ANOVA and the F distribution

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  • #1
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Hello all,

Does anyone know where I could find a formal proof that

[tex]\frac{\text{MS between}}{\text{MS within}}[/tex]

has a F distribution under the null in ANOVA?
 

Answers and Replies

  • #2
EnumaElish
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Wikipedia states that the ratio of two chi-square random variables is F. If each MS term is normal then their sum will be Chi-squared.
 
  • #3
statdad
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In ANOVA each sum of squares can be pictured as a quadratic form, and under the null hypothesis the quadratic forms are either exactly chi-squared (if normality is assumed) or approximately chi-squared (under some general regularity conditions). The model assumptions and the null hypothesis ensure that the different quadratic forms are independent, so

(MS between)/(MS within)

is a ratio of independent chi-squares over their degrees of freedom which, by definition, gives an F distribution.
 

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