Statistical Inference

Samples and Sampling

Why analysts draw samples is easy to understand: it may be too costly, time-consuming, or even inefficient to study all the people in the target population—all voters or all people with heart disease. More difficult to understand is how researchers make a statistical inference (for example, 70 percent of all American voters have confidence in the president) and assess its quality (that is, indicate how uncertain they are about the 70 percent figure, as indicated by the ± 5%). It is one thing, in other words, to say that 70 percent of the voters in the sample have confidence in the president; but it is quite another to say that 70 percent of all voters have confidence.

To support the first claim, all the analysts need to do is tally the responses to their survey. To support (and evaluate) the second, they must (1) draw a random probability sample of the population of interest and (2) determine how certain (or uncertain) they are that the value they observe from their sample of voters (70 percent), the sample statistic, reflects the population of voters, the population parameter.

A random probability sample involves identifying the population of interest (all American voters) and selecting a subset (the sample) according to known [Page 1435]probabilistic rules. To do this, a researcher must assign each member of the population a selection probability and select each person into the observed sample according to these probabilities. (Collecting all the observations is a special case of random selection with a selection probability of 1.0 for every element in the population.) Several different forms of random probability sampling exist, but the important point is that random selection is the only selection mechanism (in large-n studies, where n = number of participants) that automatically guarantees the absence of bias in the sample; that is, it guarantees that the sample is representative of the population. This is crucial because if a sample is biased (for instance, if Democrats had a better chance of being in the pollsters' sample than Republicans), researchers cannot draw accurate conclusions.

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