Association Statistics

Computes the Pearson chi-Squared test, the Likelihood Ratio chi-Squared test, the phi coefficient, the contingency coefficient and Cramer's V for possibly stratified contingency tables.

assocstats(x)

Arguments

x

a contingency table, with possibly more than 2 dimensions. In this case, all dimensions except the first two ones are considered as strata.

Value

In case of a 2-dimensional table, a list with components:

chisq_tests

a \(2 \times 3\) table with the chi-squared statistics.

phi

The absolute value of the phi coefficient (only defined for \(2 \times 2\) tables).

cont

The contingency coefficient.

cramer

Cramer's V.

In case of higher-dimensional tables, a list of the above mentioned structure, each list component representing one stratum defined by the combinations of all levels of the stratum dimensions.

References

Michael Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

Fleiss, J. L. (1981). Statistical methods for rates and proportions (2nd ed). New York: Wiley

Author

David Meyer David.Meyer@R-project.org

Examples

data("Arthritis")
tab <- xtabs(~Improved + Treatment, data = Arthritis)
summary(assocstats(tab))
#> 
#> Call: xtabs(formula = ~Improved + Treatment, data = Arthritis)
#> Number of cases in table: 84 
#> Number of factors: 2 
#> Test for independence of all factors:
#> 	Chisq = 13.055, df = 2, p-value = 0.001463
#>                     X^2 df  P(> X^2)
#> Likelihood Ratio 13.530  2 0.0011536
#> Pearson          13.055  2 0.0014626
#> 
#> Phi-Coefficient   : NA 
#> Contingency Coeff.: 0.367 
#> Cramer's V        : 0.394 
#> 

assocstats(UCBAdmissions)
#> $`Dept:A`
#>                     X^2 df   P(> X^2)
#> Likelihood Ratio 19.054  1 1.2707e-05
#> Pearson          17.248  1 3.2804e-05
#> 
#> Phi-Coefficient   : 0.136 
#> Contingency Coeff.: 0.135 
#> Cramer's V        : 0.136 
#> 
#> $`Dept:B`
#>                      X^2 df P(> X^2)
#> Likelihood Ratio 0.25864  1  0.61105
#> Pearson          0.25372  1  0.61447
#> 
#> Phi-Coefficient   : 0.021 
#> Contingency Coeff.: 0.021 
#> Cramer's V        : 0.021 
#> 
#> $`Dept:C`
#>                      X^2 df P(> X^2)
#> Likelihood Ratio 0.75098  1  0.38616
#> Pearson          0.75354  1  0.38536
#> 
#> Phi-Coefficient   : 0.029 
#> Contingency Coeff.: 0.029 
#> Cramer's V        : 0.029 
#> 
#> $`Dept:D`
#>                      X^2 df P(> X^2)
#> Likelihood Ratio 0.29787  1  0.58522
#> Pearson          0.29798  1  0.58515
#> 
#> Phi-Coefficient   : 0.019 
#> Contingency Coeff.: 0.019 
#> Cramer's V        : 0.019 
#> 
#> $`Dept:E`
#>                      X^2 df P(> X^2)
#> Likelihood Ratio 0.99039  1  0.31965
#> Pearson          1.00107  1  0.31705
#> 
#> Phi-Coefficient   : 0.041 
#> Contingency Coeff.: 0.041 
#> Cramer's V        : 0.041 
#> 
#> $`Dept:F`
#>                      X^2 df P(> X^2)
#> Likelihood Ratio 0.38362  1  0.53567
#> Pearson          0.38409  1  0.53542
#> 
#> Phi-Coefficient   : 0.023 
#> Contingency Coeff.: 0.023 
#> Cramer's V        : 0.023 
#>