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... The
expected standard error of the differences between m1 and m2
(assuming many samples of the same size were collected) ,
according to a textbook (David Moore, Standard Statistics), is:
SE=sqrt( s1^2/25 + S2^2/25) = sqrt (4/25 + 1.96/25)=0.488
This leads to the two-sample statistics t = (m1-m2)/SE=6.14.
Ludwik Kowalski
**********************************************
Jack Uretsky wrote:
...
the sigma of the distribution is an unknown 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's1%.
The t-test for the difference of two means when the s.d. of the
underlying distribution is the unknown 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.
> 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.