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Dataplot Vol 2 Vol 1

ISO 13528 EZMINUS SCORE
ISO 13528 EZPLUS SCORE

Name:
    ISO 13528 EZMINUS SCORE (LET)
    ISO 13528 EZPLUS SCORE (LET)
Type:
    Let Subcommand
Purpose:
    Generate an Ez- or an Ez+ score based on the ISO 13528 standard.
Description:
    The ISO 13528 standard for proficiency testing defines the following Ez scores

      Ez-(i) = (X(i) - (Xref - u(ref))/u(X)
    and
      Ez+(i) = (X(i) - (Xref + u(ref))/u(X)

    with Xref, u(ref), and u(x) denoting the "assigned value", the expanded uncertainty of the assigned value, and the laboratory's estimate of the expanded uncertainty of its result, respectively.

    Determing an assigned value and its associated uncertainty is discussed on pages 5-10 of the standard.

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

    The ISO 13528 standard recommends comparing these scores to a critical value of 1.0. Specifically,

    1. If both Ez- and Ez+ are within the -1 to 1 range, the laboratory's performance is satisfactory.

    2. If one of Ez- and Ez+ falls outside the -1 to 1 range, the laboratory's performance is questionable.

    3. If both Ez- and Ez+ are outside the -1 to 1 range, the laboratory's performance is unsatisfactory.
Syntax 1:
    LET <y> = ISO 13528 EZMINUS SCORE <x> <ulab> <xref> <uref>
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is the response variable;
                <ulab> is a variable containing the lab standard uncertainties;
                <xref> 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 Ez- score values are stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    The <x> vector and the <ulab> vector should be of the same length.

Syntax 2:
    LET <y> = ISO 13528 EZPLUS SCORE <x> <ulab> <xref> <uref>
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is the response variable;
                <ulab> is a variable containing the lab standard uncertainties;
                <xref> 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 Ez+ score values are stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    The <x> vector and the <ulab> vector should be of the same length.

Examples:
    LET Z = ISO 13528 EZMINUS SCORE X ULAB XREF UREF
    LET Z = ISO 13528 EZPLUS SCORE X ULAB XREF UREF
Default:
    None
Synonyms:
    None
Related Commands: Reference:
    ISO 13528, First Edition, Statistical Methods for Use in Proficiency Testing by Interlaboratory Comparisons, 2005, pp. 30.
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 sd    = sd y
    let uref  = 2*sd
    let ulab  = cross tabulate sd y x
    let ulab  = 2*ulab
    .
    let ezm = iso 13528 ezminus score y ulab xref uref
    let ezp = iso 13528 ezplus score y ulab xref uref
    .
    set write decimals 3
    print x y ulab ezm ezp
        
