Re: Simple binomial test question

Jack Tomsky said


*** Afonso has never understood hypothesis testing. When one hypothesis is tested against another, a decision is made on the basis of the sample as to which hypothesis is to be accepted. That's why we have type I and type II errors. Under the Afonso theory of hypothesis testing, the OC curve, which is the probability of accepting the null hypothesis, must always be uniformly zero.

Extending his ideas to parameter estimation problems, just as he would never allow himself to accept a hypothesis, he would never allow himself to estimate a parameter.***


My response

Tomsky against all is stated by all authors of Hypotheses Test states that an (whatever) hypotheses can be proved true. THIS IS NOT TRUE, at all.
His indication of th type I and II errors is a trick to evade discussion. Because this is not the point.
_____1- alpha measures NOT the probability that H0 is true but simply the criterion under what we should not reject the null hypotheses.
ALL (no stupid) authors are sure on one thing: the impossibility to reject H0 is not coincident with proving that it is proved true. (Neyman-Pearson theorem).
This is so basic that a simple problem assures what I said.
____How many coin flips (at least) should I observe in order to prove that a coin is fair.? ___________
Who answers?

Another thing.

His *extension* to parameters estimation is FALSE.
The only thing that I can assert – from a THETA parameter estimated confidence interval of probability 1-alpha from data - is that repeating same data infinite times under the same conditions - I will find that the true value of the parameter THETA will fall in the interval with the relative frequency 1-alpha; AND alpha is the frequency that the estimated interval FAILS to cover the true THETA value
This is anything to do with if a hypotheses can be proved to be true(?) or false(?).

Jack Tomsky learned (many years ago) something about, crystallize the idea that he understood the point, and at present day refuse to rethink how wrong he is.

_________licas (Luis A. Afonso)
.

Relevant Pages