<- file 96chisq.html ->

Why use the *Pearson* contingency chisquared?

=====================Rich Ulrich, 5 Jun 1996==========sse From: wpilib+@pitt.edu (Richard F Ulrich) Subject: Re: Goodness-of-fit statistics Message-ID: <4p4fkt$rj6@usenet.srv.cis.pitt.edu> Rich Strauss (y8res@ttacs1.ttu.edu) wrote: Strauss asked about Pearson's chi-square statistic for goodness of fit, : (1) Is there any rationale, other than historical convenience, for using the : particular weighting scheme of Pearson's statistic? Let me recommend to you an article from a few months ago, "A single general method for the analysis of cross classified data: Reconciling [...<various existing statistics>...]", Leo Goodman, JASA, March 1996, Vol 91 #443:408-428. This discusses not only Pearson's test; (Fisher's) maximum likelihood log-linear test which is fairly common; a test advocated by Yule, and the whole family. The family was also mentioned in Agresti's _Categorical data analysis_ , which cites Cressie and Read for introducing it as "power divergence" statistics. ===================original post from Strauss : I'm interested in comparing a data distribution of counts against a : corresponding theoretical distribution that is given by theory. (I don't : believe that the details are relevant to my question, but I'd be glad to : provide them.) Of course, the conventional statistical test for this : situation is based on Pearson's "chi-square" statistic, which is convenient : because it approximately follows a chi-square distribution. However, : because Pearson's statistic weights the squared deviations by the reciprocal : expectations, the assessment of degree of fit is highly dependent on values : in the tail of the distribution. This leads to the standard rules of thumb : about avoiding cells having expectations less than 5, and so on. It seems : to me that a simple least-squares test statistic (with the null distribution : generated by repeated random sampling from the theoretical distribution) : would suitably balance the degree of fit throughout the entire distribution. : So, my questions are: : (1) Is there any rationale, other than historical convenience, for using the : particular weighting scheme of Pearson's statistic? : (2) Can anyone provide references for use of an unweighted least-squares : goodness-of-fit statistic? : Rich Strauss * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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