lawstat (version 2.3)

cmh.test: The Cochran-Mantel-Haenszel Chi-square Test

Description

This function performs the Cochran-Mantel-Haenszel (CMH) procedure. The CMH procedure tests independence of two variables in each stratum, conditionally on the levels of a third variable. This procedure is widely used in various law cases, in particular, on equal employment and discrimination, as well in biopharmaceutical studies (Agresti, 2002; Gastwirth, 1984; Hall et al., 1999).

Usage

cmh.test(x)

Arguments

x

a numeric 2 x 2 x k array of data values.

Value

• A list with class htest containing the following components:
• cmh
  the Cochran-Mantel-Haenszel test statistic (chi-squared distributed).
• df
  degrees of freedom of the Cochran-Mantel-Haenszel test statistic (equal to 1).
• p.value
  the p-value of the Cochran-Mantel-Haenszel test.
• MH.ESTIMATE
  the Mantel-Haenszel odds ratio estimator.
• OR
  Direct Pooled Odds Ratio Estimator of the data.
• ORK
  vector of Odd Ratios for each level data.
• DNAME
  a character string giving the name of the data.
• method
  type of the performed test.

Details

The data input is in a form of an array of 2 rows x 2 columns x k levels. The output includes the Cochran-Mantel-Haenszel (CMH) test statistic which is chi-squared distributed with 1 degree of freedom, the corresponding p-value for the CMH statistic, the Mantel-Haenszel odds ratio estimator, the direct pooled odd ratio estimator, and the odd ratios between the rows and columns at each level. The null hypothesis is that two variables in each stratum are independent, conditionally on the levels of a third variable. Hence, under the null hypothesis, estimators of odds ratio, i.e. the Mantel-Haensel and direct pooled estimators, are to be 1.

References

Agresti, A. (2002). Categorical data analysis. (second edition). New York: Wiley. Gastwirth, J. L.(1984) Statistical Methods for Analyzing Claims of Employment Discrimination, Industrial and Labor Relations Review, Vol. 38, No. 1. (October 1984), pp. 75-86. Hall, D.B., Woolson, R.F., Clarke, W.R., Jones, M.F. (1999). Cochran-Mantel-Haenszel Techniques: Applications Involving Epidemiologic Survey Data. In: Handbook of Statistics Volume 17: Bio-Environmental and Public Health Statistics. PK Sen and CR Rao, Eds. New York, NY: John Wiley and Sons.

See Also

mantelhaen.test (in stats)

Examples

## Sample Salary Data

data(blackhire)
cmh.test(blackhire)


## Sample Output
##
##        Cochran-Mantel-Haenszel Chi-square Test
##
## data:  blackhire 
## CMH statistic = 145.840, df = 1.000, p-value = 0.000, 
## MH Estimate = 0.477, Pooled Odd Ratio = 0.639 
## Odd Ratio of level 1 = 1.329, Odd Ratio of level 2 = 0.378, 
## Odd Ratio of level 3 = 0.508, Odd Ratio of level 4 = 0.357, 
## Odd Ratio of level 5 = 0.209, Odd Ratio of level 6 = 0.412, 
## Odd Ratio of level 7 = 0.250, Odd Ratio of level 8 = 0.820
## 
## Note: P-value is significant and we should reject the null hypothesis.