Disproportionate Allocation to Strata

One type of random sampling employed in survey research is the use of disproportionate allocation to strata. Disproportionate allocation to strata sampling involves dividing the population of interest into mutually exclusive and exhaustive strata and selecting elements (e.g. households or persons) from each stratum.

Commonly used strata include geographic units; for example, high-minority-density census tracts in a city are put into one stratum and low-minority-density census tracts are put into another stratum. In epidemiology case-control studies, strata are used where persons in one stratum have a condition of interest (e.g. Type I diabetes) and persons without the condition are put into a second stratum. After dividing the population into two or more strata, a “disproportionate” number of persons are selected from one stratum relative to others. In other words, the persons in one stratum have a higher probability of being included in the sample than are persons in the other strata.

This type of sampling can be used to create a more efficient sample design with more statistical power to detect key differences within a population than a simple random sample design or a proportionate stratified sample design. An example of a difference within a population is the comparison of older and younger persons with respect to some characteristic, such as having health insurance. However, a disproportionate allocation can also produce some results that are much more inefficient than a simple random sample or a proportionate stratified sample design.

Disproportionate allocation to strata as a technique can be more efficient than a simple random sample design. Efficiency is determined by whether the sample variances are smaller or larger than they would have been if the same number of cases had been sampled using a simple random sample.

Researchers use disproportionate allocation to strata in order to increase the number of persons with important characteristics within their final study sample and to increase the efficiency of the sample design over simple random sampling. When making estimates using a sample that has used disproportionate allocation to strata sampling, it is important to control for the differences in the probabilities of selection into the sample. Persons from some strata will have been more likely to be included than persons from other strata. To accomplish this task, survey weights are used to adjust each person for their probability of selection into the sample when making estimates of specific characteristics for the entire population.

Disproportionate allocation to strata can make some estimates more (or less) efficient than if the same number of cases had been selected using simple random sampling. Efficiency is gained to the extent that the variables used to stratify the target population are related to the characteristic being studied. For example, when stratifying a health insurance survey by age into two strata—those 65 years of age and older and those under 65 years—the outcome variable of interest, “health insurance coverage,” is strongly related to the variable used to stratify. People 65 years of age and over are much more likely to be insured than those under 65 years. The same is true for case-control studies where the condition of interest is used to stratify the target population and the resulting sample is more efficient for studying differences between those with a condition and those that are known to have the condition than would have been possible through a simple random sample of the population.

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