Numbre of cluster in PPS sampling method I chose the sampling method based on probability proportional to size (PPS) to conduct a survey among school children. The total number of schools (clusters) in my population is 140. My concern is how to set the number total of clusters to select? There are conditions to be respected?
I would be grateful for any advice or guidance.
 A: This is not a question that has a simple answer, so I'll just give some general guidance. The calculation will either minimize cost for a fixed precision or will minimize the standard error for a fixed cost. You first select the optimum number of students per school; then the number of schools needed to meet your precision or cost constraint.
For the calculations, it would be best to group schools into primary sampling units (PSUs) that are approximately equal in size; or, perhaps, to stratify schools by size to accomplish the same thing. For references, see: Valliant et al., 2013, Section 9.3.1, who give R programs; also  Lohr, 2009, section 5.3. Valliant's text links to an R package that will do some of the calculations. If you do have strata, then you will also need to optimize allocation of the sample to each.
Some questions you will need to answer:


*

*Do you have a single important outcome on which you can base calculations, or are there several? 


If several, then you might need to find a compromise solution. Valliant et al. propose linear programming as a solution. 


*Have you any subgroups of schools or of students for which you want separate estimates?

*Do you have preliminary information on means, proportions, and the relative sizes of between- and within-school SDs? 

*Do you have  fixed budget or time constraints?

*Do you know preliminary estimates of fixed costs $C_0$;  the cost $C_1$ of studying one school (cost of travel, set-up); and $C_2$, the cost of studying one additional child, given the school has been selected. Actually you only need rough estimates of $C_1$ and $C_2$.

*Have you decided on your precision, criteria e.g. values for standard error or relative standard error? 
When I've done this kind of calculation in the past (sampling villages and households), I  ignored the fact that villages were of different sizes. These features had only a small influence on overall cost and time, the limiting factors. The major costs were travel to villages, setting up, and listing.  Some larger villages took a bit longer to map and list than smallers ones, but the work took about the same amount of time. Costs of study each household were about the same, once in the village. Also, although village sizes varied somewhat, I manipulated the second stage probabilities of selection so that final weights were (almost) equal (epsem sampling). (Kish, 1965, p.20 & p. 30)  I followed standard practice of selecting the the same number of households in each village. I was fortunate to have just one outcome; there were studies of similar diseases in other areas and I was able to calculate sample sizes for a range of assumptions.
Because of uncertainties, you won't be doing just one calculation, but many. If you don't have all the preliminary information you need to plan the study, do a small pilot test to get it.
Good luck!
References:
Kish, Leslie. 1965. Survey sampling. New York: Wiley.
Lohr, Sharon L. 2009. Sampling: Design and Analysis. Boston, MA: Cengage Brooks/Cole.
Valliant, Richard, Jill A. Dever, and Frauke Kreuter. 2013. Practical Tools for Designing and Weighting Survey Samples. Statistics for Social and Behavioral Sciences. Springer
