
ROBUST POOLED STANDARD DEVIATIONName:
Let w_{1}, w_{2}, ... , w_{p} be the standard deviations from the p labs. The degrees of freedom for w_{i} = n_{i}  1 where n_{i} is the number of replications for lab i. Compute the limit factor, \( \eta \),
with \( \chi_{\nu}^{2} \) denoting the percent point function of the chisquare distribution \( \xi = \frac{1} {\sqrt{\chi_{\nu+2}^{2}(\nu \eta^2) + 0.1 \eta^2}} \) with \( \chi_{\nu}^{2} \) denoting the cumulative distribution function of the chisquare distribution. The limit factor and adjustment factor assume that each lab has the same number of replications. If the number of replications are not equal, Dataplot will use the average number of replications. The initual value of w* is set to the median of the w_{i}'s. To update the value of w* compute
For each w_{i},
The updated value of w* is
The value of w* is iterated until the difference between two successive values of w* is sufficiently small. The ISO 13528 standard also allows this computation to be performed on the lab ranges. In this case, the robust pooled range uses the same computation as above with the exception that the degrees of freedom, \( \nu \), is set to 1. The input for this command is the sample standard deviations. To specify the sample size, enter
<SUBSET/EXCEPT/FOR qualification> where <ysd> is the variable containing the sample standard deviations; <x> is the labid variable; <par> is a parameter where the computed robust pooled sd is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<SUBSET/EXCEPT/FOR qualification> where <yrange> is the variable containing the sample ranges; <x> is the labid variable; <par> is a parameter where the computed robust pooled range is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET SD = ROBUST POOLED STANDARD DEVIATION YSD LET SD = ROBUST POOLED STANDARD DEVIATION YSD ... SUBSET TAG > 2 LET SD = ROBUST POOLED RANGE YRANGE
SKIP 25 READ GEAR.DAT Y X . SET LET CROSS TABULATE COLLAPSE LET YSD = CROSS TABULATE SD Y X LET NSIZE = CROSS TABULATE SIZE X LET NREPL = MEAN NSIZE . LET A = ROBUST POOLED STANDARD DEVIATION YSDThe returned value is 0.5335508E02.  
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Date created: 01/06/2011 