Page:Sm all cc.pdf/22

 population. If our subset is representative of the overall population, if it exhibits similar characteristics to any randomly chosen subset of the population, then our generalization may have applicability to behavior of the unsampled remainder of the population. If not, then we have merely succeeded in describing our subset.

Representative sampling is essential for successful averaging of random errors and avoidance of systematic errors, or bias. Random sampling achieves representative sampling. No other method is as consistently successful and free of bias. Sometimes, however, random sampling is not feasible. With random sampling, every specimen of the population should have an equal chance of being included in the sample. Every specimen needs to be numbered, and the sample specimens are selected with a random number generator. If we lack access to some members of the population, we need to employ countermeasures to prevent biased sampling and consequent loss of generality. Stratification is such a countermeasure. Stratification does not attempt random sampling of an entire population. Instead, one carefully selects a subset of the population in which a primary variable is present at a representative level.

Stratification is only useful for assuring representative sampling if the number of primary variables is small. Sociologists, for example, cannot expect to find and poll an ‘average American family’. They can, however, investigate urban versus rural responses while confining their sampling to a few geographical regions, if those regions give a stratified, representative sample of both urban and rural populations.

For small samples, stratification is actually more effective in dealing with a primary variable than is randomization: stratification deliberately assures a representative sampling of that variable, whereas randomization only approximately achieves a representative sample. For large samples and many variables, however, randomization is safer. Social sciences often use a combination of the two: stratification of a primary variable and randomization of other possible variables [Hoover, 1988]. For example, the Gallup and Harris polls use random sampling within a few representative areas.

In 1936, the first Gallup poll provided a stunning demonstration of the superiority of a representative sample over a large but biased sample. Based on polling twenty million people, the Literary Digest projected that Landon would defeat Roosevelt in the presidential election. The Literary Digest poll was based on driver’s license and telephone lists; only the richer segment of the depression-era population had cars or telephones. In contrast, George Gallup predicted victory for Roosevelt based on a representative sample of only ten thousand people. The concept of random sampling is counterintuitive to many new scientists and to the public. A carefully chosen sample seems preferable to one selected randomly, because we can avoid anomalous, rare, and unusual specimens and pick ones exhibiting the most typical, broad-scale characteristics. Unfortunately, the properties of such a sample probably cannot be extrapolated to the entire population. Statistical treatment of such data is invalid. Furthermore, sampling may be subconsciously biased, tending to yield results that fulfill the researcher’s expectations and miss unforeseen relationships (Chapter 6). Selective sampling may be a valid alternative to random sampling, if one confines interpretations to that portion of the population for which the sample is a representative subset.

Even representative sampling cannot assure that the results are identical to the behavior of the entire population. For example, a single coin flip, whether done by hand or by a cleverly designed unbiased machine, will yield a head or a tail, not 50% heads and 50% tails. The power of random sampling is that it can be analyzed reliably with quantitative statistical techniques such as those described in this chapter, allowing valid inferences about the entire population. Often these inferences