[R] How to find statistics like that.

[Duncan Murdoch]

On 11/10/2005 7:31 AM, Adaikalavan Ramasamy wrote:
> 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

Thanks for your explanation.  I think your interpretation is one that is 
sometimes taught, but I think it's more useful to think of a p-value as 
just another statistic, whose null distribution (in the ideal case, but 
not always in practice) is a uniform distribution on (0,1), and whose 
distribution when the alternative is true (again, ideally) tends to be 
more concentrated near 0.  This takes a lot of the mysticism out of them.

Duncan Murdoch
> 
> 
> 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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>>
>>