2. We have discussed predicting allele, genotype, and phenotype frequency using the Hardy-Weinberg equation But how much of a deviation is actually significant? One way is to use a chi-square (χ 2 ) test Essentially, if data deviates from predicted values too much, the χ 2 statistic will exceed a certain value

3. χ 2 = When this is computed, it is compared to established χ 2 which have been calculated based solely on chance The values are based on the degrees of freedom If it is exceeded, we reject the hypothesis

4. Degrees of Freedom5% Critical Value 13.841 25.991 37.815 49.488 511.070

5. Example The number of expected flowers of red, pink, and white phenotypes is listed below, along with the observed values. We hypothesize that the observed values are within statistical norms. Do a chi-square test to confirm or deny the hypothesis PhenotypeObservedExpected Red6263 Pink131125 White5761 Total250

6. Answer Use the equation: χ 2 = = = 0.875 The critical value is 5.991, so the hypothesis is not rejected.