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In the article: The reasons to use stratified sampling rather than simple random sampling include[2] 1. If measurements within strata have lower standard deviation, stratification gives smaller error in estimation.

But I read in the reference: https://onlinecourses.science.psu.edu/stat506/node/27/

Stratification may produce a smaller error of estimation than would be produced by a simple random sample of the same size. This result is particularly true if measurements within strata are very homogeneous.

In my interpretation this is a whole other statement.

Paul Nollen (talk) 17:06, 15 July 2018 (UTC)[reply]

The first mathematical formulae in the article are introduced with the phrase "The mean and variance of stratified random sampling". However "mean" and "variance" are quantities that are defined for random variables, not for sampling procedures. Unless a sampling procedure employs a unique and universally understood random variable, it doesn't make sense to refer to the mean and variance of that procedure.

In the case of stratified sampling, there are examples on the internet (e.g. https://jkim.public.iastate.edu/teaching/book5.pdf Example 5.1) where the random variable associated with stratified sampling lacks the factor of 1/N that is suggested by formula given in the article. The article would be improved by stating explicitly what random variables are involved.

In particular, the meaning of ${\displaystyle s_{h}^{2}}$ should be explained by stating what random variable it refers to. It appears to be the variance of the random variable defined by taking a random sample of size 1 taken from (the entire population of) strata ${\displaystyle h}$ (as opposed to the variance of the random variable that is the mean value of a sample of size ${\displaystyle n_{h}}$ taken from that population.

Tashiro~enwiki (talk) 12:43, 16 May 2019 (UTC)[reply]

The results in this article are all found in the book "Sampling Techniques, Third Edition" by William G. Cochran (https://www.wiley.com/en-us/Sampling+Techniques%2C+3rd+Edition-p-9780471162407) I have no experience editing Wikipedia pages, but perhaps someone else with access to the book and knowledge of how to edit could follow up on this comment. WpeditTscott (talk) 18:58, 30 July 2023 (UTC)[reply]