Re: Simple binomial test question

Jack Tomsky wrote

. . . Since your calculated p-value of 0.054 exceeds
the pre-asssigned significance level, you accept the
null hypothesis H.
Intuitively you had the right idea, but you used the
e wrong terminology. Jack.


My response

*** NOT AT ALL.
The correct conclusion to be drawn is different than
Jack’s one:
We have NOT (by the data) SUFFICIENT EVIDENCE TO
O REJECT H0 at the pre-assigned significance level
***

(The absence of evidence it is not the evidence of
absence)

Furthermore:

If X, number of heads, is such that is greater or
than 2 and less than 8
___H0 is not rejected at 5% significance level
___because there is not sufficient evidence to do
it.
NOTE that
___________p( 2 > X < 8 ) = 0.890

(H0 : five heads IT IS NOT CORRECT, at all,
p(X=5)=0.246).


________licas (Luis A. Afonso)


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.

Jack
.