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Dataplot Vol 1 Auxiliary Chapter

ROBUST POOLED STANDARD DEVIATION

Name:
    ROBUST POOLED STANDARD DEVIATION (LET)
Type:
    Let Subcommand
Purpose:
    Compute the robust pooled standard deviation of a variable.
Description:
    The definition for the robust pooled standard deviation from the ISO 13528 standard. It is computed as follows.

    Let w1, w2, ... , wp be the standard deviations from the p labs. The degrees of freedom for wi = ni - 1 where ni is the number of replications for lab i.

    Compute the limit factor, eta,

      eta = SQRT(CHSPPF(0.9,nu)/nu)

      with CHSPPF denoting the percent point function of the chi-square distribution

    and the adjustment factor, xi,

      xi = 1/SQRT(CHSCDF(nu*eta**2,nu+2) + 0.1*eta**2)

      with CHSCDF denoting the cumulative distribution function of the chi-square 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 wi's.

    To update the value of w* compute

      psi = eta times w*

    For each wi,

      w(i)* = psi    if w(i) >  psi
 = w(i)   if w(i) <= psi

    The updated value of w* is

      w* = Adjustment Factor * SQRT(SUM[i=1 to p][(w(i))**2]/p)

    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.

Syntax 1:
    LET <par> = ROBUST POOLED STANDARD DEVIATION <y> <x>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y> is the response variable;
                <x> is the lab-id variable;
                <par> is a parameter where the computed robust pooled sd is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 2:
    LET <par> = ROBUST POOLED RANGE <y> <x>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y> is the response variable;
                <x> is the lab-id variable;
                <par> is a parameter where the computed robust pooled range is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET SD = ROBUST POOLED STANDARD DEVIATION Y X
    LET SD = ROBUST POOLED STANDARD DEVIATION Y X SUBSET TAG > 2
    LET SD = ROBUST POOLED RANGE Y X
Note:
    Dataplot statistics can be used in a number of commands. For details, enter

      HELP STATISTICS
Default:
    None
Synonyms:
    ROBUST POOLED SD is a synonym for ROBUST POOLED STANDARD DEVIATION
Related Commands: Applications:
    Data Analysis, Proficiency Analysis
Reference:
    ISO 13528 (2005), "Statistical Methods for use in proficiency testing by interlaboratory comparisons," Section C.2 Algorithm S.
Implementation Date:
    2010/12
Program:
     
    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 YSD
        
    The returned value is 0.5335508E-02.

Date created: 01/06/2011
Last updated: 01/06/2011
Please email comments on this WWW page to alan.heckert@nist.gov.