 Critical values of the Chi-square distribution at p = 0.05, 0.01, & 0.001 for d = 1 - 20 degrees of freedom

The critical value of a statistical test is the value at which, for any per-determined probability (p), the test indicates a result that is less probable than p.  Such a result is said to be statistically significant at that probability. Under most circumstances in experimental biology, the pre-determined p = 0.05, which indicates that the result that would happen by chance only once in twenty trials. Under some circumstances, p = 0.01 or 0.001, that is, the result would occur only once in a hundred or a thousand trials; p may also be reported as the upper bound of the probability of the observed result.

For a typical test of genotype frequencies in a two-allele model, there are three possible genotypes but only one degree of freedom, because the value of q automatically determines p = (1 - q). For example, if a chi-square comparison of the expected versus observed numbers of genotypes in a two-allele model (d = 1) gave a value of 2.0, the result would not be significant, and would be reported as p[0.05, df=1] = 2.0ns, where ns means not significant. A result of 5.0 would be reported as significant at p < 0.05, a result of 8.0 significant at p < 0.01, and a result of 20.0 as p < or << 0.001. The last three values might also be marked as 5.0*, 8.0**, and 20.0***, to indicate the level of significance.

See here for a further discussion of significance and statistical hypothesis testing.

Table rearranged from © 2013 by Sinauer; Text material © 2019 by Steven M. Carr