Re: Jarque-Bera test: confidence intervals for normal data
- From: Jack Tomsky <jtomsky@xxxxxxxxxxxxx>
- Date: Sun, 11 Mar 2007 20:31:30 EDT
wwwpub.utdallas.edu/~herve/Abdi-Lillie2007-pretty.pdf
UUUUUUUUUUUUUUUUUUUUUUUUUUUUU
MY VALUES
size___alpha=5%_1% ___Connover_____Abdi.
_10___0.264___0.305___.258_.294__.2616_.3037
_15___0.220___0.255___.220_.257__.2196_.2545
_20___0.192___0.224___.190_.231__.1920_.2226
_25___0.174___0.202___.173_.200__.1726_.2010
_30___0.159___0.185___.161_.187__.1590_.1848
_35___0.148___0.172_____________.1478_.1720
_40___0.139___0.161_____________.1386_.1616
_45___0.131___0.152_____________.1309_.1525
_50___0.124___0.145_____________.1246_.1457
(for each sample size, 500´000 samples were
simulated
by my work, 100´000 by Abdi & Molin).
JACK TOMSKY is so unlearned and shameless that
deserves to be exposed every time he posts an opinion
on Hypotheses Tests. The less experience people
should take in attention that HE IS A CLOWN.
Although there is no evidence that anyone has ever used any of Afonso's faulty statistics, it is important that his errors be corrected so that no one will ever think that confidence levels and significance levels are synonomous, that null hypotheses are never allowed to be accepted, and that no one can tell if 8/13 is greater than 5/13.
Jack
.
Readers. Do appreciate what I found out at WEB.
*** Lilliefors/Van Soest´s test of normality ***
_____Hervé Abdi & Paul Molin
1. OVERVIEW
The normality assumption is at the core of the
majority of standard statistical procedures, and it
is important to be able to test this assumption. In
addition, showing that a sample does not come from a
normally distributed population is sometimes of
importance per se. Among the many procedures used to
test this assumption, one of the most well-known is a
modification of the Kolmogorov-Smirnov test of
goodness of fit, generally referred to as the
Lilliefors test for normality (or Lilliefors test for
short).This test was developed independently by
Lilliefors (1967) and by Van Soest (1967). The null
hypotheses for this test is that the error is
normally distributed (i.e. there is no difference
between the observed distribution f and the normal
distribution). The alternative hypotheses is that the
error is not normally distributed.
Like most statistical tests, this test of normality
defines a criterion and gives its sampling
distribution. When the probability associated with
the criterion s smaller than a given [alpha]-level,
the alternative hypotheses is accepted (i.e. we
conclude that the sample does not come from a normal
distribution). An interesting peculiarity of the
Lilliefors test is the technique used to derive the
sampling distribution of the criterion. In general
mathematical statisticians derive the sampling
distribution of the criterion using analytical
techniques. However in this case, this approach fails
and consequently Lilliefors decided to calculate an
approximation of the sampling distribution by using
the Monte Carlo technique.
Essentially the procedure consists of extracting a
large number of samples from a Normal Population and
computing the value of the criterion for each of
these samples. The empirical distribution of the
values o the criterion gives an approximation of the
sampling distribution of the criterion under the null
hypotheses.
Specifically, both Lilliefors and Van Soest used, for
each sample size chosen, 1000 random samples derived
from a standardized normal distribution to
approximate the sampling distribution of a
Kolmogorov-Smirnov criterion of goodness of fit. He
critical values given by Lilliefors and Van Soest are
quite similar, the relative error being of the order
of 10^ (-2).
According to Lilliefors (1967) this test of normality
is more powerful than others procedures for a wide
range of nonnormal conditions. Dagnelie (1968)
indicated, in addition, that the critical values
reported by Lilliefors can be approximated by an
analytical formula. Such a formula facilitates
writing computer routines because it eliminates the
risk of creating errors when keying in the values of
the table. Recently, Molin and Abdi (1998), refined
the approximation given by Dagnelie and computed new
tables using a larger number o runs (i.e. K=100,000)
in their simulations. ***
(End of citation).
____TOMSKY´s ABSOLUTELY K.O.!!!!!
____licas (Luis A. Afonso)
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