Generally sample size calculation is done before the study begins. Do you mean effect size?

@Mehmet Sinan Iyisoy Thank you for your answer, i have conducted the analysis on pilot  data that i have done before. I want to caculate sanple size for the actual study using these results. Sorry for not clarifying that in the question above.

you can use PASS 11 Software.

Israa -

I am not familiar with your particular application, but if you are fairly certain that you do not have substantial model bias, you can base your sample size on projected estimates of the variance of the prediction error.  In general, there is a standard deviation of the residuals that should be fixed, so your pilot study may give you a good estimate of the sigma value.  Then it is a matter of what sample size with that sigma will give you a satisfactory variance of the prediction error. 

The variance of the prediction error will vary greatly from point-to-point if you have heteroscedasticity, but even then you can check points in the range of interest.

If you are looking at estimated means or totals from a finite population, then you can get the estimated variance of the prediction error for the estimated total, but that is more involved. 

I suspect that you are looking at the  individual estimated variance of the prediction error, and in your application I assume you may be using software that can tell you what it is for your pilot study, for each dependent variable, but you do not know the estimator 'formula' used by your software so that you can plug in the sample size, n, that will give you the desired anticipated variance of the prediction error  (the square root of which is the standard error associated with a given point).  You could consult manuals or software experts to see what 'formula' is being used, or perhaps derive it yourself, but it sounds rather messy.  Perhaps a better solution may be to use a bootstrap variance estimate, or even plug in several copies of your pilot data to see how quickly the variance of the prediction error drops. 

Some may say that last suggestion is not very rigorous, but this is all roughly approximate anyway.  Data quality will matter, and your pilot study has to have had some 'glitches.'   I did not have this problem, because I worked with official statistics where we had frequent samples and less frequent census surveys that generally provided a great deal of good test data appropriate to given circumstances, so I am just conjecturing.  So, this is just a suggestion, but if you had, say 100 data points in your test/pilot study, and it gave you estimated variance of the prediction errors for each of your questions/dependent variables, that gave standard error estimates that were too large, you might assume that the 100 points covered the range of results fairly well, and create a test data set repeating these 100 points c times.  If c were, say, 5, then your test data set would be the 100 pilot data points 5 times each, so test n=500.  If that gave you acceptable estimated standard errors of the prediction errors for each of your dependent variables, then you could say you have an estimated sample size requirement.  Your pilot study would thus, presumably, have been used to decide on your model, and now used to estimate sample size needs.  Now your study can proceed with new data collection.  Of course results will differ from what you anticipated, but this is about as reasonable as you can be for such cases, I think.   If you have a design such that you can stop or continue collecting data at any point, for example you are collecting data at random from within various categories, and you check your estimates and their associated  estimated standard errors at various points along the way, you might be able to revise your sample size requirements. Note that if you stretch your resources and start having data quality issues, that can artificially inflate the residual standard deviations.  (Such standard deviations should remain constant, while standard error decreases with increased sample sizes.  You get a better estimate of standard deviations with increased sample size, but it is basically a 'constant,' unlike the standard error here, and analogously for the standard deviation of a given population and the standard error of its mean.)

I am not familiar with the PASS 11 software mentioned and whether or not it will let you project your sample size needs.  You could check that, but I doubt that it does.  However, as with any other software for performing regressions that may let you use the format you chose, you might be able to use it for the experiment I suggested above. 

Perhaps some software will do this for you, or you might choose some bootstrap method, or there may be a better way to handle this, but it just occurred to me that the experiment I'm suggesting above may be as easy as is possible, and provide results that are about as good as you are going to get in estimating your sample size needs. You could just try different values for "c" in experimental runs to estimate sample size needs.  At least it sounds reasonable to me.

If you are looking at something in particular about that interaction term that I am missing, I still think that the experiment above will still help you find the approximate sample size need for doing what you want.

Cheers - Jim

Israa -

After revisiting your question to see the details of your model, might you want to look at two models, one for females and one for males?  Might this be a good place to apply multivariate multiple regression?   Just wondering.

Best wishes - Jim