A new approach to distribution free tests in contingency tables

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• 作者：Thuong T. M. Nguyen
• 关键词：Contingency table ; Parametric testing ; Goodness of fit test ; Unitary transformation
• 刊名：Metrika
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：80
• 期：2
• 页码：153-170
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance; Probability Theory and Stochastic Processes; Economic Theory/Quantitative Economics/Mathematical Methods;
• 出版者：Springer Berlin Heidelberg
• ISSN：1435-926X
• 卷排序：80

文摘

We suggest an extremely wide class of asymptotically distribution free goodness of fit tests for testing independence in two-way contingency tables, or equivalently, independence of two discrete random variables. The nature of these tests is that the test statistics can be viewed as definite functions of the transformation of \(\widehat{T}_n = (\widehat{T}_{ij})=\Big (\frac{\nu _{ij}- n\hat{a}_i\hat{b}_j}{\sqrt{n\hat{a}_i\hat{b}_j}}\Big )\) where \(\nu _{ij}\) are frequencies and \(\hat{a}_i, \hat{b}_j\) are estimated marginal distributions. Our method is also applicable for testing independence of two discrete random vectors. We make some comparisons on statistical powers of the new tests with the conventional chi-square test and suggest some cases in which this class is significantly more powerful.