Calculate Goodman-Kruskal Gamma for ordered tables

The Goodman-Kruskal \(\gamma\) statistic is a measure of association for ordinal factors in a two-way table proposed by Goodman and Kruskal (1954).

Usage

GKgamma(x, level = 0.95)

<!-- %\method{print}{GKgamma}{x, digits = 3, ...} -->

Arguments

x: A two-way frequency table, in matrix or table form. The rows and columns are considered to be ordinal factors
level: Confidence level for a significance test of \(\gamma \ne =\)

Value

Returns an object of class "GKgamma" with 6 components, as follows

gamma: The gamma statistic
C: Total number of concordant pairs in the table
D: Total number of discordant pairs in the table
sigma: Standard error of gamma
CIlevel: Confidence level
CI: Confidence interval

References

Agresti, A. Categorical Data Analysis. John Wiley & Sons, 2002, pp. 57–59.

Goodman, L. A., & Kruskal, W. H. (1954). Measures of association for cross classifications. Journal of the American Statistical Association, 49, 732-764.

Goodman, L. A., & Kruskal, W. H. (1963). Measures of association for cross classifications III: Approximate sampling theory. Journal of the American Statistical Association, 58, 310-364.

Author

Michael Friendly; original version by Laura Thompson

Examples

data(JobSat)
GKgamma(JobSat)
#> gamma        : 0.221 
#> std. error   : 0.117 
#> CI           : -0.009 0.451