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Dataplot Vol 2 Vol 1

ISO 13528 ZSCORE

Name:
    ISO 13528 ZSCORE (LET)
Type:
    Let Subcommand
Purpose:
    Generate a z-score based on the ISO 13528 standard.
Description:
    The standard definition of a z-score is

      Z(i) = (X(i) - xbar)/s

    with xbar and s denoting the sample mean and standard deviation, respectively.

    The ISO 13528 standard for proficiency testing defines the following z-score

      Z(i) = (X(i) - Xref)/sigma

    with Xref and sigma denoting the "assigned value" and the standard deviation of the proficiency assessment, respectively.

    Determing an assigned value is discussed on pages 5-10 of the standard. Determining a value for sigma is discussed on pages 15-18 of the standard.

    Since there are a mumber of different methods for determining Xref and sigma, these values will be defined by the user rather than being determined from the data.

    The ISO 13528 standard recommends that z-scores with an absolute value greater than 3 should be considered an "action signal" and those with an absolute value greater than 2 should be considered a "warning signal".

Syntax:
    LET <y> = ISO 13528 ZSCORE <x> <xref> <sigma>
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is the response variable;
                <xref> is a parameter that defines the assigned value;
                <sigma> is a parameter that defines the assigned value;
                <y> is a variable where the z-score values are stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET Z = ISO 13528 ZSCORE X XREF SIGMA
Default:
    None
Synonyms:
    None
Related Commands: Reference:
    ISO 13528, First Edition, Statistical Methods for Use in Proficiency Testing by Interlaboratory Comparisons, 2005, pp. 25-26.
Applications:
    Proficiency Testing
Implementation Date:
    2012/1
Program: 
     
.  Note: this example is just meant to demostrate the
.        mechanics of the command.  This is not in fact
.        proficiency data, but it can be used to demonstrate
.        how to use the command.
.
skip 25
read gear.dat y x
.
let xref  = 1.
let sigma = sd y
.
let yz = iso 13528 zscore y xref sigma
.
set write decimals 3
print x y yz
    The following output is generated. 
    ---------------------------------------------
              X              Y             YZ
---------------------------------------------
          1.000          1.006          0.955
          1.000          0.996         -0.637
          1.000          0.998         -0.318
          1.000          1.000          0.000
          1.000          0.992         -1.274
          1.000          0.993         -1.114
          1.000          1.002          0.318
          1.000          0.999         -0.159
          1.000          0.994         -0.955
          1.000          1.000          0.000
          2.000          0.998         -0.318
          2.000          1.006          0.955
          2.000          1.000          0.000
          2.000          1.002          0.318
          2.000          0.997         -0.477
          2.000          0.998         -0.318
          2.000          0.996         -0.637
          2.000          1.000          0.000
          2.000          1.006          0.955
          2.000          0.988         -1.911
          3.000          0.991         -1.433
          3.000          0.987         -2.070
          3.000          0.997         -0.477
          3.000          0.999         -0.159
          3.000          0.995         -0.796
          3.000          0.994         -0.955
          3.000          1.000          0.000
          3.000          0.999         -0.159
          3.000          0.996         -0.637
          3.000          0.996         -0.637
          4.000          1.004          0.796
          4.000          1.002          0.318
          4.000          0.994         -0.955
          4.000          1.000          0.000
          4.000          0.995         -0.796
          4.000          0.994         -0.955
          4.000          0.998         -0.318
          4.000          0.996         -0.637
          4.000          1.002          0.318
          4.000          0.996         -0.637
          5.000          0.998         -0.318
          5.000          0.998         -0.318
          5.000          0.982         -2.866
          5.000          0.990         -1.592
          5.000          1.002          0.318
          5.000          0.984         -2.548
          5.000          0.996         -0.637
          5.000          0.993         -1.114
          5.000          0.980         -3.185
          5.000          0.996         -0.637
          6.000          1.008          1.433
          6.000          1.012          2.070
          6.000          1.008          1.433
          6.000          0.997         -0.477
          6.000          0.988         -1.911
          6.000          1.002          0.318
          6.000          0.995         -0.796
          6.000          0.998         -0.318
          6.000          0.981         -3.026
          6.000          0.996         -0.637
          7.000          0.990         -1.592
          7.000          1.004          0.637
          7.000          0.996         -0.637
          7.000          1.000          0.159
          7.000          0.998         -0.318
          7.000          1.000          0.000
          7.000          1.018          2.866
          7.000          1.010          1.592
          7.000          0.996         -0.637
          7.000          1.002          0.318
          8.000          0.998         -0.318
          8.000          1.000          0.000
          8.000          1.006          0.955
          8.000          1.000          0.000
          8.000          1.002          0.318
          8.000          0.996         -0.637
          8.000          0.998         -0.318
          8.000          0.996         -0.637
          8.000          1.002          0.318
          8.000          1.006          0.955
          9.000          1.002          0.318
          9.000          0.998         -0.318
          9.000          0.996         -0.637
          9.000          0.995         -0.796
          9.000          0.996         -0.637
          9.000          1.004          0.637
          9.000          1.004          0.637
          9.000          0.998         -0.318
          9.000          0.999         -0.159
          9.000          0.991         -1.433
         10.000          0.991         -1.433
         10.000          0.995         -0.796
         10.000          0.984         -2.548
         10.000          0.994         -0.955
         10.000          0.997         -0.477
         10.000          0.997         -0.477
         10.000          0.991         -1.433
         10.000          0.998         -0.318
         10.000          1.004          0.637
         10.000          0.997         -0.477

Date created: 01/27/2012
Last updated: 01/27/2012
Please email comments on this WWW page to alan.heckert@nist.gov.