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There are good articles that I have read so far to understand power analysis. But I was not able to find good example to calculate power for multiple condition (factorial design) situation.

Lets assume we have 2 by 2 experiment design and we randomly assign users into to each group/condition and each condition test some element of a picture. For this question purpose lets say each condition has the picture in a different color. Eventually we want to understand significant of people's choice of color.

How many users we need in this experiment to obtain 0.05 significant level of preference of choice (color).

I went over following question but I couldn't find similarity to above setup up.

Previously Asked Question

Here we don't know any prior information but simply want to understand do we have enough or how many number of users do we need for successful experiment.

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