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Dataplot Vol 2 Vol 1

ISO 13528 ZPRIME SCORE

Name:
    ISO 13528 ZPRIME SCORE (LET)
Type:
    Let Subcommand
Purpose:
    Generate a z'-score based on the ISO 13528 standard.
Description:
    The ISO 13528 standard for proficiency testing defines the following z'-score

      Z'(i) = (X(i) - Xref)/SQRT(sigma**2 + u(Xref)**2)

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

    Determing an assigned value and its associated uncertainty 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, uXref, 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 ZPRIME SCORE <x> <xref> <sigma> <uref>
                            <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;
                <uref> is a parameter that defines the standard uncertainty of 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 ZPRIME SCORE X XREF SIGMA UREF
Default:
    None
Synonyms:
    None
Related Commands: Reference:
    ISO 13528, First Edition, Statistical Methods for Use in Proficiency Testing by Interlaboratory Comparisons, 2005, pp. 28-29.
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 uref = 0.001
.
let yz = iso 13528 zprime score y xref sigma uref
.
set write decimals 3
print x y yz
    The following output is generated. 
    ---------------------------------------------
              X              Y             YZ
---------------------------------------------
          1.000          1.006          0.943
          1.000          0.996         -0.629
          1.000          0.998         -0.314
          1.000          1.000          0.000
          1.000          0.992         -1.258
          1.000          0.993         -1.100
          1.000          1.002          0.314
          1.000          0.999         -0.157
          1.000          0.994         -0.943
          1.000          1.000          0.000
          2.000          0.998         -0.314
          2.000          1.006          0.943
          2.000          1.000          0.000
          2.000          1.002          0.314
          2.000          0.997         -0.471
          2.000          0.998         -0.314
          2.000          0.996         -0.629
          2.000          1.000          0.000
          2.000          1.006          0.943
          2.000          0.988         -1.887
          3.000          0.991         -1.415
          3.000          0.987         -2.044
          3.000          0.997         -0.471
          3.000          0.999         -0.157
          3.000          0.995         -0.786
          3.000          0.994         -0.943
          3.000          1.000          0.000
          3.000          0.999         -0.157
          3.000          0.996         -0.629
          3.000          0.996         -0.629
          4.000          1.004          0.786
          4.000          1.002          0.314
          4.000          0.994         -0.943
          4.000          1.000          0.000
          4.000          0.995         -0.786
          4.000          0.994         -0.943
          4.000          0.998         -0.314
          4.000          0.996         -0.629
          4.000          1.002          0.314
          4.000          0.996         -0.629
          5.000          0.998         -0.314
          5.000          0.998         -0.314
          5.000          0.982         -2.831
          5.000          0.990         -1.572
          5.000          1.002          0.314
          5.000          0.984         -2.516
          5.000          0.996         -0.629
          5.000          0.993         -1.100
          5.000          0.980         -3.145
          5.000          0.996         -0.629
          6.000          1.008          1.415
          6.000          1.012          2.044
          6.000          1.008          1.415
          6.000          0.997         -0.471
          6.000          0.988         -1.887
          6.000          1.002          0.314
          6.000          0.995         -0.786
          6.000          0.998         -0.314
          6.000          0.981         -2.988
          6.000          0.996         -0.629
          7.000          0.990         -1.572
          7.000          1.004          0.629
          7.000          0.996         -0.629
          7.000          1.000          0.157
          7.000          0.998         -0.314
          7.000          1.000          0.000
          7.000          1.018          2.831
          7.000          1.010          1.572
          7.000          0.996         -0.629
          7.000          1.002          0.314
          8.000          0.998         -0.314
          8.000          1.000          0.000
          8.000          1.006          0.943
          8.000          1.000          0.000
          8.000          1.002          0.314
          8.000          0.996         -0.629
          8.000          0.998         -0.314
          8.000          0.996         -0.629
          8.000          1.002          0.314
          8.000          1.006          0.943
          9.000          1.002          0.314
          9.000          0.998         -0.314
          9.000          0.996         -0.629
          9.000          0.995         -0.786
          9.000          0.996         -0.629
          9.000          1.004          0.629
          9.000          1.004          0.629
          9.000          0.998         -0.314
          9.000          0.999         -0.157
          9.000          0.991         -1.415
         10.000          0.991         -1.415
         10.000          0.995         -0.786
         10.000          0.984         -2.516
         10.000          0.994         -0.943
         10.000          0.997         -0.471
         10.000          0.997         -0.471
         10.000          0.991         -1.415
         10.000          0.998         -0.314
         10.000          1.004          0.629
         10.000          0.997         -0.471

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