Digby's H is a measure of association for a 2 × 2 contingency table. It is a nonlinear transformation of the odds ratio, proposed by P. G. N. Digby in 1983 as a computationally simple approximation to the tetrachoric correlation coefficient, which otherwise requires iterative numerical estimation.
For a 2×2 table of binary variables U and V with cell frequencies or proportions
| V = 0 | V = 1 | |
|---|---|---|
| U = 0 | a | b |
| U = 1 | c | d |
the odds ratio is
Digby's H is defined as
Equivalently, in terms of the odds ratio,
Digby's H ranges from −1 to 1. It equals zero under statistical independence of U and V, since independence implies and hence . Positive values indicate positive association; negative values indicate negative association.
Because H depends on the table only through the ratio ad/bc, it is invariant under multiplication of all four cell frequencies by the same positive constant, and — like any function of the odds ratio alone — its value is determined by ω independently of the row and column marginal totals.
Digby's H belongs to a one-parameter family of odds-ratio transformations sometimes called generalized Yule coefficients,
where gives Yule's Q,
gives Yule's Y,
and gives Digby's H. All members of this family are zero under independence and share the same sign as .