Dear community,
I would like to challenge with you whether my understanding of G*Power is correct. I run the power analysis as you can see on the attached.
I entered the data since we will conduct an experiment with three tests with two groups and 80 participants is a realistic number we can test. To my understanding, the most critical output is the effect size f. Does this result mean that already small effect sizes of 0.18 could be measured which is relatively good? I found one similar meta-review with a Hedges g=0.122 effect size. Since hedges' g seems to be relatively close to Cohen's d see here, and since the effect size f seems to be generally half of that of d and thus g see here, I would assume that I would not be able to measure significant results if the effect size in our experiment is as large as in the experiment (since f=0.18 is roughly d/g=0.36>0.122). Is this interpretation correct?
How could I generally interpret the f=0.18? Can you recommend literature on converting f to Cohen's d as it would be easier to interpret as a low-medium effect then?
Thank you very much in advance for your help!
Hello Alexander,
What the result tells you is that you'd have a power of at least .80 to detect ES values of f = .1831 or larger, if they exist in the population, given the rest of the proposed values concerning alpha, sample size, groups, and number of DVs. This applies to the main effect of groups only; if you're using a repeated measures design, please note that the groups effect evaluates groups on their profiles of DV scores, each summed across occasions. (Often, in groups x occasions designs, a key test is whether the interaction is significant, implying different score trajectories across groups.)
As I'm sure you know, power simply means protection level against type II errors (failing to reject a false null hypothesis, if the alternative case represents a difference equal to your computed ES for this example).
Good luck with your work.
David Morse Thank you very much for the good explanation! Can you please further explain "This applies to the main effect of groups only; if you're using a repeated measures design, please note that the groups effect evaluates groups on their profiles of DV scores, each summed across occasions". What does summed across occasions mean? Does it mean that the values of each group are summed across the measurements and the sum is compared?
Hello again Alexander,
In a mixed design (one between subjects factor and one repeated measures factor), there are three basic effects: (a) main effect of the between subjects factor (in your case, groups); (b) main effect of the within subjects/repeated measures factor (occasion); and (c) group X occasion interaction.
The main effect of groups tests the hypothesis that the mean score for each group is equal (average of what, you ask? the sum of scores for each case across occasions).
The main effect of occasions tests the hypothesis that the mean score for each occasion is equal (average of scores summed across groups).
Because these main effects essentially ignore the other factor, they may not be of high import for the researcher. On the other hand, the test of interaction helps inform as to whether one group has a different score profile across occasions than other(s).
These explanations are simplified slightly for the univariate case. To make them applicable to the multivariate case, just change "mean" to "vector of means."
Good luck with your work.
Thank you again, David! This makes the main effects very lively. So the power analysis considers the sum of scores for all three measures and does not consider the main effect of occasions?
Hello again Alexander,
Occasions are not ignored, it's just that any main effect is evaluated by summing across any and all levels of other factors in a crossed or factorial desig. When one of the factors is a repeated measures factor, then scores for individual are summed in the way I described when computing SS for the between-sujects factor(s). Of course, a main effects for occasions SS computation sums across levels of the between-subjects factor.
Good luck finishing your project.
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