Re: Normality - A two-fold test
- From: "\"Luis A. Afonso\"" <licas_@xxxxxxxxxxx>
- Date: Wed, 17 Aug 2005 09:03:33 EDT
Ratio * a / u * (Geary test over David - Hartley – Pearson´s)
__________G = a = sad / sqrt ( n * ssd )
__________D = u = range / sqrt ( ssd /(n-1))
sad = sum of the absolute deviations
n = sample size
range = sample range (Mathworld) = maximum - minimum
ssd = sum of squared deviations
sqrt = square root (function).
The ratio is :
_________a /u = sqrt ((n-1) / n) * sad / range
*****
The range estimating a Population standard deviation
Simulation (Monte Carlo) allows us to estimate the standard deviation of a normal population (sigma) based on the range obtained by a random samples.
______k = range / sigma______ sigma = range / k
where k shows a size dependence.
Table of results from samples N(0,1)
__n_____k_____s.d._____Bibl.
_10____3.077__0.334___3.078
_20____3.735__0.271
_30____4.085__0.247
_40____4.322__0.233
_50____4.499__0.223___4.498
Note: s.d. is the standard deviation of sigma (see above).
(Bibl. P. Hoel , Introduction to Mathematical Statistics, Portuguese Brazilian translation).
Numerical example
Suppose that a sized 40 sample gave the range 7.502. (think that this value is independent from the Population standard deviation).
The first job is to evaluate sigma:
_____________sigma =7.502 / 4.322 = 1.736
The error (s.d.) of this estimate is
____________1.736 * 0.233 = 0.404
resulting
____________1.736 +/- 0.404
______________licas
.
- References:
- Normality - A two-fold test
- From: \"Luis A. Afonso\"
- Normality - A two-fold test
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