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Topic: Lab rats
Replies: 2   Last Post: Oct 8, 2012 4:57 PM

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Luis A. Afonso

Posts: 4,758
From: LIsbon (Portugal)
Registered: 2/16/05
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.


Evaluating: JB= 3.3732 ______
____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:
______n= 50_____4.9757
______n= 75_____5.2777
Then we should decide that H0, normality, is not rejected.


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.


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

Date Subject Author
Read Lab rats
Luis A. Afonso
Read Re: Lab rats
Luis A. Afonso
Read Re: Lab rats
Luis A. Afonso

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