THE BIG BANG (OR the pyramidal BLUNDER)

Bob (Reef Fish said:


*** Date: Apr 29, 2006 3:32 PM
Author: Large_Nassau_Grouper@xxxxxxxxx
Subject: Rejection of a Null Hypothesis Ho

Luis A. Afonso of sci.stat.math has so polluted this and other related threads that I have to pull the original discussion into this more precise subject, as in killing two birds with one stone. I asked Bob O'Hara, > > Anon Bob O'Hara,


What is "not proven"? If you meant to say that the non-rejection of a Null Hypothesis or the acceptance of a Null Hypothesis is synoymous with "Ho is not proven", then you have missed the boat, the harbour, and the ocean of this thread.

And Bob O'Hara responded:


You either reject the null hypothesis ("guilty"), or fail to reject it "not proven").That was what I was trying to explain to you that "not proven" carried the wrong implication that it CAN be proven. That is why "not proven" is WRONG for saying that Ho is not rejected.
This is apt because in practice the null hypothesis is a straw man, so hypothesis testing can be seen as little more than asking if you have enough data to reject a hypothesis that you know is wrong anyway. > --
Bob O'Hara

You are wrong in the assertions in your preceding paragraph also!


A simple counterexample to your assertion could be: what's below, or hundreds of other hypothesis tests: If you sample from a normal population with mean 10 (unknownto the statistician) and variance 1, and test the Null Hypothesis that mu = 0, vs the Alternative H1: mu<0. You can sample forever and not be able to reject the Ho. –


Reef Fish Bob. ***



My response

H0 u H1 represent all real numbers (with eventually same sub-intervals of H1 with probability ZERO).
THIS IS the most ELEMENTARY PRINCIPLE of Hypotheses Tests.
Therefore
Being H0: mu=0 then, necessarily, H1: mu NOT ZERO.

Conclusion : the so-called Bob´s counter-example is the more evident example, along with others, that HE KNOWS NOTHING on this matter.

_____licas (Luis A. afonso)

*** asking if you have enough data to reject a hypothesis that you know is wrong anyway. ***

WHAT?
___Testing an Hypotheses under the condition it is WRONG?
WHAT?
___The first principle of PROBABILITY is that p=1 is not allowed. Otherwise: IF WE ARE SURE OF AN EVENT it was not random, we must not test it. (Tomorrow Earth will stop its rotation, or will be Wednesday, or the past February had 29 days, ).
Watch what is a RANDOM EVENT.

____licas (Luis A. Afonso)
.

Relevant Pages

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