[R] How to find statistics like that.

[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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> >>
> > 
> > 
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>