Like all non-parametric statistics, the Chi-square is robust with respect to the distribution of the data. The Chi-square statistic is a non-parametric (distribution free) tool designed to analyze group differences when the dependent variable is measured at a nominal level. Unfortunately, these tests are also among the more commonly… The examination of cross-classified category data is common in evaluation and research, with Karl Pearson's family of chi-square tests representing one of the most utilized statistical analyses for answering questions about the association or difference between categorical variables. The Chi-Square Test: Often Used and More Often MisinterpretedĮRIC Educational Resources Information Centerįranke, Todd Michael Ho, Timothy Christie, Christina A. Government work and is in the public domain in the USA. The proposed methods are applied to a data set collected from a PET/CT imaging study for illustration. We develop large sample properties of the new proposed tests and estimators and evaluate their performance by simulations. In this article, we apply the within-cluster resampling technique to U-statistics to form new tests and rank-based correlation estimators for possibly tied clustered data.
When each sampling unit consists of a cluster of paired responses, the assumption of independent pairs is violated. However, the established statistical properties of these tests are only valid when each pair of responses are independent, where each sampling unit has only one pair of responses. Spearman rank correlation and Kendall's tau are often used for measuring and testing association between two continuous or ordered categorical responses. Pearson's chi-square test has been widely used in testing for association between two categorical responses. Pearson's chi-square test and rank correlation inferences for clustered data.
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