Strata

Stratification Variables

The final set of strata used for sampling is usually some type of cross-classification of the stratification variables. For example, stratification of individuals by two gender categories (i.e. male or female) and four educational attainment categories (i.e. less than a high school diploma, high school diploma, some college, or college degree and beyond) would imply 2×4 = 8 fully cross-classified strata. If the number of males in the population with some college or a college degree and beyond were considered to be too small, a partially collapsed set of seven strata might be formed from these two stratification variables by using all four female strata and by considering all males with [Page 849]some college or a college degree and beyond to comprise one stratum.

The choice of stratification variables depends on how sample stratification is to be used. When the purpose of stratification is to reduce the variance of the estimate of a characteristic of the population as a whole, it is best for the stratification variables to be statistically correlated with key outcome variables (i.e. member measurements that define the characteristics of interest). Thus, for example, if the outcome variable, annual income, is correlated with educational attainment among population members, then stratification by educational attainment would be a good choice when the population characteristic to be estimated is the average annual income of all population members.

Stratification may also be used to improve the quality of estimates for population subgroups. For instance, when stratification is used to disproportionately sample the subgroup, it is preferable to define strata by whatever characteristics define the subgroup. For instance, educational attainment, as defined earlier, should be a stratification variable when disproportionately sampling persons with less than a high school diploma. Note however, that equally valid though slightly less precise estimates can be obtained for subgroups, even if the categorical variables that would isolate the subgroup are not used to form the strata.

Defining Useful Strata

The ultimate goal in forming strata to improve the quality of estimates for the population as a whole is to define strata that are as internally homogeneous as possible with respect to the survey's key outcome variables. Thus, for example, if the main purpose of a sample of persons is to estimate their average annual income, then one hopes to sample from strata where members of each stratum have relatively similar income levels. This would mean that some strata have low-income earners, others have high-income earners, and the rest separately include those with various intermediate income levels.

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