Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.stat.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Luis A. Afonso

Posts: 4,743
From: LIsbon (Portugal)
Registered: 2/16/05
Lab rats
Posted: Jul 29, 2011 6:18 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum 1994-2015. All Rights Reserved.