Hardy-Weinberg calculator.

The Hardy-Weinberg equation

For a gene with two alleles at frequencies p and q, where p + q = 1, a population with random mating and none of the disturbing forces has genotype frequencies p² (AA), 2pq (Aa) and q² (aa). Wikipedia lists seven assumptions: diploid organisms, sexual reproduction, non-overlapping generations, random mating, a very large population, equal allele frequencies in the sexes, and no migration, gene flow, admixture, mutation or selection.

Worked example (chi-square). Wikipedia's example uses E. B. Ford's 1971 scarlet tiger moth data: 1469 AA, 138 Aa and 5 aa (1612 moths). The tool gets p = 0.9541 and expects 1,467.4, 141.2 and 3.4, for a chi-square of 0.83. With 1 degree of freedom (3 genotypes minus 2 alleles) the 5% critical value is 3.84, so the population is not rejected as being in Hardy-Weinberg proportions. The smallest expected count here is only 3.4, below the rule-of-thumb 5, so the result is approximate.

Worked example (carriers). Wikipedia's carrier example assumes about 1 in 2,500 babies are born with cystic fibrosis in Northern European populations. Then q² = 0.0004, q = 0.02, p = 0.98 and 2pq = 0.0392, roughly 1 carrier in 25.5. Wikipedia's shortcut of about twice the square root of the birth frequency gives 1 in 25.