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.