Dear Ibrahim

I do not know if you are only testing the quality of the questionary in a pilot study or if you are sizing the result of a new psychology intervention.

In the second instance you should have to consider the objetive of your study. The sample size depend for example if you are comparing two or more interventions, or if you are estimatin the grade of improvement of the intervention.

Dear Guillemots

Thank you very much for the taking the time to answer my question. I apologise the question was not clear. I'm trying to provide a better explanation here. I would really appreciate your assistance. 

 My interest is testing the efficacy of a psychology intervention, not a questionnaire. Let's say i want to design a randomized placebo controlled experiment, how would I decide  on the size of the sample to ascertain whether the intervention brings about a statistically significant result.?

Thank you so much

Ibrahim

OK. Then your first consideration should be how you should measure the efficacy. For example if you have a theoric proportion (P) of people that after the intervention would get a good score in the questionary, and you obtain a sample estimation of this proportion (p) with variance that depends on the sample design.

For example if the sample design is a Simple Random Sample Without Replication, your statistic's variance would be: V(p)= (N-n)/(N-1) P(1-P)/n, but if N (size of the population) is large and n (size of the sample) small, this may be approximated by: V(p)=PQ/n, where Q=1-P is the proportion that could not get a good score.

This result shows that this variance is larger when P is more near to 0.5 and smaller if P es very large or very small.

We can get a conservative size considering what size is required for P=0.5, because this size would be sufficient for each other P. If you want to produce an estimate of P with a confidence interval of 95% and a wide of 5%, a sample of 400 persons would be enough (This is because the limits of the interval are: Ls: 100(p + 2 (0.5x0.5/400)^.5)= 100 (p+ 2x.5x1/20)=100 p + 5% and Li:p - 2 (0.5x0.5/400)^.5= 100p - 5%

If you know that P