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Topic: NHST: Comparing the effect with a standard. The size.
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Luis A. Afonso

Posts: 4,743
From: LIsbon (Portugal)
Registered: 2/16/05
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.

-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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