GOLD - Available Statistics

Notation

Consider markers A and B, with r and c alleles, respectively. As usual, define the following variables based on observed haplotype counts:

These can be used to derive the haplotype frequencies:

The available measures of disequilibrium are defined in terms of the above quantities.

Lewontin's Disequilibrium Coefficient D and D'

The definition of Hedrick (1987), which allows for multi-allelic markers is used:

Delta-Squared Measure of disequilibrium

This is only defined for bi-allelic markers. The conventional definition (see for example, Devlin and Risch, 1995) is used:

Other Measures of Association - Chi-Squared

The usual contingency table chi-squared is calculated, and its significant is estimated from an asymptotic distribution with (r-1)(c-1) degrees of freedom.

Other Measures of Association - Uncertainty Coefficient U

The definition of Press, Teukolsky, Vetterling and Flannery, NRC (2nd Edition), is used:

H(A), H(B), H(A,B) refer to the informativeness of marker A, marker B, and the two marker genotypes together. U refers to how much information one marker provides on the other's genotype. It varies between 0 (independent) and 1 (completely dependent).

Other Measures of Association - Cramer's V

This is a transformation of the chi-squared statistic into the zero to one interval and is useful for comparing the relative intensity of association between marker pairs with the r and c. The definition of Press, Teukolsky, Vetterling and Flannery, NRC (2nd Edition), is used: