The Logic of Hypotheses Tests

The LOGIC of Hypotheses Tests


Jack Tomsky said ( Feb. 3 , 2007 6.39 PM)

*** Ho means that the two means are equal.*** **************************


My Comment:

A HT at the, frequencist point of view, intends to evaluate

___________p (data | H0)

being H0 the null hypotheses.

Once the above quantity is obtained:

_____do not accept H0, at the ALPHA significance level (usually 5% or 1%) only if:

_____p(data | H0) < ALPHA

Otherwise,

______ p(data | H0) <= 1 - ALPHA

conclude that there is not SUFFICIENT EVIDENCE to reject H0.

Note
___Because H0 includes a null quantity for the parameter value, e.g. m=0 (or mX - mY = 0) this equation CANNOT BE UNDERSTOOD as an algebraic one: it’s impossible to have a procedure that guarantees such equality. The equation should be standing entirely on NOT DETERMINISTIC GROUNDS.

************
Alternatively

ONE – TAIL TEST

Let be, Cv, named the critical value, of the TEST FUNCTION, TF, and we observe TF(data), and let be p( TF(data) <= Cv ) = 1 – ALPHA

The Decision Criterion is:

___if ____ p( TF(data) <= Cv )

THEN we conclude that there is not sufficient evidence to reject H0.


TWO – TAIL TEST

In similar way let be the fractiles U and V (left and right critical values) such that:

____p(TF < U) = ALPHA / 2
____p(TF > V) = 1 - ALPHA / 2

The if TF(data) belongs to [U, V] conclude that there is no sufficient evidence to reject H0, otherwise reject H0 in favour to H1.

One caneasily infer that Jack Tomsky even the most elementary concepts in Testing hypotheses are TOO MUCH FOR HIM.


Luis Amaral Afonso
.