The genesis of Critical Values
Luis A. Afonso
A pair, or couple, of idiots (that are unable to understand the basis of DECISIONS of Hypotheses Tests) compelled me to open a new thread concerning the same matter.
I apologize Sci. Stat. Math.
Critical Values are a direct consequence of the Test Statistics Distribution Function.
In order to legitimate Monte Carlo two questions are pertinent:
_1) Am I able to simulate a large set of the Sample Space?
_2) Can I attain a set of the Test Statistics Values such that its cumulative frequencies be very close to the theoretical Distribution, difference in absolute value = d? How many values (n) should I to consider?
The answer is YES.
In fact the Dvoretzky-Diefer-Wolfowitz assures us that 2) is surely attained:
________p(d>e)<= 2*EXP(-2*n*e*e)
Suppose that n=1E7 , e=5E(-4)= 0.0005
Then the right side: 2*EXP(-5) = 0.013.
The final prove is that I was able to obtain exactly the Critical Values in the case of known exact theoretical Sample Distributions (namely Normal and Chi-Square).
Furthermore I found the values relative to other known Distributions obtained exactly by Random Simulation.
Only those that didn’t read any Bibliography the last 40 years can be surprised before these results.
When reality is uncomfortable something’s wrong.
_____
Luis A. Afonso
John Smith
"A pair, or couple, of idiots (that are unable to understand the basis of DECISIONS of Hypotheses Tests) compelled me to open a new thread concerning the same matter."
It's obvious why you open a new thread, because your last thread displayed your ignorance.
Before you move on to a new display of your ignorance, let's finish discussing your last one.
On Nov 11, 4:22 am
You wrote:
"From this values we obtain the CONFIDENCE INTERVALS of the two-tailed tests relative to the probabilities 99%, 98%, 95% the parameter be inside."
Either the parameter is INSIDE or OUTSIDE. The probability that the parameter is inside is either 100% or 0%. Same for the probability that the parameter is outside.
Please defend your assertion that there can be a 99% probability that a parameter is inside the interval.
John