During the 1930’s or prior to that, researchers that focused on poverty and demographic-related issues were divided into two different schools of thought. The first group advocated for separating the sampling frame into groups that are distinct from one another and select units that was important to “represent” the population. The second group advocated the random sampling to give each person an equal chance of selection through randomization. Jerzy Newman combined the strengths of the two approaches into his own allocation method. His approach can be down in the following steps:
Before a random selection is conducted, the population / sampling frame are separated into different strata.
Use random sampling to sample from each stratum. Obtain the confidence limits. In this approach, the sample size is weighted by both the population proportions (Wh) and standard deviation (Sh) for that stratum. As such, more is sampled from stratum with stratum with larger population proportion (Wh) and more variability (Sh).
This approach can provide more accurate estimates over the simple random sampling and proportionate allocation sampling approaches. However it has several limitations:
Very large % differences between strata is needed for it to work. Variables that fulfill that criterion are rare.
The population proportion (Wh) and variability (Sh) will tend to vary from variable to variable, thus, a different allocation may be needed for each variable. The allocation for one variable may not be application for another variable.
Allocation done based on standard deviation (Sh) for that stratum may inflate the standard errors. See ProportionateVsNewman.pdf.
Nonresponse, coverage, and measurement errors are not taken into account in this allocation approach.