Luis A. Afonso
Posts:
4,275
From:
LIsbon (Portugal)
Registered:
2/16/05
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Lab rats
Posted:
Jul 29, 2011 6:18 PM
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Lab rats
For those that were taught that p-values evaluation of a hypotheses test statistics do demand to be known:
___ Its analytical expression and that of its inverse,
shall be surprised a lot how simple and straightforward Monte Carlo simulations deal with the problem.
Data: A seventy values sample (rats weight, below).
Objective: see if it could be originated from a normal population: sample mean = 112.3, stdev.= 9.06
Method: Jarque-Bera test.
___firstly
Evaluating: JB= 3.3732 ______
and
____Skewness___S = m3 / m2 ^ 1.5 = -0.066
____Kurtosis ___K = m4 / (m2 ^ 2) = 4.067
Taking in account Tables of critical values one have:
D. Wurtz, H.G. Katzberger:
arxiv.org/abs/math/0509423
______n= 50_____4.9757
______n= 75_____5.2777
Then we should decide that H0, normality, is not rejected.
__secondly
HOWEVER: What about the Excess Kurtosis = 1.067 compared with the expected value = 0?
It seems too HIGH . . .
The p values (10 000 samples each, repeated 10 tines) had shown:
__0.032, 0.032, 0.031, 0.035, 0.032, 0.034, 0.034, 0.033, 0.034, 0.032: all lesser than 0.05.
and we became suspicious that the sample could be leptokurtic.
___thirdly
It´s time to test S0 = -0.066.
Value : 0.577
pK = 0.034, pS=0.577
Using the Fisher´s formula
H= -2* (ln pK + ln pS) = 7.863
Because we are dealing with a 4df Chi square
____p(chi<=7.863| 4df) = 0.9033 then alpha=9.67%
Is this 2% compatible to the Sidak analysis? Let see:
Alpha = 0.05 leads to alpha comp.= 0.025320565 for the composite test._____ From Wikipedia: < A related correction, called the ?idák correction (or Dunn- Sidak correction) that is often used is 1 - (1 - ?)^(1 / n) . This correction is often confused with the Bonferroni correction. The ?idák correction is derived by assuming that the individual tests are independent >.
Conclusion: Because 0.0253?< 0.0967 the Sidak critical value is located at right the observed alpha. We should conclude that H0 no rejection is more likely.
****
Critics: My say (pardon me): Classical Statisticians concerning Significance Tests are compared to sec. XIX physicians: in total (or almost) absence of clinical analysis, illnesses were detected throughout SYMPTOMS and PERSONAL EXPERIENCE . . .
In fact we don?t know fundamental things as:
___is Sidak appropriated in this context? I don?t know.
___and are they independent? Unlikely!
Luis A. Afonso
DATA 120,116,094,120,112,112,106,102,118,112
DATA 116,098,116,114,120,124,112,122,110,084
DATA 106,122,124,112,118,128,108,120,110,106
DATA 140,102,122,112,110,130,112,106,102,114
DATA 108,110,116,118,118,108,102,110,104,112
DATA 122,112,116,110,112,118,098,104,120,106
DATA 108,110,102,110,120,126,114,098,116,100
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