    The following output is generated.
    ---------------------------------------------------------------------------
                  X              Y           ULAB            EZM            EZP
    ---------------------------------------------------------------------------
              1.000          1.006          0.008          2.134          2.134
              1.000          0.996          0.008          0.984          0.984
              1.000          0.998          0.008          1.214          1.214
              1.000          1.000          0.008          1.444          1.444
              1.000          0.992          0.008          0.524          0.524
              1.000          0.993          0.008          0.639          0.639
              1.000          1.002          0.008          1.674          1.674
              1.000          0.999          0.008          1.329          1.329
              1.000          0.994          0.008          0.754          0.754
              1.000          1.000          0.008          1.444          1.444
              2.000          0.998          0.010          1.011          1.011
              2.000          1.006          0.010          1.778          1.778
              2.000          1.000          0.010          1.203          1.203
              2.000          1.002          0.010          1.395          1.395
              2.000          0.997          0.010          0.916          0.916
              2.000          0.998          0.010          1.011          1.011
              2.000          0.996          0.010          0.820          0.820
              2.000          1.000          0.010          1.203          1.203
              2.000          1.006          0.010          1.778          1.778
              2.000          0.988          0.010          0.053          0.053
              3.000          0.991          0.007          0.447          0.447
              3.000          0.987          0.007         -0.055         -0.055
              3.000          0.997          0.007          1.201          1.201
              3.000          0.999          0.007          1.452          1.452
              3.000          0.995          0.007          0.950          0.950
              3.000          0.994          0.007          0.824          0.824
              3.000          1.000          0.007          1.578          1.578
              3.000          0.999          0.007          1.452          1.452
              3.000          0.996          0.007          1.075          1.075
              3.000          0.996          0.007          1.075          1.075
              4.000          1.004          0.007          2.278          2.278
              4.000          1.002          0.007          1.889          1.889
              4.000          0.994          0.007          0.851          0.851
              4.000          1.000          0.007          1.629          1.629
              4.000          0.995          0.007          0.980          0.980
              4.000          0.994          0.007          0.851          0.851
              4.000          0.998          0.007          1.370          1.370
              4.000          0.996          0.007          1.110          1.110
              4.000          1.002          0.007          1.889          1.889
              4.000          0.996          0.007          1.110          1.110
              5.000          0.998          0.015          0.696          0.696
              5.000          0.998          0.015          0.696          0.696
              5.000          0.982          0.015         -0.359         -0.359
              5.000          0.990          0.015          0.168          0.168
              5.000          1.002          0.015          0.960          0.960
              5.000          0.984          0.015         -0.227         -0.227
              5.000          0.996          0.015          0.564          0.564
              5.000          0.993          0.015          0.366          0.366
              5.000          0.980          0.015         -0.491         -0.491
              5.000          0.996          0.015          0.564          0.564
              6.000          1.008          0.019          1.090          1.090
              6.000          1.012          0.019          1.292          1.292
              6.000          1.008          0.019          1.090          1.090
              6.000          0.997          0.019          0.483          0.483
              6.000          0.988          0.019          0.028          0.028
              6.000          1.002          0.019          0.736          0.736
              6.000          0.995          0.019          0.382          0.382
              6.000          0.998          0.019          0.533          0.533
              6.000          0.981          0.019         -0.325         -0.325
              6.000          0.996          0.019          0.432          0.432
              7.000          0.990          0.015          0.162          0.162
              7.000          1.004          0.015          1.050          1.050
              7.000          0.996          0.015          0.543          0.543
              7.000          1.000          0.015          0.860          0.860
              7.000          0.998          0.015          0.670          0.670
              7.000          1.000          0.015          0.797          0.797
              7.000          1.018          0.015          1.939          1.939
              7.000          1.010          0.015          1.431          1.431
              7.000          0.996          0.015          0.543          0.543
              7.000          1.002          0.015          0.924          0.924
              8.000          0.998          0.007          1.455          1.455
              8.000          1.000          0.007          1.731          1.731
              8.000          1.006          0.007          2.558          2.558
              8.000          1.000          0.007          1.731          1.731
              8.000          1.002          0.007          2.006          2.006
              8.000          0.996          0.007          1.179          1.179
              8.000          0.998          0.007          1.455          1.455
              8.000          0.996          0.007          1.179          1.179
              8.000          1.002          0.007          2.006          2.006
              8.000          1.006          0.007          2.558          2.558
              9.000          1.002          0.008          1.759          1.759
              9.000          0.998          0.008          1.275          1.275
              9.000          0.996          0.008          1.034          1.034
              9.000          0.995          0.008          0.913          0.913
              9.000          0.996          0.008          1.034          1.034
              9.000          1.004          0.008          2.000          2.000
              9.000          1.004          0.008          2.000          2.000
              9.000          0.998          0.008          1.275          1.275
              9.000          0.999          0.008          1.396          1.396
              9.000          0.991          0.008          0.429          0.429
             10.000          0.991          0.010          0.333          0.333
             10.000          0.995          0.010          0.709          0.709
             10.000          0.984          0.010         -0.322         -0.322
             10.000          0.994          0.010          0.615          0.615
             10.000          0.997          0.010          0.896          0.896
             10.000          0.997          0.010          0.896          0.896
             10.000          0.991          0.010          0.333          0.333
             10.000          0.998          0.010          0.990          0.990
             10.000          1.004          0.010          1.553          1.553
             10.000          0.997          0.010          0.896          0.896
        

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