Calculate gamma (γ) for ordinal association in contingency tables
Try It FreeGoodman-Kruskal gamma (γ) measures the strength and direction of association between two ordinal variables. It ranges from −1 (perfect negative association) to +1 (perfect positive association), with 0 indicating no ordinal association. Gamma ignores tied pairs entirely, focusing only on concordant and discordant pairs.
Gamma is the simplest of the concordance-based measures:
Where C = number of concordant pairs and D = number of discordant pairs
A pair of observations is concordant if the observation that ranks higher on X also ranks higher on Y. It is discordant if the observation ranking higher on X ranks lower on Y. Tied pairs (where both observations have the same value on X or Y) are excluded from gamma's calculation.
Because gamma ignores ties, it tends to be larger in absolute value than tau-b or Somers' d for the same data. This can be an advantage (gamma focuses on the "pure" concordance signal) or disadvantage (gamma may overstate association when there are many ties). CrossTabs.com computes all ordinal measures simultaneously for comparison.
Use gamma when you want to ignore tied pairs and focus purely on concordance/discordance. Use tau-b when you want a more conservative measure that accounts for ties. Gamma is common in sociology and political science; tau-b is more common in other fields.
Yes. If all non-tied pairs are concordant (even if there are many ties), gamma = 1. This is both a strength and a limitation — gamma can reach its extremes more easily than tau-b, which is why some researchers prefer tau-b.
CrossTabs.com uses the Brown and Benedetti asymptotic standard error (ASE) formula to compute confidence intervals. For small samples, bootstrap CIs are also available.