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Topic: Kolmogorov-Smirnov-Lilliefors Test statistics
Replies: 10   Last Post: Jun 8, 2013 7:39 PM

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Luis A. Afonso

Posts: 4,617
From: LIsbon (Portugal)
Registered: 2/16/05
Re: Kolmogorov-Smirnov-Lilliefors Test statistics
Posted: Jun 7, 2013 5:18 PM
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Data was treated Jarque-Bera Test way: the results were (JB-DATA routine):
_____LM = 1.840___ ALM = 1.802
These values should be compared with the respective 5% significance critical values respectively
_____LM = 5.4300__ ALM = 6.3192
http://mpra.ub.uni-muenchen.de/id/eprint/19155

Conclusion
Unless one want to cheat people stating normality where it is highly suspicious, this test must be promptly banned from usual practice, even for large sample sizes. We had shown yet, with all evidence, that this data was notoriously rejected with very small p-value by the Lilliefors (Kolmogorov-Smirnov) criterion: the normality distribution is enormously unlike, impossible, no chance.
Even that the test be restricted to Economicists users the danger is not despicable, I mean.


Luis A. Afonso

REM "JB-DATA"
CLS
DEFDBL A-Z
RANDOMIZE TIMER
PRINT : PRINT
PRINT "__________________________ JB-DATA "
n = 100
DIM x(n)
DEF fng (z, j) = -.5 * z * z * (2 * j + 1) / ((j + 1) * (2 * j + 3))
pi = 4 * ATN(1): c = 1 / SQR(2 * pi)
c1 = 6 * (n - 2) / ((n + 1) * (n + 3))
c2 = 3 * (n - 1) / (n + 1)
c3 = 24 * n * (n - 2) * (n - 3) / ((n + 1) ^ 2 * (n + 3) * (n + 5))
REM
DATA 457,457,455,457,454,454,457,455,456,459
DATA 457,458,456,456,461,457,458,452,457,460
DATA 453,458,452,454,454,456,455,456,451,454
DATA 456,457,457,453,455,459,458,457,458,457
DATA 461,457,455,458,458,455,457,458,456,463
DATA 455,455,455,456,456,456,455,456,460,456
DATA 456,457,458,454,455,456,459,457,457,451
DATA 450,453,453,459,450,453,452,458,456,457
DATA 451,458,456,460,455,455,456,460,457,456
DATA 457,456,460,459,457,455,461,455,457,457
mean = 0: ss = 0
FOR i = 1 TO n: READ x(i)
mean = mean + x(i) / 100
ss = ss + x(i) * x(i)
NEXT i
ssd = ss - n * mean * mean
var = ssd / 99: sd = SQR(var)
PRINT : PRINT : PRINT : PRINT : PRINT
PRINT " ";
PRINT " mean, sdev. ";
PRINT USING "###.### "; mean; sd
REM
FOR i1 = 1 TO n: d = x(i1) - mean
m(2) = m(2) + d * d / n
m(3) = m(3) + d * d * d / n
m(4) = m(4) + d * d * d * d / n
NEXT i1
skw = m(3) / (m(2) ^ 1.5)
kurt = m(4) / (m(2) ^ 2)
REM
REM
alm = (skw ^ 2) / c1 + ((kurt - c2) ^ 2) / c3
REM
lmm = (skw ^ 2) / 6 + ((kurt - 3) ^ 2) / 24
lm = n * lmm
REM
REM
PRINT : PRINT : PRINT
COLOR 12
PRINT " ";
PRINT USING "ALM= ###.### "; alm;
PRINT USING "LM = ###.### "; lm
END



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