Mariam -

I'm not certain that you have the correct concept of a cluster. A cluster sample is one where the primary sampling unit is a group, like a city block, or a classroom, from which you select a random sample, or even census, at the next step (called multistage sampling when you use some randomized selection at each stage).  A cluster sample generally requires even more observations than simple random sampling, but is often more logistically feasible and cost effective.

A stratified random sample generally requires a smaller sample size than simple random sampling, so it's design effect is more favorable, because the idea is to group your sample and population such that the variance within each stratum is reduced, and the difference between strata is greater, to obtain a smaller overall variance.  But this is just to improve the aggregate level results. If you really want to get results for each stratum, then your goal is not the same. You are then not looking for stratified random sampling, but really breaking the population into smaller ones for which you have goals, so anything you read about optimized allocation overall would not apply.

As for sample size, for a complex survey, that can be challenging. For any stratum or group where you might do simple random sampling, you might find good, straightforward information, such as the chapter on sample size for continuous and for yes/no data in Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. 

I worked mostly with continous data in establishment surveys, and model-based sampling and estimation, which is a different concept, but for both that and the continuous data in Cochran with randomized selection, you need information on the standard deviation for each of those subpopulations or strata, here from your data, in my case something similar for residuals. (Yes/no data are similar, but there is an easier way to get a worst case estimate that is commonly used in online calculators.)

Also, regarding sample size needs, you may need to familiarize yourself with the finite population correction  (fpc) factor.  (I have a definition on my RG page that I did for a Sage Publications encyclopedia.) 

At any rate, to obtain needed information, one thing Cochran suggested is a pilot study. In your case, especially if you do not have a good full time statistician and good software she/he can use, a pilot study would be very useful to get an idea of what you need. It might also help test your questionnaire, etc.  But big changes in your questionnaire may make changes to your sample size needs. And beware that different questions may have very different sample size needs.  Also, if you need a sample size that is too large for your resources, you might substantially increase nonsampling error - an area that is often too much neglected - which can badly distort everything.

So, in summary, I suggest that you review the difference between cluster and stratified random sampling; note where you might mean strata versus separate subpopulations of interest; review multistage sampling  (which increases the complexity of variance estimation); and beware of nonsampling errors.  A good reference(s) such as Cochran is important.  Standard errors are important. A pilot study may be essential.

Beware of both bias and standard errors for both sampling and nonsampling errors.

Note that I am not familiar with count data or likert scales, and information on those are likely found elsewhere, but the concepts of stratification and cluster sampling, bias and perhaps nonsampling error, and of possibly using a pilot study, should, I think, still apply in an analogous manner.

Cheers - Jim

Mariam -

I'm not certain that you have the correct concept of a cluster. A cluster sample is one where the primary sampling unit is a group, like a city block, or a classroom, from which you select a random sample, or even census, at the next step (called multistage sampling when you use some randomized selection at each stage).  A cluster sample generally requires even more observations than simple random sampling, but is often more logistically feasible and cost effective.

A stratified random sample generally requires a smaller sample size than simple random sampling, so it's design effect is more favorable, because the idea is to group your sample and population such that the variance within each stratum is reduced, and the difference between strata is greater, to obtain a smaller overall variance.  But this is just to improve the aggregate level results. If you really want to get results for each stratum, then your goal is not the same. You are then not looking for stratified random sampling, but really breaking the population into smaller ones for which you have goals, so anything you read about optimized allocation overall would not apply.

As for sample size, for a complex survey, that can be challenging. For any stratum or group where you might do simple random sampling, you might find good, straightforward information, such as the chapter on sample size for continuous and for yes/no data in Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. 

I worked mostly with continous data in establishment surveys, and model-based sampling and estimation, which is a different concept, but for both that and the continuous data in Cochran with randomized selection, you need information on the standard deviation for each of those subpopulations or strata, here from your data, in my case something similar for residuals. (Yes/no data are similar, but there is an easier way to get a worst case estimate that is commonly used in online calculators.)

Also, regarding sample size needs, you may need to familiarize yourself with the finite population correction  (fpc) factor.  (I have a definition on my RG page that I did for a Sage Publications encyclopedia.) 

At any rate, to obtain needed information, one thing Cochran suggested is a pilot study. In your case, especially if you do not have a good full time statistician and good software she/he can use, a pilot study would be very useful to get an idea of what you need. It might also help test your questionnaire, etc.  But big changes in your questionnaire may make changes to your sample size needs. And beware that different questions may have very different sample size needs.  Also, if you need a sample size that is too large for your resources, you might substantially increase nonsampling error - an area that is often too much neglected - which can badly distort everything.

So, in summary, I suggest that you review the difference between cluster and stratified random sampling; note where you might mean strata versus separate subpopulations of interest; review multistage sampling  (which increases the complexity of variance estimation); and beware of nonsampling errors.  A good reference(s) such as Cochran is important.  Standard errors are important. A pilot study may be essential.

Beware of both bias and standard errors for both sampling and nonsampling errors.

Note that I am not familiar with count data or likert scales, and information on those are likely found elsewhere, but the concepts of stratification and cluster sampling, bias and perhaps nonsampling error, and of possibly using a pilot study, should, I think, still apply in an analogous manner.

Cheers - Jim

Hi Mariam - the following might be helpful once you've sorted out the cluster and stratification.  If I understand your design, I think your cluster is the college. 

Since you can't randomize students to 1st or 4rth year,  the "observational" part of this article might help: 

Lancaster, G. A., et al. (2007). "Design of a clustered observational study to predict emergency admissions in the elderly: statistical reasoning in clinical practice." J Eval Clin Pract 13(2): 169-178.

Dear Mariam

Two of best books in sampling and sampling design are:

Cochran,W.G. (1977). Sampling techniques, Wiley.

Snedecor, W.G. and Cochran,W.G. (1989). Statistical Methods, Blackwell.

Regards,

Zuhair

Please read the following article " Stratified cluster sampling " https://www.bmj.com/content/347/bmj.f7016.full