Date: Nov 23, 2012 2:54 PM
Author: Luis A. Afonso
Subject: Re: An intrusive note on Hypothesis Tests (II)
If someone asks me an idea/word/concept//limitation I think that do impinges all null hypotheses statistical tests (NHST) decisions at once Plausibility was chosen.
In spite of some unsound (but insistent) critics, inclusively some had propose even its ban from Scientific Revues, NHST can stand, by its proper merits, a useful tool, rightly and often, throughout an hundred years used by Statisticians, all over the world.
Firstly because it has the merit of wiping up the idea that whatever in probability-statistics is conformable with the classical dilemmatic cut-of true-untrue. For example if data reveals that the p-value is extremely small we should say something like: given the data, the null hypothesis is so that is not plausible it is true, instead to state that it is false. In fact it can happen that data, in spite H0 true, is so odd that leads us to the rejection. Then, Type I error is made.
Ryan Martin (On a ´plausible´ interpretation of p-values, Nov. 12, 2012) follows these ones ideas, which
What usually is said: (From Wikipedia)
the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.
Because we want that this probability should be less than alpha (preset) in order that we reject the null we have a way to decide if it is the case. But, anywhay, we prove the Null is true. Not to reject is not synonimouous to accept. By NHST we are unable to accept whatever, the Null, or the Alternative Hypotheses.
By the other hand, never could be thought that is the maximum (one tail-right) observable probability. It is not: whatever the test the p-values are freely locate in the interval [0, 1] and alpha cuts it in two sub-intervals [0, alpha] the acceptance interval (mistakabily so-said), and (alpha, 1] the rejection one. Or instead (-infinity, critical value], and (critical value, +infinity] for continuous test statistics real straight line defined.
Of course H0 is less and less plausible as p-value approaches 1, leading to reject the Null if p-value < alpha holds.
Luis A. Afonso