Stratified random sample

A properly drawn simple random sample or a systematic random sample is a trustworthy way to select a sample, but for some investigations a stratified random sample is more appropriate.   A stratified random sample can be easily understood by defining its two key terms — stratified and random.   You already know that random means selection by chance.   Stratified simply refers to selection within subgroups that make up some population. The student population of a university, for example, can be stratified in several ways — by gender, into males and females; into class level, first, second, third and fourth years; by the college in which they are enrolled; or by undergraduate versus graduate levels.   Most populations can be stratified in one or more ways.

Selecting

In selecting a stratified random sample, the same steps are followed as with a simple random sample, except that an independent sample is selected from each of the strata of the population. The specific steps are:

1. Define the target population and strata to be used. As with all sampling, it is necessary to clearly define the target population and sampling element. In addition, for a stratified random sample, each strata to be sampled has to be defined. Definition of strata is a matter of choice and depends on the nature of the problem being investigated. A suitable sampling frame must be available for each strata.
2. Obtain or develop a suitable sampling frame for each strata. As described for a systematic sample, care must be taken to avoid conditions that could bias sample selection.
3. Decide on the sampling rate to be used for each strata. With stratified sampling, different rates can be used for each strata.   The value of this feature will become clear shortly.
4. Select a simple random or systematic sample within each strata. Either a simple random or a systemic sampling method can be used.

Strengths and limitations

A great advantage of stratified sampling is that different rates can be used for sampling different strata.   To illustrate, imagine you were studying differences on some issue between male and female students in a university with 2,500 male and 500 female students.   And suppose you wanted a sample of 300 students or 10% of this population.   If you used a simple or systematic sample you would get approximately 250 males and 50 females, give or take a certain number due to chance variations that occur with every sample.   But do you need 250 males to get enough data and would having data from only 50 females be enough?   Why make a comparison based on 250 versus 50?    Would it not be more sensible to base the comparison on an equal number of males and females?

Yes, it would; and this illustrates the great feature of stratified sampling.   Instead of selecting 10% of all the students, you could select separate samples of males and females of equal size.    Let's say you decide that the comparisons should be based on 100 students in each strata (male versus female).   To get 100 males you would select 100 out of the 2,500 males or a sample of about 4% while for females the sampling rate would be 100 out of 500 or about 20%.   Although different rates were used, each sample would be a legitimate sample for its strata.   Results from each strata could be used to describe characteristics of males versus females, provided, of course, that proper procedures were followed in selecting each of the samples. In addition, results from the samples could be safely generalized to the population represented by each strata; from the sample of males to the population of males, and the same for the females.

Stratified sampling, however, has some drawbacks First, to use it properly you have to know the proportion of each stratum in the population.   In our example, we did, but often in research in developing countries the proportions for strata are now known.    Some strata, therefore, may not be properly represented in the final sample.   Also, use of different sampling rates for various strata requires an adjustment called weighting when data from the strata are combined to describe some variable for the population as a whole.   A simple example of weighting is described later in this chapter. Weighting procedures, however, can become complicated.