Measuring association between nominal categorical variables: an alternative to the Goodman-Kruskal lambda

As a measure of association between two nominal categorical variables, the lambda coefficient or Goodman-Kruskal's lambda has become a most popular measure. Its popularity is primarily due to its simple and meaningful definition and interpretation in terms of the proportional reduction in error when predicting a random observation's category for one variable given (versus not knowing) its category for the other variable. It is an asymmetric measure, although a symmetric version is available. The lambda coefficient does, however, have a widely recognized limitation: it can equal zero even when there is no independence between the variables and when all other measures take on positive values. In order to mitigate this problem, an alternative lambda coefficient is introduced in this paper as a slight modification of the Goodman-Kruskal lambda. The properties of the new measure are discussed and a symmetric form is introduced. A statistical inference procedure is developed and a numerical example is provided.