I have several issues with your request:

1) G*Power seems not to be equiped for factorial within designs. The field "Number of Measurements" is ambigous. Does it require you to set it to 9 in a 3x3 design (since you have obviously 9 data points from each person) or to 3, the smallest number of measures for one factor. As you can see in this statexchange discussion, one member directly asked the G*Power team, which stated that factorial designs are not possible for rm ANOVAs.

https://stats.stackexchange.com/questions/59235/repeated-measures-within-factors-settings-for-gpower-power-calculation

2) Maybe you should abandon the ANOVA approach completely and think about a multilevel model / linear mixed model to analyze your data. I assume that you did not measure sound1, sound2 etc with only one trial, but with several trials within each condition. Typically, you calculate the mean of all trials to have a factor level "sound1" for example. But this approach is typically not recommended anymore, since you throw away (or better: aggregate over lots of...) data. But even if you would have only a single trial for each condition, a LMM should be beneficial. For the former case, you would tyically add person_ID and trial_ID as random factors, whereas in the latter case only person_ID

I did not use it myself (only tried it to see what it does), but you could try GLIMMPSE for powercalculation, which is more flexible and you are able to directly give your expected estimated values for each group, instead of a global effect size like f^2

https://glimmpse.samplesizeshop.org/

P.S.: you did not mention what your dependent variable is, but for example reaction times or errors ary typically not optimally analyzed with OLS models, like ANOVA. The generalized linear mixed model appraoch would allow for other distributions, like Poisson in case of count data (like errors).

Dear Tatiana,

Detailed though, hope this helps!

When conducting a study on the effects of sounds on face perception using a 3 x 3 repeated measures design, it’s important to calculate the sample size to ensure the study has sufficient power to detect significant effects. Two different analysis approaches can be used in this context:

1. Sample Size Estimation for a 3 x 3 Repeated Measures ANOVA (Within-Subjects Design)

This approach involves running a 3 x 3 repeated measures ANOVA, where both sound condition (sound1, sound2, sound3) and gaze direction (left, direct, right) are within-subject factors. G*Power can be used to calculate the required sample size based on the following parameters:

G*Power Steps for Repeated Measures ANOVA:

• Test Family: Select F tests.
• Statistical Test: Choose ANOVA: Repeated measures, within factors.
• Effect Size (f): Cohen (1988) defines standard effect sizes as small (0.10), medium (0.25), and large (0.40) for ANOVA designs. Based on prior research on perceptual experiments, a medium effect size (f = 0.25) is a reasonable assumption for psychological experiments (Lakens, 2013)ha Level (α)**: Set the significance level at 0.05, which is common in psychological studies to control for Type I error (Cohen, 1992) .
• *Po: Set power at 0.80, the standard value for detecting an effect with sufficient certainty (Cohen, 1992) .
• **Number of Get to 1 group, as it is a within-subjects design.
• Number of Measurements: Input 9 (reflecting the 3 x 3 combination of sound conditions and gaze directions).
• Correlation among repeated measures: A conservative estimate of 0.5 is suggested if no pilot data is available (Girden, 1992) .
• *Non-sphericity corre: If no estimate is available, a value of 0.7 can be used to account for potential violations of sphericity (Maxwell & Delaney, 2004) .

Using these parameters, G*Power ate the required sample size. For a medium effect size, the estimated sample size is approximately 30–40 participants, which is in line with previous perceptual psychology experiments using repeated measures designs (Brysbaert, 2019) .

2. Sample Size Estimation for ANOVAs

a) 2 (sound1, sound2) x 3 (gaze: left, direct, right) Repeated Measures ANOVA

For the first ANOVA, which examines only two sound conditions (sound1 and sound2) with gaze directions, the following parameters should be entered into G*Power:

b) One-Way ANOVA on Silent Trials

For the silent trials, where you are only testing the effect of gaze direction, a one-way ANOVA is appropriate. The steps for calculating sample size in G*Power are as follows:

G*Power will estimate a sample size of approximately 30–40 participants for a medium effect size.

Combining the Sample Sizes

• Important Note: You do not need to add the sample sizes from the separate ANOVAs. Since the participants are the same across both analyses, the larger sample size estimate (from either the 2 x 3 repeated measures ANOVA or the one-way ANOVA) should be used as your target. Typically, the 3 x 3 repeated measures ANOVA will require the largest sample size, which means 30–40 participants is a reasonable estimate for your entire study.

Conclusion and Recommendations

• For the 3 x 3 repeated measures ANOVA: You will need approximately 30–40 participants to detect a medium effect size with a power of 0.80.
• For the separate ANOVAs: The sample size for each analysis will be similar, and the larger sample size estimate (usually from the 2 x 3 repeated measures ANOVA) can be used.
• Using G*Power for accurate sample size estimation ensures that your study is sufficiently powered, avoiding issues of underpowered studies or inflated false positives, which are common in perceptual psychology research (Brysbaert, 2019) .

References: