What is a disproportionate stratified sample and why would you use one? In your answer, please include an example.

What will be an ideal response?

If we wished to analyze a population as a whole, a simple random sample might be an acceptable sample. But if we wished to investigate a question by looking at a small stratum within a large population using a simple random sample, we would find that the number of observations from the stratum of interest is too small a sample with which to draw inferences. To get around this problem we could use a disproportionate stratified sample—by including a far larger proportion of observations from the stratum of interest than is found in the population. Then we would have enough observations to draw inferences about the population of interest. For example, suppose we are conducting a survey of 200 students at a college in which there are 500 liberal arts majors, 100 engineering majors, and 200 business majors, for a total of 800 students and we wished to investigate students in each major separately, we would find that 25 engineering students was too small a sample with which to draw inferences about the population of engineering students. To get around this problem we could sample disproportionately—for example, we could include 100 liberal arts majors, 50 engineering majors, and 50 business majors in our study. Then we would have enough engineering students to draw inferences about the population of engineering majors. The problem now becomes evaluating the student population as a whole, since our sample is biased due to an undersampling of liberal arts majors and an oversampling of engineering majors. Suppose engineering students have high GPAs. Our sample estimate of the student body’s GPA would be biased upward because we have oversampled engineering students. Therefore, when we wish to analyze the total sample, not just a major, we need some method of adjusting our sample so that each major is represented in proportion to its real representation in the total student population.