The “Law of Large Populations” Does Not Herald a Paradigm Shift in Survey Sampling
The “Law of Large Populations” Does Not Herald a Paradigm Shift in Survey Sampling (DOI: https://doi.org/10.1162/99608f92.6b049957) was written by Roderick J. Little in 2023. It was published in the Harvard Data Science Review (issue 5, no. 3). It is a comment on Bailey (2023).
The author proposed an alternative formulation of bias: b = (1 - f)(Ȳn - ȲN-n) given sampling fraction f = n/N.
The conventional measure of accuracy, i.e. precision (variance) plus bias, is the RMSE:
The important difference between this and the Meng equation is that errors depend on sample size n rather than population size N.
The author also notes a parallel between the data defect component in Meng's equation and the more conventional Heckman correction. At the same time, the author notes that other approaches may be more transparent, as they decompose the bias into the difference in proportions between the selected and unselected cases.
Lastly, the author notes that data defect component cannot be treated as a universal constant; for the equation to hold it must vary with the population size, all else equal.