Question

A stratified random sample was conducted to examine diabetes risk factors in Community X (N=3000). This small southeastern community only had non-Hispanic (NH) black (10%) and NH white (90%) residents. An investigator first stratified the population by race and then randomly selected an equal number of NH blacks (n=200) and NH whites (n=200) for the study.

Does this sampling strategy utilize equal allocation or proportional allocation?

Answer 1

Here N=3000

As proportion of NH blacks in the population is 0.10 so

Total number of NH blacks in the population=3000*0.1=300

While for NH whites proportion is 0.90

So number of NH whites =3000*0.9=2700

As 200 NH blacks and 200 NH whites selected for study

So total sample size =n=200+200=400

But according to proportional allocation in the stratified sampling : proportion of the any strata in the sample should be equal to proportion of that starta in the population.

So a/c to proportional allocation only 400*0.1=40 WH blacks have been selected for the study while 360 from WH blacks so it's not proportional allocation.

So this strategy utilities equal allocation.