WORMTOMSKY EXPRESS
The HYSTERICAL claim from the IMBECILE DUO that?s impossible two different Parameters estimation to have two equal HYPOTHESE TEST DECISIONS is absolutely WRONG.
As long as I decide to give up I assure you, the Readers, that I will inform you what the advantages (and drawbacks), are associated to Monte Carlo Method when applied to Statistical Decision.
The IMBECILE DUO is completely incompetent to give a reason by which (quotation):
*** The 95% Afonso confidence intervals are based on him assuming that the population median is zero. Therefore, the confidence interval for the population median is [0, 0] = {0} for all confidence levels and sample sizes.. The results Afonso presents have the property that for certain median values known to be untrue, the probability of coverage is 100% rather than 0%. For example, for n = 5, all nonzero medians between -2.012 and +2.012 have 100% coverage. That is, they are contained in the Afonso confidence intervals for every sample. Because of these poor properties, I recommend that the Afonso confidence intervals never be used. ***
I will respond AGAIN, point by point, and in order, to swap up the absurdities they don?t stop to say
__1__All Test Statistics is based on H0 is true: here is that Cauchy Distribution has zero median
__2__The Confidence Interval is [0, 0] THE TWO IMBECILES STATED is a complete absurdity: every test supposes the parameter value, even being a constant is faced, is taken as an INSTRUMENTALLY variable which experimental evidence is just the observed parameter value. By this expression one have a random variable estimated from the sample showing a a value only exceptionally EQUAL TO THE PARAMETER´s ONE.
__3__Because the probability of an event is (by a majority lot of statisticians) experimentally evident by its frequency the so-called coverage interval IS NOT at all 0% or 100%, AS THE IMBECILE DUO SAYS: it is, simply and directly, given by the frequency attached to it. The example [-2.012, +2.012] covers exactly 95% of the simulated (at random) as few as 4 ´000´000 Cauchy samples of size 5. I?m sure because I observed, if someone doubts, DO CHECK IT!
__4__ALL READERS ARE INVITED TO JOIN THE LOT OF STATISTICIANS THAT USE MONTE CARLO IN TEST HYPOTHESES DECISIONS.
__5__The fundamental difference between the Before -Lillefors Era and the nowadays is striking: From the concept that the confidence interval is based on its ESTIMATE FROM ONE ONLY SAMPLE, TOGHETER WITH THE KNOWLEDGE OF THE TEST STATISTICS EXPRESSION, resulting, consequently, the paradigm: one sample, one C.I., the evolution turns up to be if I know the probability, I CAN ATTACH TO WHATEVER INTERVAL OF THE EMPIRICAL TEST STATISTICS THE RESPECTIVE RELATIVE FREQUENCY ( PROBABILITY).OBTAINED THROUGH MONTE CARLO SIMULATIONS. The degree of approximation Relative Frequency toward Probability is given by the Dvoretzky- Kiefer -Wolfowitz inequality.
Luis Amaral Afonso [The Moderators Destroyer]

Perry,

In Adumbostistics, it is not necessary to specify null and alternative hypotheses.  A case in point is given by Luis Amaral Afonso in THREAD: An RNG test by the DKW formula  THREAD STARTED:  Jul 14 2007, 5:56 pm

He makes a complicated simulation whose goal is to determine if a sequence of random numbers is random.  He arbitrarily chooses a test statistic (without reference to a null hypothesis) and arbitrarily (without reference to a tail area) chooses a "critical value" of 1E6.  

He says right there in the first post (where "LAST VALUE" is his "test statistic"): "SINCE THIS LAST VALUE IS LESS THAN 1E6 we conclude that there is no EVIDENCE that the *numbers FACTORY* is working erratically."

When I asked him whether 1E6 corresponds to a 1% critical value, he could not respond.  Eventually he admitted that the choice of 1E6 is something he made up.  But he still insisted that what he was doing constituted a statistical test.

So, Perry, this is an example of Adumbostistics.  You don't need null and alternative hypotheses, nor do you need true critical values.  Isn't it amazing that all this has been invented by Luis Amaral Afonso???  

John ` Smith