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