Methods and formulas for other measures of association for Cross Tabulation and Chi-Square

Select the method or formula of your choice.

Cramer's v2

Cramer's v2 measures association based on Pearson's chi-square statistics.

Formula

Notation

TermDescription
χ2 Pearson chi-square statistic
r number of rows
c number of columns
n++ total number of observations

Kappa statistic

Kappa measures the level of agreement between two raters that assign units to a set of categories. A kappa value of 1 corresponds to perfect agreement. A kappa value of 0 reflects no better agreement than would be expected by chance.

Formula

Notation

TermDescription
ni+ number of observations in the ith row
n+i number of observations in the ith column
nii observation in the cell corresponding to the ith row and ith column
n++ total number of observations

Lambda

Goodman-Kruskal lambda is a measure of association for cross tabulations of nominal-level variables. Lambda measures the improvement in predictability of the dependent variable (column or row variable) given the value of other variables (row or column variable). Misclassification probabilities are calculated based on assignment to the category with the greatest probability.

Formula

Lambda with Y (column variable) as the dependent variable:

Lambda with X (row variable) as the dependent variable:

Notation

TermDescription
c number of columns
r number of rows
ni+ number of observations in the ith row
n+j number of observations in the jth column
nij observations in the cell corresponding to ith row and jth column
n++ total number of observations

Tau

Goodman-Kruskal tau is a measure of association for cross tabulations of nominal-level variables. Tau measures the improvement in predictability of the dependent variable (column or row variable) given the value of other variables (row or column variable).The misclassification probabilities are calculated based on random category assignment with probabilities given by marginal or conditional proportions.

Formula

Tau with Y (column variable) as the dependent variable:

Tau with X (row variable) as the dependent variable:

Notation

TermDescription
ni+ number of observations in the ith row
n+i number of observations in the jth column
nij observations in the cell corresponding to the ith row and jth column
n++ total number of observations
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