Is your goal to build a regression model that predicts the amount of infectious and non-infectious waste by size and location of hospital?  You really don't have a large enough population to be able to say something about every cluster, but by sampling one hospital from every cluster, you would have 12 data points that cover the universe of interest, and could probably come up with a decent model - IF you have reason to believe that number of beds and location are the appropriate variables.  Mr. Shi, above, is correct in saying that a regression model would be better with more data, but given your additional information, I think it is probably the most practical solution.

A this point I have more questions for you than answers. 

Once you have the answers to those questions there are standard techniques to determine the sample size (which should be the same for each cluster).

If your answer to question 1 is "no" then see below.

If you are distributing a survey at the hospital level, the sampling is not really the issue: your population is small enough that you should survey every hospital, and possibly consider only one axis (probably hospital size) because you really can't say anything about a population of one other than to report the responses.

Although the picture is not fully clear but I can give some clue. You better stratify on one side e.g. the beds or the location. If  you take the beds you can do dichotomy ( 0-30 and more than 30). It is not advisable to have more cells specially if the sample is small.

Stratification also needs sometimes to multiply by a factor to increase the sample (design effect).

Still we do not know the unit of yr study. is it patients? If so sample is going to be divided according to population size. If the unit of sampling is patients then a calculated random sample can be taken to be representative. Again you need to have another sampling method to select patients may be simple random sampling.

regards

Hi,

Yes, the cluster sampling should be used only when it is economically justified.  This is most likely to occur is as following:

Constructing a complete list of population elements is a difficult task, it involves a costly one, or impossible one.

For example, it may not be possible to list all of the customers of a chain of hardware stores. However, it would be possible to randomly select a subset of stores by stage 1 of cluster sampling and then interview a random sample of customers who visit those stores by stage 2 of cluster sampling.  Minimum sample needed to do this analysis was 30 and more.

Parametric regression is not recommended because of small sample size. Assumed distributions might not fit well in small data or might not fit at all. Also hypothesis testing tends to be weak. For parametric analysis, the more data you have the better. Optimal Discriminant Analysis (ODA) and the related classification tree analysis (CTA) could help you. I think this book by Paul R. Yanold will provide you with a good guidance on how to carry out UniODA analysis:

http://www.amazon.com/Optimal-Data-Analysis-Guidebook-Software/dp/1557989818/ref=sr_1_3?ie=UTF8&qid=1417518400&sr=8-3&keywords=Paul+R.+Yarnold

The book is easy to follow coming with the UniODA software.

He also has many papers on RG and his website: http://odajournal.com/

I'm going to sort and weigh infectious and non-infectious wastes at these hospitals. Since the minimum amount of time spent per hospital would be a week, I want to avoid spending 31 weeks to cover all the hospitals. 

Is your goal to build a regression model that predicts the amount of infectious and non-infectious waste by size and location of hospital?  You really don't have a large enough population to be able to say something about every cluster, but by sampling one hospital from every cluster, you would have 12 data points that cover the universe of interest, and could probably come up with a decent model - IF you have reason to believe that number of beds and location are the appropriate variables.  Mr. Shi, above, is correct in saying that a regression model would be better with more data, but given your additional information, I think it is probably the most practical solution.

Syed - 

If you look at a survey sampling book, you can find cluster sampling and stratified random sampling. I think you may mean you have strata, not clusters. For each stratum, if you did a simple random sample, you would have a stratified random sample. 

One really easy to read book is by Sharon Lohr (2nd ed 2010) on survey design and analysis, though I think rather expensive. A really good old sampling book that would cover simple random, cluster, and stratified random sampling info and sample size would be WG Cochran (3rd ed 1977), Sampling Techniques, John Wiley & Sons. 

Jim

From your presentation, I would say that your grouping could qualify more as "strata" than "clusters". In cluster sampling, the selected clusters must approximate all of the clusters in terms of characteristics, which in your case cannot.

I agree with James.