By J.C.W. Rayner
"The equipment complex during this booklet have their genesis in conventional nonparametrics. They include the ability of recent pcs to make the process extra entire and extra legitimate than formerly attainable. The authors' unified therapy and readable sort make the topic effortless to keep on with and the concepts simply applied, even if you're a fledgling or a professional researcher."--BOOK JACKET.
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Additional info for A contingency table approach to nonparametric testing
R, and j = 1, ... , c, such that p i1 + ... + pic = 1 for i = 1, ... , r. Observations Ni1, ... , i = 1, ... , r that were known before the collection of the data. j, j = 1, ... , c; the total count is n... Suppose that the columns are ordered categories, and it is of interest to compare rows for similarity of location and dispersion effects. The null hypothesis is equality of the corresponding row probabilities. j = (p1j + ... + prj)/r for j = 1, ... j for i = 1, ... , r, and j = 1, ... , c, against the alternative hypothesis, not the null.
212217). This likelihood can be expressed as a product of extended or multivariate hypergeometric probability functions: r c i=2 j=1 ∏ ∏ n 1j + ... + n ijC n ij /n 1. + ... C n i. To find moments of the Nij, expectations may be taken with respect to the distribution of the second row conditional on knowledge of the column sums of the first two rows, then conditional on the column sums of the first three rows, and so on. It suffices to know the moments of the extended hypergeometric distribution.
Chapter 4 deals with two-way tables where only one margin is fixed. For Kruskal-Wallis-type data when there are no ties, the location component of an appropriate scalar multiple of Pearson’s X 2P statistic is the Kruskal-Wallis test. Our approach enables us to generalise to when there are ties, and to when there is a fixed number of categories and a large number of observations. For the generalisation of the well known median test, we show that the location detecting first component of X 2P reduces to the usual median test statistic when there are only two categories.
A contingency table approach to nonparametric testing by J.C.W. Rayner