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Luis A. Afonso
Posts:
4,276
From:
LIsbon (Portugal)
Registered:
2/16/05
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Statisticaj Significance Tests usefulness
Posted:
Sep 27, 2012 8:51 AM
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Much ?ado? about nothing
A deadly misunderstanding leads some ?experts? to condemn the Statistical Significance Tests (SST) usefulness a way that gave birth to a really deplorable series of papers during the last decades.
The main problem, I suppose, is that there is people that demand SST to answer things to which it wasn?t able to do, namely if a result is significant at other contexts, economical for example, apart the strictly mathematical one. Utmost stupid is to claim, as I read yet, that the null hypotheses are always false: in fact one cannot assert, through a test, if a parameter has precisely the value we presume it has beforehand . . .
In reference to the test of parameters the Test Statistics W is often represented by (two-tails test), T the assumed (conventional, ordinary, habitual) and T0 the observed at present:
_______________W = ( T - (T0 + d) ) / S
Let be W´ the alpha/2 fractiles and W´´ the 1-alpha/2. Then the aimed difference, positive, with a probability 1 - alpha can be stated when is inside the interval
____________S*W´ < T - T0 - d < S*W´´
__________- S*W´ > d + T0 - T > - S*W´´
____(T0 ? T) - S*W´ > d > (T0 - T) - S*W´´
(T0 - T) - S*W´´< d < (T0 ? T) - S*W´
For example if W is N(0, 1), alpha = 0.05, W´= -1.96, W´´= -W´
___(T0 - T) - 1.96 * S < d < (T0 - T) + 1.96 *S
, interval 2*1.96*S amplitude, centred at T0 - T), T0> T.
I would call them, say, d-uneducated people.
Luis A. Afonso
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