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Luis A. Afonso
Posts:
4,699
From:
LIsbon (Portugal)
Registered:
2/16/05


Statisticaj Significance Tests usefulness
Posted:
Sep 27, 2012 8:51 AM


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 (twotails 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 1alpha/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, duneducated people.
Luis A. Afonso



