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Distribution of Chi-square and F


Date: 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/   
    
Associated Topics:
High School Statistics

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