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Luis A. Afonso
Posts:
4,758
From:
LIsbon (Portugal)
Registered:
2/16/05


What changes a NHST into a NoNHST?
Posted:
Dec 13, 2012 10:43 AM


What changes a NHST into a NoNHST?
Some class of Statistics users claim that Null Hypotheses Statistical Tests are useless because a reject result does´nt inform how much data differs from a null one. They are right: The insignificance of Significance tests as it was said . . . A parameter´s test statistics is in general expressed as ________W = (Obs  Common)/s______NHST Obs = observed value compared with Common, the Null Hypotheses, H0, value. Let be W0 and W1 the critical values (at a preset alpha) bounding the norejection interval. Then the set of values less than W0 or larger than W1 do contain the Rejection values of W. A simple and sufficiently known ?mending?: Subtracting a positive D to the numerator we, if so, intend to warrant that at least the Obs is larger than the H0 value by D. Then it must be NoNHST (my acronym): _____ s * W0 < (Obs  H0)  D < s * W1____(1) Then if D > 0 is inside the interval: [(Obs  H0)  (s*W1), (Obs  H0)  (s*W0)] we cannot warrant (at alpha significant level) at least D differs from H0 + D : to, in fact to get a gain D over H0 must 0 be at left to this interval. Note that (1) defines a norejection D centered interval, with amplitude given by s * (W1  W0), _______[U  s * W1, U  s * W0] Conclusion: Only if the observed difference noted U (U=ObsH0) is larger than s*W1 our purpose is fulfilled. Symmetric critical values Let be s=1, W0= 1.96, W1= 1.96. We have ____ 1.960 < U  D < 1.960; Therefore: __ U  1.960 < D < U + 1.960. We have not a positive gain unless U > s * W1, i.e., the left bound with 0 at its left. The norejection C.I. is centred at ObsH0 and its semiamplitude is W1 * s with W0=  W1.
Luis A. Afonso



