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Luis A. Afonso
Posts:
4,293
From:
LIsbon (Portugal)
Registered:
2/16/05
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NHST: Comparing the effect with a standard. The size.
Posted:
Oct 26, 2012 7:03 AM
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NHST: Comparing the effect with a standard. The size.
We are, supposedly, trying to reprove the accepted fact that the observed/measured Normal Population has mean= 3. Following my experiment I had found, with a size 30 random sample, mean=5.917, standard deviation=0.663, we intend to build a 95% Confidence Interval containing D, the excess from established mean=3.
Hence
-2.045 * 0.663/sqrt (30) < 5.917 - (3 + D) <
< 2.045 * 0.663/sqrt (30)
(2.045 are the 97.5% quantile of Student T, 29 degrees of freedom). Therefore we discover that D stays inside the interval [2.67, 3.16]: because it doesn?t contain 0, we can state our find will falls down the common value 3.
Recurring to only standard statistical procedures, the problem could be correctly solved.
__________
The size an effect is revealed
The above scientist intending to forecast how much data should to use in order to prove H0: mean > 5.8, do the following:
sqrt(n) > (0.663 * 2.045)/(5.947 - 5.8) = 11.588, resulting that the size should be at least 135.
Of course . . . if it happens, this time, the standard deviation be a little larger than 0.662 and the intent is spoiled: if it was 1.000 the size amounts to194 or more.
Luis A. Afonso
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