Cases of interest using affected sib-pair methods to distinguish between recessive and additive (dominant) modes of inheritance of a disease-predisposing gene involve goodness-of-fit tests with a small expected number in the "share-zero parental haplotypes" category, as well as an unknown parameter, the frequency of the disease-predisposing allele. Our simulations demonstrate that the real significance level of the chi-square test using the three-haplotype-sharing IBD values (share 2, 1, and 0 parental haplotypes) is close to the assumed (.05) level in these cases, so that the haplotype-sharing classes do not have to be lumped, which would leave no degrees of freedom for a statistical test. The validity of the chi-square approximation in cases of small expected frequencies has previously been described, but the situations that have been considered do not cover the very small values in the share-zero category that are often expected in the affected sib-pair analysis, nor do they involve estimation of an unknown parameter. Although including IBD values from affected kin pairs other than sibs can be a very powerful tool in demonstrating linkage of a marker and disease, these pairs do not add power, in fact they reduce the power, of the chi-square tests of goodness-of-fit of modes of inheritance.