A Coefficient of Association Between Categorical Variables With Partial or Tentative Ordering of Categories

TY - JOUR

T1 - A Coefficient of Association Between Categorical Variables With Partial or Tentative Ordering of Categories

AU - Siersma, Volkert

AU - Kreiner, Svend

PY - 2009

Y1 - 2009

N2 - Goodman and Kruskal's gamma coefficient measuring monotone association and its partial variants are useful for the analysis of multiway contingency tables containing ordinal variables. When the categories of a variable are only partly ordered and the variable is treated as a nominal variable, information in the ordering of the categories and statistical power is lost. The authors suggest a (P)gamma measure that is the maximum of the ordinary gamma coefficients obtained by permuting the categories of nominal or partially ordered variables, while leaving the partial ordering intact. When the assumption of a monotone underlying association is justified, this measure has higher power than nominal tests for association. Furthermore, the resulting optimal monotone ordering gives insight into the nature of this association, which is not obtained by tests for nominal variables. The properties of the (P)gamma coefficient are investigated in a simulation study and its use illustrated in two data sets.

AB - Goodman and Kruskal's gamma coefficient measuring monotone association and its partial variants are useful for the analysis of multiway contingency tables containing ordinal variables. When the categories of a variable are only partly ordered and the variable is treated as a nominal variable, information in the ordering of the categories and statistical power is lost. The authors suggest a (P)gamma measure that is the maximum of the ordinary gamma coefficients obtained by permuting the categories of nominal or partially ordered variables, while leaving the partial ordering intact. When the assumption of a monotone underlying association is justified, this measure has higher power than nominal tests for association. Furthermore, the resulting optimal monotone ordering gives insight into the nature of this association, which is not obtained by tests for nominal variables. The properties of the (P)gamma coefficient are investigated in a simulation study and its use illustrated in two data sets.

U2 - 10.1177/0049124109346161

DO - 10.1177/0049124109346161

M3 - Journal article

SN - 0049-1241

VL - 38

SP - 265

EP - 286

JO - Sociological Methods and Research

JF - Sociological Methods and Research

IS - 2

ER -