To ascertain the appropriate sample size for your investigation into the purchasing behavior of businesses within a total population of 100,000, categorized into 12 distinct business types, it is imperative to calculate the sample size independently for each stratum (business type) and subsequently aggregate them. This systematic approach guarantees the precise capture of behavioral diversity within each stratum.

Here is a stepwise guide for determining the sample size for a stratified sample:

Thank you. That has confirmed my thinking. Much appreciated.

Uzair Essa Kori

Rod -

Because you have 12 business types for which you want information, I would not think of them as strata, but as subpopulations. For optimum strata you only want to know overall results, not necessarily information such as totals on the individual strata.

For quantitative information on each business, once you decide on the variables you need, you have to have a sampling plan for each subpopulation. If you use a simple random sample, that is very inefficient for businesses, because data are generally highly skewed. If you use an unequal probability sample (probability proportional to size, for example), that is problematic when you have multiple variables for which you want to collect data as this can be very bad for some variables and better for others. If you could use model-based sampling and 'prediction' (estimation for a random variable) - my area - that could work very well for each variable, but you need auxiliary (regressor) data, which I doubt that you have. However, you might try stratification by size within each subpopulation (business type). That way, you take a stratum of perhaps the largest businesses of a certain type, and perhaps census them. You could do a random sample of smaller cases in one or more other strata. However, for your quantitative results (such as totals) you need to weight the sampled cases appropriately, say by the inverse of the probability of selection. Once you obtain your results, it sounds like you need them to then do your analysis.

If you have questions about sample designs, you could do an internet search on your key word of interest, and include "Pennsylvania State University" in the search term. They provide a great deal of good information.

Best Wishes - Jim