[R] How to find statistics like that.

[Liaw, Andy]

The definition of a statistic that I learned in grad school is that it's a
function of a random sample from a population.  Any p-value would fit that
definition.

Andy

> From: Adaikalavan Ramasamy
> 
> If my usage is wrong please correct me. Thank you.
> 
> Here are my reason :
> 
> 1. p-value is a (cumulative) probability and always ranges 
> from 0 to 1.
> A test statistic depending on its definition can wider range 
> of possible
> values.
> 
> 2. A test statistics is one that is calculated from the data 
> without the
> need of assuming a null distribution. Whereas to calculate 
> p-values, you
> need to assume a null distribution or estimate it empirically using
> permutation techniques.
> 
> 3. The directionality of a test statistics may be ignored. 
> For example a
> t-statistics of -5 and 5 are equally interesting in a 
> two-sided testing.
> But the smaller the p-value, more evidence against the null 
> hypothesis.
> 
> Regards, Adai
> 
> 
> 
> On Thu, 2005-11-10 at 06:05 -0500, Duncan Murdoch wrote:
> > On 11/9/2005 10:01 PM, Adaikalavan Ramasamy wrote:
> > > I think an alternative is to use a p-value from F 
> distribution. Even
> > > tough it is not a statistics, it is much easier to 
> explain and popular
> > > than 1/F. Better yet to report the confidence intervals.
> > 
> > Just curious about your usage:  why do you say a p-value is 
> not a statistic?
> > 
> > Duncan Murdoch
> > 
> > > 
> > > Regards, Adai
> > > 
> > > 
> > > 
> > > On Wed, 2005-11-09 at 17:09 -0600, Mike Miller wrote:
> > > 
> > >>On Wed, 9 Nov 2005, Gao Fay wrote:
> > >>
> > >>
> > >>>Hi there,
> > >>>
> > >>>Suppose mu is constant, and error is normally 
> distributed with mean 0 and 
> > >>>fixed variance s. I need to find a statistics that:
> > >>>Y_i = mu + beta1* I1_i beta2*I2_i + beta3*I1_i*I2_i + 
> +error, where I_i is 1 
> > >>>Y_i is from group A, and 0 if Y_i is from group B.
> > >>>
> > >>>It is large when  beta1=beta2=0
> > >>>It is small when beta1 and/or beta2 is not equal to 0
> > >>>
> > >>>How can I find it by R? Thank you very much for your time.
> > >>
> > >>
> > >>That's a funny question.  Usually we want a statistic 
> that is small when 
> > >>beta1=beta2=0 and large otherwise.
> > >>
> > >>Why not compute the usual F statistic for the null 
> beta1=beta2=0 and then 
> > >>use 1/F as your statistic?
> > >>
> > >>Mike
> > >>
> > >>______________________________________________
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> > >>https://stat.ethz.ch/mailman/listinfo/r-help
> > >>PLEASE do read the posting guide! 
> http://www.R-project.org/posting-guide.html
> > >>
> > > 
> > > 
> > 
> > ______________________________________________
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> > 
> >
> 
> 
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