# Empirical Generalization

A form of inductive reasoning in which a general statement is made about an entire group (the “target population”) based on observing some members of the group (the “sample population”)

One of the most important tools used by both natural and social scientists is empirical generalization. Have you ever wondered how the major television and radio networks can accurately predict election results hours before the polls close? These predictions are made possible by the power of empirical generalization, a first major type of inductive reasoning that is defined as reasoning from a limited sample to a general conclusion based on this sample.

Network election predictions, as well as public opinion polls that occur through- out a political campaign, are based on interviews with a select number of people. Ideally, pollsters would interview everyone in the target population (in this case, voters), but this, of course, is hardly practical. Instead, they select a relatively small group of individuals from the target population, known as a sample, who they have deter- mined will adequately represent the group as a whole. Pollsters believe that they can then generalize the opinions of this smaller group to the target population. And with a few notable exceptions (such as in the 1948 presidential election, when New York governor Thomas Dewey went to bed believing he had been elected president and woke up a loser to Harry Truman, and the 2000 election, when Al Gore was briefly declared the presidential winner over George W. Bush), these results are highly accurate.

There are three key criteria for evaluating inductive arguments:

• Is the sample known?

• Is the sample sufficient?

• Is the sample representative?

IS THE SAMPLE KNOWN?

An inductive argument is only as strong as the sample on which it is based. For example, sample populations described in vague and unclear terms—“highly placed sources” or “many young people interviewed,” for example—provide a treacher- ously weak foundation for generalizing to larger populations. In order for an inductive argument to be persuasive, the sample population should be explicitly known and clearly identified. Natural and social scientists take great care in selecting the members in the sample groups, and this is an important part of the data that is available to outside investigators who may wish to evaluate and verify the results.

IS THE SAMPLE SUFFICIENT?

The second criterion for evaluating inductive reasoning is to consider the size of the sample. It should be sufficiently large to give an accurate sense of the group as a whole. In the polling example discussed earlier, we would be concerned if only a few registered voters had been interviewed, and the results of these inter- views were then generalized to a much larger population. Overall, the larger the sample, the more reliable the inductive conclusions. Natural and social scientists have developed precise guidelines for determining the size of the sample needed to achieve reliable results. For example, poll results are often accompanied by a qualification such as “These results are subject to an error factor of 63 percentage points.” This means that if the sample reveals that 47 percent of those interviewed prefer candidate X, then we can reliably state that 44 to 50 percent of the target population prefer candidate X. Because a sample is usually a small portion of the target population, we can rarely state that the two match each other exactly—there must always be some room for variation. The exceptions to this are situations in which the target population is completely homogeneous. For example, tasting one cookie from a bag of cookies is usually enough to tell us whether or not the entire bag is stale.

IS THE SAMPLE REPRESENTATIVE?

The third crucial element in effective inductive reasoning is the representativeness of the sample. If we are to generalize with confidence from the sample to the tar- get population, then we have to be sure the sample is similar to the larger group from which it is drawn in all relevant aspects. For instance, in the polling example the sample population should reflect the same percentage of men and women, of Democrats and Republicans, of young and old, and so on, as the target population. It is obvious that many characteristics, such as hair color, favorite food, and shoe size, are not relevant to the comparison. The better the sample reflects the target population in terms of relevant qualities, the better the accuracy of the generalizations. However, when the sample is not representative of the target population—for example, if the election pollsters interviewed only females between the ages of thirty and thirty-five—then the sample is termed biased, and any generalizations about the target population will be highly suspect.

How do we ensure that the sample is representative of the target population? One important device is random selection, a selection strategy in which every member of the target population has an equal chance of being included in the sample. For example, the various techniques used to select winning lottery tickets are supposed to be random—each ticket is supposed to have an equal chance of winning. In complex cases of inductive reasoning—such as polling—random selection is often combined with the confirmation that all of the important categories in the population are adequately represented. For example, an election pollster would want to be certain that all significant geographical areas are included and then would randomly select individuals from within those areas to compose the sample.

Understanding the principles of empirical generalization is of crucial importance to effective thinking because we are continually challenged to construct and evaluate this form of inductive argument in our lives.

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