```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 valuesWhereas 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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