Use of Pearson’s Chi-Square for Testing Equality of Percentile Profiles across Multiple Populations


In large sample studies where distributions may be skewed and not readily transformed to symmetry, it may be of greater interest to compare different distributions in terms of percentiles rather than means. For example, it may be more informative to compare two or more populations with respect to their within population distributions by testing the hypothesis that their corresponding respective 10th, 50th, and 90th percentiles are equal. As a generalization of the median test, the proposed test statistic is asymptotically distributed as Chi-square with degrees of freedom dependent upon the number of percentiles tested and constraints of the null hypothesis. Results from simulation studies are used to validate the nominal 0.05 significance level under the null hypothesis, and asymptotic power properties that are suitable for testing equality of percentile profiles against selected profile discrepancies for a variety of underlying distributions. A pragmatic example is provided to illustrate the comparison of the percentile profiles for four body mass index distributions.

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Johnson, W. , Beyl, R. , Burton, J. , Johnson, C. , Romer, J. and Zhang, L. (2015) Use of Pearson’s Chi-Square for Testing Equality of Percentile Profiles across Multiple Populations. Open Journal of Statistics, 5, 412-420. doi: 10.4236/ojs.2015.55043.

Conflicts of Interest

The authors declare no conflicts of interest.


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[2] Zhang, L., Beyl, R., Burton, J., Johnson, C.M., Han, H. and Johnson, W.D. (2014) A Large Sample Statistical Test for Equality of Percentile Profiles across Multiple Populations. Proceedings of the Joint Statistical Meetings of the American Statistical Association, Biometric Society and Institute of Mathematical Statistics Section on Statistics in Epidemiology, Boston, 2-7 August 2014, 3851-3857.

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