# Find the null and alternate hypothesis.

The result is chi-square=5.61, 1 d.f., *P*=0.018, indicating that you can reject the null hypothesis; there are significantly more left-billed crossbills than right-billed.

## The latter has a lower variance under the null hypothesis.

### where the expected value from Hardy–Weinberg equilibrium is given by

If your critical value is less than 3.84 then there is a 95%probability that the difference between observed and expected was caused bychance alone; therefore you would accept the null hypothesis that the observedand expected values are not significantly different, and that your population isindeed in Hardy Weinberg equilibrium.

### In otherwords, we use Hardy-Weinberg equilibrium as a null model.

The principle was thus known as *Hardy's law* in the until 1943, when pointed out that it had first been formulated independently in 1908 by the German physician .^{}^{} Others have attempted to associate name with the Law because of his work in 1903, but it is only rarely seen as the Hardy–Weinberg–Castle Law.

## EvoMath 2: Testing for Hardy-Weinberg Equilibrium

Population differentiation can be assessed by determining whether allelic composition is independent of population assignment (Raymond and Rousset, 1995a). The statistical test is based on analysis of contingency tables using a Markov Chain procedure to derive an unbiased estimate of the exact probability of being wrong in rejecting the null hypothesis, i.e. allelic composition is independent of population assignment (no differentiation). The test is performed for pair-wise inter-population comparisons on contingency tables containing data from each of the microsatellite loci studied. The FSTAT, and POPULATIONS statistical program’s can be used to perform the computations.

## Hardy-Weinberg Equilibrium and Chi-Square Analysis

can be applied to testing for Hardy–Weinberg proportions. Because the test is conditional on the allele frequencies, *p* and *q*, the problem can be viewed as testing for the proper number of heterozygotes. In this way, the hypothesis of Hardy–Weinberg proportions is rejected if the number of heterozygotes are too large or too small. The conditional probabilities for the heterozygote, given the allele frequencies are given in Emigh (1980) as