To fail to reject the null Hypotheses is NOT to have EQUALITY

To fail to reject the null Hypotheses
IS NOT to HAVE EQUALITY


Warning against Bob Ling´s statements.

If the NULL HYPOTHESES, H0, is the equality of two parameters, H0: m1 = m2, against H1: m1 > m2, and performing the one-tailed test, we conclude that we cannot reject H0, the ONLY thing we are sure, at the chosen confidence level, (C.L.) is that the two sample under test are unable to distinguish m1 from m2. The real difference between the two Population parameters is not possible to be achieved, and FOR A STILL STRONGER REASON we are not allowed to state that are EQUAL, i.e., that m1-m2 =0.

Critical Value: is the maximum value of the test statistic to which we are not allowed to reject H0. To we define an interval (Acceptance Interval) associated to a high probability p0 = 1-alpha of not to reject H0, that is usually 95% (less often 99%).
Therefore probability alpha, 5%, is the risk we take to reject H0 (Rejection Interval) if H0 is true, i.e., if the Population proportions are not *equal*.

When we reject H0 are we sure that is there a difference? NOT AT ALL. We simply are sure that in 95 out of 100 cases (in mean) if we repeat drawing the samples (at random, and at the same C.L.) we reach the same result: H0 rejection.


________licas (Luis A. Afonso)
.

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