Date: Apr 27, 2013 6:49 PM
Author: Luis A. Afonso
Subject: Re: Normal or Uniform data using Fingerprints (II)
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