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how can we show selecting a 1-in-k systematic sample from a population of size N is...

how can we show selecting a 1-in-k systematic sample from a population of size N is the same as selecting a unique cluster in the population of clusters. DON'T PROOF EXPLAIN IN WORDS USING GENERAL NOTATIONS(N,k,n）

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Answer #1

Basically in 1 in k systematic sampling the units of population are ordered in some way and 1 of the first k units is selected from thepopulation of size N and then we go on sampling those observations which are at kth unit/position from the previous sample till we have n samples with us therfore we denote this by (N,k,n).

In case of cluster sampling we first divide the N observations of population in k clusters such that each cluster have n observations in it that is N=k*n and then we select a cluster at random and all the n observations from that cluster are chosen.

So in both these cases only 1 sample is chosen randomly and at the end we have our desired n samples hence both the methods are the same.

Thank you !!

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