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This almost answered my question below, but not quite.

I want to calculate the sample size required in order to reach a certain level of a priori statistical power in my experiment. My question is about what ‘sample size’ means in this type of calculation. Does it mean the number of participants or the number of data points? If there is one data point per participant, then these numbers will obviously be the same. However, I’m using a mixed-effects logistic regression model in which there are multiple data points nested within each participant. (Each participant produces multiple ‘yes/no’ responses.)

If the number of data points is what matters, and I am using GPower, do I just enter this number into the 'sample size' window, with no adjustments anywhere else in GPower?

It would seem odd if the calculation of a priori statistical power did not differentiate between whether each participant produces one response or multiple responses.

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Short answer: According to the GPower manual the total sample size is equivalent to the number of subjects.

Discussion: Statistical tests that aim to answer the question whether data comes from the same distribution, then you obviously need less samples to reach a conclusion with the same confidence than when you have more variability (conditions). Pairing your data, restricts the possible combinations, requiring less samples. In your example, when using multiple samples, it matters whether those are independent or not for example. Interestingly, you could encode responses from multiple questions in a single value. This would provide an upper bound for the sample size using this methodology, as some kind of mutual information would probably lower the samples needed.

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