[1][2][3][4] The estimate of gamma, G, depends on two quantities: where "ties" (cases where either of the two variables in the pair are equal) are dropped.
, where and where Ps and Pd are the probabilities that a randomly selected pair of observations will place in the same or opposite order respectively, when ranked by both variables.
Critical values for the gamma statistic are sometimes found by using an approximation, whereby a transformed value, t of the statistic is referred to Student t distribution, where[citation needed] and where n is the number of observations (not the number of pairs): A special case of Goodman and Kruskal's gamma is Yule's Q, also known as the Yule coefficient of association,[5] which is specific to 2×2 matrices.
Consider the following contingency table of events, where each value is a count of an event's frequency: Yule's Q is given by: Although computed in the same fashion as Goodman and Kruskal's gamma, it has a slightly broader interpretation because the distinction between nominal and ordinal scales becomes a matter of arbitrary labeling for dichotomous distinctions.
The sign depends on which pairings the analyst initially considered to be concordant, but this choice does not affect the magnitude.