Because the Hardy-Weinberg principle tells us what to expect concerning the genetic composition of a sample when no evolutionary forces are operating, one of the first questions population geneticists often ask is ``Are the genotypes in this sample present in the expected, i.e., Hardy-Weinberg, proportions?'' We ask that question because we know that if the genotypes are not in Hardy-Weinberg proportions, at least one of the assumptions underlying derivation of the principle has been violated, i.e., that there is some evolutionary force operating on the population, and we know that we can use the magnitude and direction of the departure to say something about what those forces might be.
Of course we also know that the numbers in our sample may differ from expectation just because of random sampling error. For example, Table 1 presents data from a sample of 1000 English blood donors scored for MN phenotype. M and N are co-dominant, so that heterozygotes can be distinguished from the two homozygotes. Clearly the observed and expected numbers don't look very different. The differences semm likely to be attributable purely to chance, but we need some way of assessing that ``likeliness.''
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