Distribution of Chi-square and FDate: 12/03/2001 at 10:53:09 From: Mike Subject: Statistics; chi-square and F I've noticed that the distributions of chi-square and F have similar shapes. My question is, do chi-square and F have a mathematical relation? Date: 12/05/2001 at 05:58:28 From: Doctor Mitteldorf Subject: Re: Statistics; chi-square and F The chi-square distribution is used to test how well a set of data conforms to a pre-existing expectation of what those data should be. The variation of each measured number from the expected value is the raw material. The F-distribution is used to test a hypothesis: without this hypothesis there's so much scatter in the data; with the hypothesis, there's less scatter. How well has our hypothesis managed to make order out of what was previously considered scatter? The F and chi-square distributions are indeed related. The mathematical relation is described a little cryptically in these references: The Normal Distribution and Related Continuous Probability Distribution - ThinkQuest http://library.thinkquest.org/10030/7ndfd.htm?tqskip=1 The F Distribution - Virtual Laboratories in Probability and Statistics http://www.math.uah.edu/stat/special/special6.html If you prefer a more verbose explanation: Test of Significance for Two Population Variances - Math Department, Trigon University http://home.xnet.com/~fidler/triton/math/review/mat170/fdist/fdist1.htm A canonical example of when you might use the F-distribution is at: Why We Use Analysis of Variance to Compare Group Means and How it Works - Prof. Sid Sytsma, Ferris State University http://www.sytsma.com/phad530/anovaworks.html - Doctor Mitteldorf, The Math Forum http://mathforum.org/dr.math/ |
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