Abstract
The sample lead can refer to the lead of one party over another in public opinion polls, of one product over another in market research surveys, of one programme over another in TV viewing surveys, etc. In applied statistics, it is common to assume that the distribution of the sample lead is approximately normal. The assumption is justified in most situations, but, when samples are small or when population proportions are extreme, the normal approximation may be inadequate. This paper describes the derivation of the exact distribution of the sample lead and employs it to test hypotheses when the normal approximation is inadequate. The exact distribution also can be used to check whether or not a particular distribution of the sample lead can be adequately represented by the normal distribution.
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