Date: Aug 5, 2011 6:10 PM
Author: Luis A. Afonso
Subject: Who cares the null hypotheses (two-tail test) is really TRUE?
Who cares the null hypotheses (two-tail test) is really TRUE?
Not me, in accordance to learned people! DEFINITIVELLY! Seeming a blasphemy, namely for those that state: H0 shows not be true if a sufficiently large sample is analysed . . . because an even a tinny difference could be detected with substantial probability, for example 99.99%.
Nothing more WRONG! The mater is absolutely other: we cannot prove the Null Hypothesis true or not true . . . IT IS IMPOSSIBLE: the most can be stated is that we should reject the null, or, on contrary, it was found no sufficient evidence to do so. Not more, not less.
The null for a parameter as been associated to mu=0: NO, is preferable to try
____1)____H0: | mu - mu0 | <= h_______ or else
____2) Ha: | um - mu0| > h
If the test statistics imply 1) we say that the obtained mu is so close to the standard mu0 that is not greater than h positive (null *accepted*), otherwise, resulting 2), indicates that the difference is at least h, at the chosen significance level, alpha. This no statistical quantity is arbitrary chosen, depending the case on study, as the minimum *interesting to research* or *economically* that worth to be stated/published as SIGNIFICANT. People that, in this instance, do not agree to let h=0 is fully right: a mu value that is only statistically significant does not indicate really in what concerns how much is different from mu0, in spite of even, perhaps, showing a very small alpha. The *insignificance* of a (statistically) significant result: what one can say is only that is well apart mu0.
Luis A. Afonso
_ 1- alpha = 0.99____ Z= [ -2.807, 2.807]
____Z= |.505 - .5| / sqrt (.5*(1-.5)/n) =2.807
_______.005/2.807 = sqrt (.5*.5 / n)
________sqrt(n)= .5*2.807/.005 = 280.7
___________n = 78792.49 +/- 394 tosses
With a difference of +/- 0.005 we should perform 79792 tosses and to find heads (or tails) in [78398, 79186] in order not to reject 1% alpha the coin is fair.