[R] How to find statistics like that.

[John Wilkinson (pipex)]

Adai,

I recently came across the following definition of a statistic
which may be relevent to the discussion.

John
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Beran’s (2003) provocative definition of statistics as “the study of
algorithms for data analysis” elevates computational considerations to the
forefront of the field. It is apparent that the evolutionary success of
statistical methods is to a significant degree determined by considerations
of computational convenience. As a result,design and dissemination of
statistical software has become an integral part of statistical research.

from this it follows that a 'Statistic' is

 " A mathematical function or  algorithm for data analysis"


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Duncan Murdoch wrote
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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

Adaikalavan Ramasamy replied
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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