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We need to compare our statistic to values from the x2 distribution. But first we need to know how much information, or the degrees of freedom (commonly abbreviated as df), was used to estimate the x2 statistic. In general, degrees of freedom are based on the number of categories of data: df = no. of classes compared - no. of parameters estimated - 1

for the x2 test itself. In this case df = 3 - 1 -1 = 1 for three genotypes and one estimated allele frequency (with two alleles: the other allele frequency is fixed once the first has been estimated).

Figure 2.9 shows a x2 distribution for one degree of freedom. Small deviations of the observed from the expected are more probable since they leave more area of the distribution to the right of the x2 value. As the x2 value gets larger, the probability that the difference between the observed and expected is just due to chance sampling decreases (the area under the curve to the right gets smaller). Another way of saying this is that as the observed and expected get increasingly different, it becomes more improbable that our null hypothesis of Hardy-Weinberg is actually the process that is determining genotype frequencies. Using Table 2.5 we see that a x2 value of 7.46 with 1 df has a probability between 0.01 and 0.001. The conclusion is that the observed genotype frequencies would be observed less than 1% of the time in a population that actually had Hardy-Weinberg expected genotype frequencies. Under the null hypothesis we do not expect this much difference or more from Hardy-Weinberg expectations to occur often. By convention, we would reject chance as the explanation for the differences if the x2 value had a probability of 0.05 or less. In other words, if chance explains the difference in five trials out of 100 or less then we reject the hypothesis that the observed and expected patterns are the same. The critical value above which we reject the null hypothesis for a x2 test is 3.84 with 1 df, or in notation x2oo5 1 = 3.84. In this case, we can clearly see an excess of heterozygotes and deficits of homozygotes and employing the x2 test allows us to conclude that Hardy-Weinberg expected genotype frequencies are not present in the population.

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