The general problem is accounting for the fact that within-subject non-independence (= correlations = clustering of observations) reduces the effective sample size. The actual sample size has to be boosted to adjust for this effect. There are two main approaches:

(1) Analytical. This means using the standard power analysis equations in combination with an adjustment factor (the design effect https://en.wikipedia.org/wiki/Design_effect ) that takes account for the degree of within-subject correlation and the number of observations per subject.

(2) Simulation. This approach is more difficult to implement (usually some programming will be required -- but perhaps other answers will identify more accessible simulation based methods), but can deal with any level of complexity (see two example articles and a tutorial below -- CoI: I co-authored two of them). The basic approach is to simulate multiple (100s or 1000s) random data sets where the alternative hypothesis is true, with a given effect size, then test the null hypothesis in each data set. The proportion of data sets where the null hypothesis is rejected is an estimate of power. The assumptions that generated the data set (e.g. sample size) can then be adjusted until the desired power is achieved.

Either approach (especially 1) will require simplifying assumptions (e.g. it will be easier to treat the two factors that you're interested independently when using approach 1. This is fine -- power analysis always involves a great deal of simplification, and often you can argue that the simplification is conservative (increases required sample size), so at least errs on the side of over-powering.

To sum up, my advice would be to use simulation if you're comfortable with it, otherwise simplify the problem and use approach 1.

A final point: I strongly discourage using general predefined effect size definitions like "medium effect size (f = 0.25)". To quote the first article listed below: "the study should be powered to detect ... the smallest effect that would be considered biologically meaningful. In other words, the study should be sufficiently sensitive to detect the smallest effect that, in the judgement of the researcher, is worth detecting." Effect size is highly context-specific, and in my experience it's always possible for a researcher with knowledge of the specific field to define an effect that is worth detecting.

--------------------

Simulation-based power analysis for clustered data using R:

Article Power analysis for generalized linear mixed models in ecolog...

http://tinyurl.com/simpowertutorial

http://onlinelibrary.wiley.com/doi/10.1111/2041-210X.12504/abstract

Hi, Do you have access to any other software or program for sample size calculation.

The general problem is accounting for the fact that within-subject non-independence (= correlations = clustering of observations) reduces the effective sample size. The actual sample size has to be boosted to adjust for this effect. There are two main approaches:

(1) Analytical. This means using the standard power analysis equations in combination with an adjustment factor (the design effect https://en.wikipedia.org/wiki/Design_effect ) that takes account for the degree of within-subject correlation and the number of observations per subject.

(2) Simulation. This approach is more difficult to implement (usually some programming will be required -- but perhaps other answers will identify more accessible simulation based methods), but can deal with any level of complexity (see two example articles and a tutorial below -- CoI: I co-authored two of them). The basic approach is to simulate multiple (100s or 1000s) random data sets where the alternative hypothesis is true, with a given effect size, then test the null hypothesis in each data set. The proportion of data sets where the null hypothesis is rejected is an estimate of power. The assumptions that generated the data set (e.g. sample size) can then be adjusted until the desired power is achieved.

Either approach (especially 1) will require simplifying assumptions (e.g. it will be easier to treat the two factors that you're interested independently when using approach 1. This is fine -- power analysis always involves a great deal of simplification, and often you can argue that the simplification is conservative (increases required sample size), so at least errs on the side of over-powering.

To sum up, my advice would be to use simulation if you're comfortable with it, otherwise simplify the problem and use approach 1.

A final point: I strongly discourage using general predefined effect size definitions like "medium effect size (f = 0.25)". To quote the first article listed below: "the study should be powered to detect ... the smallest effect that would be considered biologically meaningful. In other words, the study should be sufficiently sensitive to detect the smallest effect that, in the judgement of the researcher, is worth detecting." Effect size is highly context-specific, and in my experience it's always possible for a researcher with knowledge of the specific field to define an effect that is worth detecting.

--------------------

Simulation-based power analysis for clustered data using R:

Article Power analysis for generalized linear mixed models in ecolog...

http://tinyurl.com/simpowertutorial

http://onlinelibrary.wiley.com/doi/10.1111/2041-210X.12504/abstract

Power for Repeated Measures ANOVAs in G*Power:

https://www.youtube.com/watch?v=CEQUNYg80Y0

Power analysis is related to sample size determination and for many ANOVA situations you find the theory and R-programs in our book

Rasch, D.; Pilz, J., Gebhardt, A. and Verdooren, R.L. (2011)

Optimal Experimental Design with R,

Boca Raton, Chapman and Hall,