Lets say I am sampling from an non-normal, multivariate population of unknown size and distribution.
I'd like to know when I can stop sampling from the population (to a certain error) and have a statistically representative sample of the population. i.e. all (or most) anticipated measurement samples are represented in proportion in the sample.
Can anyone recommend a good way of doing this?
Minitab software has done some good work in this area. Take a look at it
Stat / Power and Sample Size
What you are looking for is called sequential sampling. You can find out about it at this link:
https://www.google.com/search?q=sequential+sampling&ie=utf-8&oe=utf-8&client=firefox-b-1
Best wishes, David Booth
In Spanish there is a good book for this concern: "Ciencia del Muestreo", Bubok, Madrid. Regards.
Thanks for the answers. I think sequential analysis is a great starting point.
Just be aware that Sequential Analysis has some drawbacks and it could not be applicable to your special problem.
Another approach could be to choose a small random sample to get an preliminary estimation of the variance, and then calculate a sample size with the classical formulas for each of your variables, and get the sample size for the variable with the larger variance or rather for the most important variabl. This can have also its drawbacks, as this is somewhat an univariate approach.
Non-normality might be not major problem, however if you want to use multivariate approaches there are methods to calculate a global sample size. You can check this old question from Researchgate:
https://www.researchgate.net/post/How_to_calculate_sample_size_when_there_are_several_variables_of_interest
Regards
Robert -
Sample size 'formulas' generally assume bias is not a problem, and that for a given methodology, data type, and standard deviation(s), you want to know what overall sample size is needed. Books such as the following might be helpful for you here, on this question, to varying degrees:
Thompson, S.K.(2012), Sampling, 3rd ed, John Wiley & Sons.
Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons.
Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.
Blair, E. and Blair, J(2015), Applied Survey Sampling, Sage Publications.
If the population is very large, then for systematic sampling, or sequential sampling, or whatever you do, when you take a variance 'formula' and solve for n, any finite population correction (fpc) factor can be set to 1, and thus ignored.
I am not certain as to your exact question. As I think Mauricio indicated, you want to be sure your sample size is large enough for your most important variables. But you noted that you wanted "... all (or most) anticipated measurement samples [to be] represented in proportion in the sample." That is a bit confusing to me. You are really interested in variance.
You want key standard errors to be low enough for your purposes. (Note that population standard deviations are fixed values which you estimate better with larger sample sizes, but mean, or total, or proportion standard errors are values which change, becoming smaller with larger sample sizes. That is also when the central limit theorem becomes useful.)
Cheers - Jim
PS - For the variance formulas dependent upon randomization to hold for finding sample size requirements, and for representativeness, you cannot leave out some segment of your population. Thus if sequential sampling here does not cover the population as systematic does, you could have a substantial problem. Auxiliary data on the entire population could help, but that does not sound like an option for this case, although it may be. You might want to give everyone more information about your problem/application.
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