It would help a great deal if you say what you want to find out - is it about schools or about pupils or both - for some orientation have a look at

http://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/mlpowsim-manual.pdf

https://sites.google.com/site/optimaldesignsoftware/

It would help a great deal if you say what you want to find out - is it about schools or about pupils or both - for some orientation have a look at

http://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/mlpowsim-manual.pdf

https://sites.google.com/site/optimaldesignsoftware/

There is perhaps no one best way, your research questions are important in designing a sampling plan. If you have a complete sampling frame (list of schools and students), then probably simple random sampling can be done with better representative data. However, if your population are geographically dispersed, or you need group-wise samples (like one for primary students and another for secondary students), it might cost you more.In that case, consider stratified or cluster sampling. For further information on sampling design in education research, you can download a UNESCO publication from the following link.

www.unesco.org/iiep/PDF/TR_Mods/Qu_Mod3.pdf

Both answers above are useful. Start with your research questions as there you will find your unit of analysis, ie, eg, schools or pupils. Stratified random samples are useful if you are wanting to generalise from your sample to the population.

Job -

There are several key concepts to consider.  Generally speaking, you hope to collect data carefully to reduce nonsampling error which contributes to bias and variance, and pick a sampling design that reduces variance.  That usually leads to stratification, where the idea is to pick strata-group-categories with as little variance within each stratum and as much difference between strata as possible. That reduces overall variance.  Often, lower level categories within your overall population make good strata for such purposes. However, if you also hope to make inferences for each stratum, then you will not exactly be able to use optimized allocation of your sample between them without the chance that some strata will not be known very well, and others may have more data than needed. It depends on your goals.

Cluster sampling does not really directly improve (lower) variance for a given sample size. (So the "design effect" touted by Leslie Kish does not look good for cluster sampling.)  However, if you have to travel to collect your data, cluster sampling was designed to make that more cost effective.  It is also often used in multistage sampling.  One stage may be to randomly select a region, and another would be to randomly select a unit from within each selected region.  You could use stratification in this second stage (and/or the first stage).  PPS sampling  (noted below) could be involved.  You may be able to afford a bigger sample size which more than makes up for cluster sampling 'inefficiency,' and actually provides more accurate results.  These are all randomized sample selection techniques, and I assume you are looking for continuous data or yes/no data.  I suppose a lot of these principles carry over to other areas.

There are a number of good textbooks you may want to consult.  Here are a couple:

Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. 

Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.

There are other terms you might want to research besides multistage sampling,  cluster sampling, stratified (random) sampling, bias, variance, and nonsampling error.  Probability proportional to size (PPS) sampling can be efficient, but sometimes tricky. (There is a cute story called "Basu's Elephant Fable" you might look up sometime, that was originally in a paper whose name i don't recall, where he notes the pitfalls to be avoided which tripped up a "circus statistician.")  Area sampling can be helpful, depending upon the kind of frame you have, "frame" being another word you can check.  Small area estimation is another field that may be of interest to you, and I think I recall seeing a school survey which made use of that.  It involves regression modeling, often using a Bayesian approach, but not necessarily.

If you have auxiliary/regressor data on a population, you can use regression modeling much to advantage, even when not considered "small area estimation."  In fact, you can consider model-assisted design-based methods as being very efficient in that they make good use of other data you already have - perhaps administrative data.  Here is a good source of information on model-assisted methods (which are still design-based and thus involve randomized selection):

Särndal, CE, Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang. 

Purely model-based methods, without randomization can also be used for inference, my specialty, but only under specific conditions which I doubt would apply to you.  At any rate, stratification is a key to success there too, as one condition. 

I think that there have likely been a number of educational studies done in the past that may be good guides for you, or at least may stimulate some ideas for you. You could look at websites for organizations such as the US Department of Education where you may find your way to studies and/or contacts that may have direct experience with studies similar to what you need to do.  (My specialty for most of my career was in energy statistics, not education statistics, but the books and terms I referenced above cut across many subject fields.)  You could also go to internet sources such as the American Statistical Association: 

http://www.amstat.org/

You can search on that site (enter keywords in the upper right hand corner) and be led to papers of interest. 

Best wishes with your study.

Cheers - Jim

Hi,

For your question, kindly following the Probability Proportional to Size (PPS).

The above method is the correct method to do the survey.  By this method only you have to include all the samples from various areas.

Kindly refer the following:

http://www.who.int/tb/advisory_bodies/impact_measurement_taskforce/meetings/prevalence_survey/psws_probability_prop_size_bierrenbach.pdf

You may wish to use cluster sampling not just for convenience and cost  but because you  want to measure and assess contexts (ie schools) and contextual variables - the other kids in the class - to study things like peer group effects.

You may want to have a look at

https://www.researchgate.net/publication/256802442_Multilevel_approaches_to_modelling_contexuality_from_nuisance_to_substance_in_the_analysis_of_voting_behavior

which makes the case for cluster sampling when you want to analyze things like schools that provide context for pupils.

The following reference  is also a useful read for the modern view, albeit in a different research area

Laura Stoker and Jake Bowers,"Designing Multi-level Studies: Sampling Voters and Electoral Contexts". 2002. Electoral Studies. 21(2):235-267.

From the literature:

-  Bryk and Raudenbush (1992) HLM; suggest that with 60 students in each of 160 schools you can estimate 4 random variables at school level

-  Paterson and Goldstein (1991) suggest a minimum of 25 individuals in 25 schools; in preference 100 schools in  New statistical methods for analysing social structures: an introduction to multilevel models. British Educational Research Journal, 17: 387-394.

Needles to say these experienced educational researchers suggest cluster sampling allied to multilevel analysis. It has been generally found that in multilevel analysis of pupils and schools that some 10% of the variation in pupil achievement is at the school level, That is ROH - the Rate of Homogeneity is typically 0.10.

 The big message is that substantive questions should drive the sampling design and that cluster designs - even highly clustered one - ie all the pupils in a school- can be effectively analyzed by random coefficient models.

Article Multilevel approaches to modelling contexuality: from nuisan...

A common design for health surveillance surveys is to sample schools PPS and then sample classes within schools. There will be some loss of precision due to school-level effects.

I also think PPS will be appropriate for the research

Are you using an existing survey that meets statistical requirements or generating your own?  If generating your own, what theory are you basing your questions on?  What predictors and outcomes of the theory are you focusing on?  Have you considered using a cluster sampling?  Have you requested permission from the schools since you will be doing a survey with kids less than age 18 which requires high level authorization and special consideration for children?  Without understanding where you are at, it is really hard to determine what to advise.

What type of statistical analysis software do you have access to?  Some require minimum sample size in addition to meeting other criteria.