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## Proportionate Stratified Random Sampling Technique (6 replies)

Most of my practical experience in sampling is limited to coal, iron and copper ores, concentrates and potash and I am having difficulty in visualizing a need for proportionate stratified random sampling. Of course, ordinary stratified random sampling is a good idea when there are cyclic variations in the quality of material streams that could be in phase with the timing of collection of increments using systematic sampling. Could you share an example with the group of a possible application for proportionate stratified random sampling?

I speak generally for the steps of proportionate stratified random process. The application refers to a population of farmers. I want to get a sample from this population using that method. I don’t know if someone can help me with this. :)) Just want to know the order of the process' steps.

Thank you for the clarification. I had my head stuck in minerals rather than people and I now understand that proportionate SRS means sampling the sample fraction of units/people in each stratum whereas disproportionate SRS involves targeting the same variance of the stratum mean from each stratum (using prior guesses of the variance of units within each of the various strata. Thus proportionate SRS is what I called "ordinary" SRS in the previous post. Now back to your question. The key here it seems to me is in first creating each individual stratum with minimum variance with the stratum, i.e., creating groups of farmers with characteristics of interest that are the most alike. There is guesswork in doing this, of course, as you have not yet sampled the farmers. It would help if you began with a smaller sample intended to give you the information needed for optimum design of the more expensive effort.

In paper, P. Minkkinen, Practical Applications of Sampling Theory, Chemometrics and Intelligent Laboratory Systems, 74 (2004) 85-94, you will find basics how to design/optimize a sampling plan when sampling populations consisting of substrata which differ in size, average concentration and measurement variance. If you can read German you find a good account on stratified sampling also in K. Sommer's book, Probenahme von Pulvern und koernigenMassenguetern, Springer, Berlin, 1979.

First you should identify the strata, which you assume or know to be homogeneous. How you proceed then depends what is the purpose of your sampling and how much apriority information you have. If your purpose is to estimate the mean of the whole lot consisting of different strata and the only information you have is the sizes of the strata then the number of samples taken from each stratum should be proportional to the size of the stratum. If you have carried out a pilot study to estimate the within-strata variances and have estimates for unit costs of the sampling, sample preparation and analysis, you can design an optimized sampling and analysis plan. There are two options for optimization:

You have a fixed budget. In this case you make a plan which minimizes the variance of the lot mean keeping the total cost within your budget.

Maximum allowed variance of the lot mean is given. In this case plan is made so that total cost of the study is minimized without exceeding the allowed variance of the lot mean.

In general, the dilemma in making sampling plans/protocols is that you cannot make a good sampling plan in a given sampling target before you have carried out sampling. Therefore, in all new situations and sampling targets a pilot study is necessary before making the final protocol.

Which are the steps for the Proportionate Stratified Random Sampling Technique? In which step we determine the size of the sample?