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


Re: Normal or Uniform data using Fingerprints (II)
Posted:
Apr 27, 2013 6:49 PM


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



