The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

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 

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 

   The Normal Distribution and Related Continuous Probability 
   Distribution - ThinkQuest   

   The F Distribution - Virtual Laboratories in Probability and

If you prefer a more verbose explanation:

   Test of Significance for Two Population Variances -
   Math Department, Trigon University   

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   

- Doctor Mitteldorf, The Math Forum   
Associated Topics:
High School Statistics

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.