appears to be well known in the social and behavioral sciences, we made use of his effect size measures whenever possible. In addition, wherever available G*Power provides his definitions of "small", "medium", and "large" effects as "Tool tips". The tool tips may be optained by moving the cursor over the "effect size" input parameter field (see below). However, note that these conventions may have different meanings for different tests.

if you are not familiar with Cohen's (1988) measures, if you think they are inadequate for your test problem, or if you have more detailed information about the size of the to-be-expected effect (e.g., the results of similar prior studies), then you may want to compute Cohen's measures from more basic parameters. In this case, click on the Determine button to the left the effect size input field. A drawer will open next to the main window and provide access to an effect size calculator tailored to the selected test.

For the two-groups t test, for example, users can specify the means (μ1, μ2) and the common standard deviation (σ) in the populations underlying the groups to calculate Cohen's d = |μ1-μ2|/σ. Clicking the Calculate and transfer to main window button copies the computed effect size to the appropriate field in the main window.

In addition to the numerical output, G*Power displays the central (H₀) and the noncentral (H₁) test statistic distributions along with the decision criterion and the associated error probabilities in the upper part of the main window. This supports understanding the effects of the input parameters and is likely to be a useful visualization tool in the teaching of, or the learning about, inferential statistics. The distributions plot may be copied, saved, or printed by clicking the right mouse button inside the plot area.
The input and output of each power calculation in a G*Power session are automatically written to a protocol that can be displayed by selecting the "Protocol of power analyses" tab in the main window. You can clear the protocol, or to save, print, and copy the protocol in the same way as the distributions plot.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.