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Asymptotic significance level of a test of independence defined through Goodman-Kruskal’s measure of association. (Italian. English summary) Zbl 0749.62040

Summary: An independence test for categorical data in a two-way contingency table is defined through the Goodman-Kruskal measure of association. If \(n\) is sufficiently large, the distribution on which the test is based is approximately a linear combination of random variables \(\chi^ 2\) with coefficients depending on one of the marginal distributions – say \(Y\) – related to the two-way contingency table. In the first part of this paper the terms of this dependence are illustrated. If the \(Y\) distribution is uniform – “reference configuration”– the above-mentioned test corresponds with the Pearson’s \(\chi^ 2\) test. In the second part suitable corrections are proposed, to all the other situations, by means of some tables, for the significance levels pertinent to the reference configuration (i.e. with respect to the \(\chi^ 2\) test). In the appendix, supplied with a table, some remarks are made on the effectiveness of the series representation of the quadratic form distribution on which the test is based.

MSC:

62H17 Contingency tables
62H20 Measures of association (correlation, canonical correlation, etc.)
62G10 Nonparametric hypothesis testing
62Q05 Statistical tables
62G20 Asymptotic properties of nonparametric inference
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