[R] ANOVA: F value >1 or < 1

Spencer Graves spencer.graves at pdf.com
Thu Mar 20 20:46:12 CET 2003

	  The F ratio compares the variability between groups to a supposedly 
independent estimate of what that variability would be if there were no 
group effect.

	  If F is large (much greater than 1), it suggests that there probably 
is a group effect.

	  If F is small (quite close to 0), it suggests some other violation of 
assumptions.  This can occur in a balanced 2-way layout where factor A 
is unimportant while B is large but excluded from the model.

tst.df2 <- data.frame(A=rep(letters[1:2], each=2), B=rep(letters[1:2], 
2), y = rep(1:2, 2)+0.01*rnorm(4))

anova(lm(y~A, tst.df2))
Analysis of Variance Table

Response: y
           Df  Sum Sq Mean Sq F value Pr(>F)
A          1 0.00010 0.00010   2e-04 0.9896
Residuals  2 0.96970 0.48485

Hope this helps
Spencer Graves

Rishabh Gupta wrote:
> Hello,
>   I have a question regarding anova. I am a bit comfused about the F value. My understanding is
> that the F value indicates the ability of numerical variable V to discriminate between different
> values of grouping variable G. If the F value is equal or close to 1.0, it means that all the
> variances of the groups are similar and that V is unable to discriminate for G. On the other hand
> if the F value is far from 1.0, it suggests that the variances of the groups are different.
> The issues that I am comfused about is F values of <1 vs >1. My understanding is that the values
> are equal to their reciprocal as far as the discriminance is concerned. So 0.5 is equivalent to
> 1/0.5. Could somebody please tell me whether this is correct or not, or whether I have got it
> completely wrong.
>  Your help is greatly apprecited. Many Thanks
> Rishabh
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