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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.