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Re: science for all?



Hi all-

Getting back to statistics:
Well, Brian may have been aware of his barbaric error when he
wrote "I casually assume the standard error..." The point is that the
sigma of the distribution is an unkown quantity, and one should redo the
t-test taking that fact into account. Using his numbers I find that the
probability that the two means are the same is about 10% - somewhat less
than the 30% of my previous rough estimate, but far larger than Brian's
1%..
The t-test for the difference of two means when the s.d. of the
underlying distribution is the unkown is described in Hogg & Craig,
Section 6.4.
Of course, all this assumes that the samples consist of normally
distributed random variable, an assumption that is almost certainly
untrue.
Regards,

On Mon, 31 Dec 2001, Brian Whatcott wrote:

At 08:54 AM 12/31/01, Jack Uretsky wrote:
On Wed, 26 Dec 2001, John Clement wrote:
_________________________________________snip________________________


Jack's criticism is so obviously wrong, in my view, that I progressed no
further.
I will now illustrate what I see as his error.

Clement has described a statistic, effect size, (M1 - M2) / SD where
a value 0.5 is an effective change.

To test his proposition,
I take twenty five samples from a pile and find the mean is 7
and the standard deviation is 3
I take twenty five samples from a processed pile and find the mean is 10
and the standard deviation is 3.

Am I justified in concluding the piles are significantly different using
Clement's statistic, effect size = 1??

I casually assume the standard error of the difference of the sample
means is sqrt[(3/5)^2 + (3/5)^2] = 0.849 or ~ 0.85
t statistic = (10-7)/0.85 = 3.53
Degrees of Freedom = 25 -1 + 25 -1 = 48
A table gives significance at 1% level for 48 D of F as 2.68

I conclude there is a significant difference at the 1% level.
Jack concludes there is a 30% chance this difference could have been
a chance effect.
I conclude that Jack is mistaking the statistics for an individual item for an
ensemble.

Happy New Year!




Brian Whatcott
Altus OK Eureka!


--
"But as much as I love and respect you, I will beat you and I will kill
you, because that is what I must do. Tonight it is only you and me, fish.
It is your strength against my intelligence. It is a veritable potpourri
of metaphor, every nuance of which is fraught with meaning."
Greg Nagan from "The Old Man and the Sea" in
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