# Determining sample size needed in a 4-way mixed ANOVA to reach significance

I have a data set for a 2 (between) x 3 (within) x 3 (within) x 3 (within) mixed ANOVA. I need to find the sample size necessary to find a significant result for one of the 3-way interactions including the between subjects factor and two of the within subjects factors. I'm trying to figure out the easiest/best way to simulate the addition of additional participants based on the current data. I currently have 24 subjects total (12 in each of the between subjects groups). I'm also familiar with R, MATLAB and Python. I've found some similar questions on the site but none of them seem to be trying to model the simulation based on existing data.

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Do you have any idea what size of effects you want to be able to catch? In addition, for a situation this specific & esoteric, I suspect you'll have to simulate to determine the appropriate N. I wrote about simulating for sample size here: Simulation of logistic regression power analysis - designed experiments. – gung Jan 11 '13 at 1:16
The partial eta squared for the effect is 0.033, so fairly small. One of the reviewers for a paper the analysis is in complained that the lack of an effect for this specific interaction was due to a small sample size, so I'm hoping to find the projected sample size that would be needed to find such an effect and demonstrate that the sample size is appropriate and that a 50-100% increase in sample size will do little to increase the chance of finding significance for that specific interaction. – Denton DeLoss Jan 11 '13 at 1:52
You are trying to calculate what is known as "post hoc power". Don't do it. Post hoc power gives no new information that is not already given by the p value and the degrees of freedom. See biostat.sdu.dk/courses/e12/Biostatistics/papers/hoenig2.pdf and stat.uiowa.edu/sites/default/files/techrep/tr378.pdf – Stephan Kolassa Jan 11 '13 at 22:17