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Topic: Normal or Uniform data using Fingerprints (II)
Replies: 4   Last Post: Apr 27, 2013 6:49 PM

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Luis A. Afonso

Posts: 4,617
From: LIsbon (Portugal)
Registered: 2/16/05
Re: Normal or Uniform data using Fingerprints (II)
Posted: Apr 27, 2013 6:49 PM
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Reaching to . . .
Normal Distribution exhibits the following fingerprints:

____________[000]__[001]__[010]__[011]____
_n=100_____ 0.917__0.033__0.034__0.016__
_______________(1.64)__(3.90)__(3.52)_____ G,U,V(a)
___150_____ 0.914__0.038__0.036__0.013__
_______________(1.64)__(3.88)__(3.56)_____
___200_____ 0.913__0.040__0.037__0.011__
_______________(1.64)__(3.87)__(3.59)_____
___250_____ 0.909__0.039__0.042__0.010__
_______________(1.64)__(3.87)__(3.65)_____
___300_____ 0.908__0.042__0.042__0.009__
_______________(1.64)__(3.86)__(3.65)_____
___350_____ 0.908__0.042__0.041__0.009__
_______________(1.64)__(3.84)__(3.70)_____
___400_________(1.64)__(3.82)__(3.74)_____


(a) 5% Critical values



Whereas for Uniform data:

____________[000]__[001]__[010]__[011]____

_n=100_____ 0.027__0.972__0.001__0.000__
___150_____ 0.000__0.999__0.000__0.001__
___200_____ 0.000__0.999__0.000__0.001__
___250_____ 0.000__0.999__0.000__0.001__
___300_____ 0.000__0.999__0.000__0.001__



The main features are:

__1) Empirical Critical Values do show a regular pattern: 1.64 for Geary, a slightly decreasing, 3.90 - 3.84 for U and increasing, 3.52 - 3.70 for V.

__2) Important to practical purposes: the sum of frequencies relative to [000] and [010] are 0.951, 0.950, 0.950, 0.951, 0.950, 0.949 for sizes 100(50)350 respectively. Before normal data we have 95% probability to get [000] or [010].
__3) Uniform outputs are almost impossible to be wrongly taken as Normal for sizes equal or over 150. Even for n=100 the type II error is 2.7+0.1 = 2.8 % which is the probability to occur [000] or [010] testing H0: normal against Ha=uniform.

Luis A. Afonso



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