Simultaneous Analysis of Variance Tests Using Friedman's χ       r    2     Statistics | Zendy

Jensen D. R. | Zendy

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Simultaneous Analysis of Variance Tests Using Friedman's χ r 2 Statistics

Author(s) -

Jensen D. R.

Publication year - 1988

Publication title -

biometrical journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.108

H-Index - 63

eISSN - 1521-4036

pISSN - 0323-3847

DOI - 10.1002/bimj.4710300504

Subject(s) - statistics , mathematics , multivariate statistics , marginal distribution , gaussian , variance (accounting) , multivariate analysis of variance , statistical hypothesis testing , multivariate normal distribution , econometrics , random variable , physics , accounting , quantum mechanics , business

This study develops simultaneous tests for shifts in marginal distributions pertaining to complete two‐way multivariate data not having Gaussian errors. Gerig's (1969) statistics based on ranks are used, a special case yielding Friedman's (1937) χ r 2Statistics statistics for the one‐dimensional marginal distributions. Exact α‐level procedures are not now available. Instead, approximate but conservative tests are constructed using available tables together with suitable probability inequalities. A variational result permits unlimited tests even when these are suggested by the data. The procedures are illustrated using data from field studies with peanuts; some extensions are noted; and selected percentage points are provided to support some of the tests.

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