Comparison of Different Measures of Correlation for Nominal Data
Author: Ansar Abbas

There are a number of tests available for testing association between categorical data arranged in contingency table. However, there is no clear guidance on the relative merits of these tests and about the appropriate choice of test, except for 2  2 contingency table. We evaluate various tests of independence including Pearson chisquare test of independence, Likelihood ratio chi-square test of independence, Goodman and Kruskal’s lambda test, Uncertainty coefficient, Generalized McNemar’s test (Stuart- Maxwell test), and Generalized fisher exact test (Fisher freeman-Halton test) on the basis of their size distortion and power for various alternatives by extensive Monte Carlo Simulation. We observe that there is no significant size distortion for all of these tests, therefore these tests are equivalent with respect to their size. However, the power of tests for various alternatives changes dramatically. We found that Generalized McNemar’s test (Stuart- Maxwell test) outperforms other test in terms of power. Therefor we recommends the use of Generalized McNemar’s test (Stuart- Maxwell test) for testing association in contingency table. So, this is the most powerful and robust test of independence/measures of correlation for nominal data. Supervisor:- Dr. Atiq -ur- Rehman

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Keywords : Different Measures, Nominal Data
Supervisor: Atiq Ur Rahman

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