<P> A classic example of a biased sample and the misleading results it produced occurred in 1936 . In the early days of opinion polling, the American Literary Digest magazine collected over two million postal surveys and predicted that the Republican candidate in the U.S. presidential election, Alf Landon, would beat the incumbent president, Franklin Roosevelt, by a large margin . The result was the exact opposite . The Literary Digest survey represented a sample collected from readers of the magazine, supplemented by records of registered automobile owners and telephone users . This sample included an over-representation of individuals who were rich, who, as a group, were more likely to vote for the Republican candidate . In contrast, a poll of only 50 thousand citizens selected by George Gallup's organization successfully predicted the result, leading to the popularity of the Gallup poll . </P> <P> Another classic example occurred in the 1948 presidential election . On election night, the Chicago Tribune printed the headline DEWEY DEFEATS TRUMAN, which turned out to be mistaken . In the morning the grinning president - elect, Harry S. Truman, was photographed holding a newspaper bearing this headline . The reason the Tribune was mistaken is that their editor trusted the results of a phone survey . Survey research was then in its infancy, and few academics realized that a sample of telephone users was not representative of the general population . Telephones were not yet widespread, and those who had them tended to be prosperous and have stable addresses . (In many cities, the Bell System telephone directory contained the same names as the Social Register). In addition, the Gallup poll that the Tribune based its headline on was over two weeks old at the time of the printing . </P> <P> If entire segments of the population are excluded from a sample, then there are no adjustments that can produce estimates that are representative of the entire population . But if some groups are underrepresented and the degree of underrepresentation can be quantified, then sample weights can correct the bias . However, the success of the correction is limited to the selection model chosen . If certain variables are missing the methods used to correct the bias could be inaccurate . </P> <P> For example, a hypothetical population might include 10 million men and 10 million women . Suppose that a biased sample of 100 patients included 20 men and 80 women . A researcher could correct for this imbalance by attaching a weight of 2.5 for each male and 0.625 for each female . This would adjust any estimates to achieve the same expected value as a sample that included exactly 50 men and 50 women, unless men and women differed in their likelihood of taking part in the survey . </P>

What is the difference between a representative sample and a biased sample