Dear Asif,

If you want to analyse the cluster you have to decide first, if you want to analyse the individual data of the parents and include a cluster effect in the model, or if you want to evaluate the cluster mean (see GEE models). I am not precisely an expert on cluster randomized trials, but I recommend reading the book "Design and Analysis of Cluster Randomization Trials in Health Research" by Donner and Klar. This is often used as a basis for cluster analysis. Additionally, I recommend the following papers by Hemming and Donner/Klar):

http://bmcmedresmethodol.biomedcentral.com/articles/10.1186/1471-2288-11-102

https://www.ncbi.nlm.nih.gov/pubmed/14998805

Best wishes with your research

Asif  -

I have not checked to confirm, but I suspect the numbers you show come from using an online sample size calculator.  They usually assume yes/no data, rather than continuous data. Is that the case with you?  If not, you can forget them already.  If so, they also usually assume simple random sampling, worst case (p=q=0.5) for standard deviation, and no finite population correction factor, so they can give you a large overestimate.  That would increase burden, cost, and perhaps nonsampling error such as measurement error.  In continuous data there is no analogous way to "max out" the standard deviation problem.  Estimates (or guesstimates) for standard deviations are important to sample size requirements. 

As for cluster sampling, you could check out a text such as Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons.  For unequal size cluster units, pp. 314-316, section 11.4, "Optimum Selection Probabilities and Sampling and Subsampling Rates" might be of interest to you.  But it references information outside of that one section, and looks rather involved.  

Cheers - Jim

Thank you Ann Christina Foldenauer, Hassan Alomari  and James R Knaub for sharing wonderful links and books for cluster size estimation . . .  These are really good resources . . . .