Al Amin bin Mohamed Sultan -
It depends upon the kind of data you are collecting, and your design, and your goals. You should always stratify/break the population into categories/groups which are more homogeneous when you can. Standard deviations within each need to be "guessed" through means such as previous data or a pilot study. See the first book referenced below, for example, for more on this.
If you see an online calculator beware: They are usually for yes/no data, simple random sampling, no finite population correction factor, and worst case p=q. They are not generally applicable.
If you are looking at quantitative data, say continuous or yes/no, there are a number of good texts such as the following:
Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons.
Blair, E. and Blair, J(2015), Applied Survey Sampling, Sage Publications.
Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.
If you have auxiliary data, you can do better. You might also look at these, but they are fairly advanced:
Särndal, CE, Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang.
Brewer, KRW (2002), Combined survey sampling inference: Weighing Basu's elephants, Arnold: London and Oxford University Press.
An Introduction to Model-Based Survey Sampling with Applications, 2012,
Ray Chambers and Robert Clark, Oxford Statistical Science Series
Finite Population Sampling and Inference: A Prediction Approach, 2000,
Richard Valliant, Alan H. Dorfman, Richard M. Royall,
Wiley Series in Probability and Statistics.
Survey Sampling: Theory and Methods, First Edition, 1992,
Chaudhuri, A., Stenger, H.,
Marcel Dekker, lnc., New York, Basel, Hong Kong.
My thought though, is that you may be looking at relatively small samples of small categories of highly skewed establishment survey continuous data. If so, you might look at the small example data set shown on the last page of the following, and see how it was used in this paper:
If you are looking at such continuous data from establishment surveys, and have regressor data available, then there are other papers on my RG pages you might also use.
Note that there is a difference between trying to obtain an optimal sample size at a more aggregate level, with stratification, as opposed to being able to publish information for each of those strata, in which case it is better to think of them as subpopulations or categories, not strata. If you need to publish for each subpopulation, that generally requires a larger overall sample than if you only care about the most aggregate level, and not an individual stratum. This is true no matter what kind of sampling, and I suppose that the concept carries over to all kinds of data.
For an interesting historical account which also covers different types of sampling and estimation to a nice but easier-than-usual to understand degree, for continuous data, see the following (noting that the one model-only example uses the classical ratio estimator level of heteroscedasticity, though that is just one possibility):
Ken Brewer's Waksberg Award article:
Brewer, K.R.W. (2014), “Three controversies in the history of survey sampling,” Survey Methodology,
(December 2013/January 2014), Vol 39, No 2, pp. 249-262. Statistics Canada, Catalogue No. 12-001-X.
Ken Brewer believed in using probability sampling and models together, but he explains the different approaches, the pros and cons, in this rather 'fun' paper.
Cheers -
Jim Knaub
