Population

With respect to research design and statistical analysis, a population is the entire collection of entities one seeks to understand or, more formally, about which one seeks to draw an inference. [Page 1053]Consequently, defining clearly the population of interest is a fundamental component of research design because the way in which the population is defined dictates the scope of the inferences resulting from the research effort.

When a population is small, it can be censused, meaning that the attribute of interest is measured for every member of the population and is therefore known with certainty. More often, however, a census is unrealistic because the population is not finite or because financial or logistical constraints override collection of complete information. In some cases, simply redefining the population may permit a census, perhaps by reducing the size or extent of the population of interest. When a census is still not feasible or when complete information about a population is unnecessary, a subset of the defined population called a sample is selected and measured. Attributes of the sample are used to make inferences about the entire population from which the sample was drawn. Statistical tools make use of these inductive inferences, using specific cases (the samples) to generalize or make inferences about the whole (the population). Specifically, a sample statistic provides an estimate of the population parameter, the true value of the attribute of interest. As George Snedecor and William Cochran wrote, it is the sample we observe, but the population we wish to know.

Such inductive inferences will be valid when the sample is drawn using an approach that ensures each unit of the population has a chance to be selected as part of the sample, such as a probabilistic sampling scheme, and inferences are restricted to the entities of the population that were available for sampling. For example, if data on test scores were collected from a random sample of undergraduate students enrolled in a specific calculus course at a single university, inferences apply only to that course and university and not to all undergraduates, all math courses, or all universities. If a researcher was interested in drawing general conclusions about current test scores in undergraduate calculus courses throughout the United States, undergraduate students currently enrolled in all calculus courses at universities across the United States must be available for selection as part of the random sample. This example emphasizes the importance of defining the population of interest explicitly when designing a sampling scheme because of its overriding importance on inference.