[R] Test of Homogeneity of Variances

[Liaw, Andy]

You don't need to test that the _sample_ variances are different:  They
already are.  Statistical tests of hypotheses are not about sample
statistics, but distributional charateristics.

It seems to me that reinforcement of some basic stat concept may do you
quite a bit of good.  If you don't have the basics, you're just going to
get more and more puzzled every step of the way.  Just a frank
suggestion.

Best,
Andy 

From: Daren Tan
> 
> I am testing whether the sample variances are equal. When 
> p-value < 0.05 (alpha), should accept null hypothesis (sample 
> variances are equal) or reject it ?
> 
> 
> The two new examples with each having same sample variances 
> also puzzle me. Why are the p-values different ?
> 
> bartlett.test(rep(rnorm(5),times=4), rep(1:5, each=4))
> 
> 
>         Bartlett test of homogeneity of variances
> 
> 
> data:  rep(rnorm(5), times = 4) and rep(1:5, each = 4)
> Bartlett's K-squared = 0.8681, df = 4, p-value = 0.929
> 
> 
> bartlett.test(rep(rnorm(5),times=4), rep(1:5, each=4))
> 
> 
>         Bartlett test of homogeneity of variances
> 
> 
> data:  rep(rnorm(5), times = 4) and rep(1:5, each = 4)
> Bartlett's K-squared = 3.5599, df = 4, p-value = 0.4688
> 
> 
> > From: Patrick.Richardson at vai.org
> > To: daren76 at hotmail.com; r-help at stat.math.ethz.ch
> > Date: Fri, 22 Aug 2008 11:25:36 -0400
> > Subject: RE: [R] Test of Homogeneity of Variances
> >
> > What are your hypotheses? Once you state what they are, 
> interpretation should be straightforward.
> >
> >
> >
> > -----Original Message-----
> > From: r-help-bounces at r-project.org 
> [mailto:r-help-bounces at r-project.org] On Behalf Of Daren Tan
> > Sent: Friday, August 22, 2008 11:18 AM
> > To: r-help at stat.math.ethz.ch
> > Subject: [R] Test of Homogeneity of Variances
> >
> >
> > I am testing the homogeneity of variances via bartlett.test 
> and fligner.test. Using the following example, how should I 
> interpret the p-value in order to accept or reject the null 
> hypothesis ?
> >
> > set.seed(5)
> > x <- rnorm(20)
> > bartlett.test(x, rep(1:5, each=4))
> >
> >
> > Bartlett test of homogeneity of variances
> >
> >
> > data: x and rep(1:5, each = 4)
> > Bartlett's K-squared = 1.7709, df = 4, p-value = 0.7778
> >
> > fligner.test(x, rep(1:5, each=4))
> >
> > Fligner-Killeen test of homogeneity of variances
> >
> >
> > data: x and rep(1:5, each = 4)
> > Fligner-Killeen:med chi-squared = 1.0819, df = 4, p-value = 0.8971
> >
> > ______________________________________________
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