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Re: science for all?



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

> The problem is that I have used some standard jargon from the standard
> educational literature and alluded to some results from that same
> literature.

[JU]
That does not mean that either "the standard jargon" or the
"results" quoted are using statistical analysis correctly.

[JC]
>
> Effect size is generally defined as the change in the mean on an evaluation
> divided by the standard deviation of the curve.

[JU]
OK. You have now defined which standard deviation you are
discussing.

[JC]
Most of the educational
> literature effect sizes are less than 1.0 and a curriculum which achieves
> anything over 0.5 is usually considered to be very effective.

[JU]
We're not concerned with "usually". We"re doing straight
mathematics. If the curve is taken to represent an estimate of a
probability distribution, and the distribution is normal, then an effect
size of 1.0 may be interpreted as a 30% chance that the mean did not
change.
.....
regards,
Jack


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!