I am looking to do a power analysis with assumptions about dependent observations.
I the research design, each respondent is assigned 4 short pieces of text, each of which they are asked to rate (on a continuous scale). Each text belongs to either treatment A or treatment B so each respondent reads and rates 2 texts from each treatment. Therefore, the 4 ratings that each respondent gives will be dependent on the respondent or they will be correlated.
In the following OLS regression, I would normally cluster the standard errors by respondent, but I am unsure how to implement this in a power analysis. I will assume either a small or medium treatment effect (e.g. Cohen's d of 0.2 or 0.4). Then, I am interested in knowing the power if I have a) 100, 200, 300 or 400 respondents and b) 2, 4 or 6 texts rated by each respondent.
I have tried to use the clusterPower package in R but I am not sure which function to use exactly and how.
I hope you can help. Thanks!
Dear Paul Cornelis van Leeuwen
In Simple Words. Power analysis is normally conducted before the data collection. The main purpose underlying power analysis is to help the researcher to determine the smallest sample size that is suitable to detect the effect of a given test at the desired level of significance.
Best Regards
Dr. Fatemeh Khozaei
The dependency can make a very substantial difference; have a look at my answer to this question
https://www.researchgate.net/post/Statistical_power-number_of_replications_per_unit
have a look at the manual associated with this software:
http://www.bristol.ac.uk/cmm/software/mlpowsim/
The software allows you to simulate a power curve for multilevel problems with within unit dependency.
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