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I want to know a book where "interesting" ways to select a sample are present, like selecting a sample using a coin (biased or unbiased) or sampling from a population where two groups are present, and each group is represented in the sample. An example would be, say, there are two age groups, and two genders in a population, and I want to select a sample such that inclusion probabilities are same for all units in the population, and both genders and both age groups are represented in my sample.

I have searched a lot and could not find any reference on how to systematically draw such samples. I think there should be a systematic algorithm for these, otherwise the solutions turn out to be too random and based on guessing.

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To your example, lets say the age groups are A & B and genders are M & F. If you wanted to select from a population with two age groups and two genders such that each combination has an equal probability in the final selection you would have to find and tag every point with one of the combination (A,M), (A,F), (B,M), (B,F). If the size of the sample you need is $N$, then you need $\frac{N}{4}$ from each tag. Now simply select $\frac{N}{4}$ uniformly randomly from each tagged set and you are done. Obviously you want to also check for edge cases that $\frac{N}{4}$ is less than the lowest count of the tagged set. If you want books in probability and sampling here is a good list to buy from. Hope that helps.

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