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Dataplot Vol 2 Vol 1

ISO 13528 EN SCORE

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

      En(i) = (X(i) - Xref)/SQRT(u(X)**2 + u(ref)**2)

    with Xref, uref and ux denoting the "assigned value", the standard uncertainty of the assigned value, and the laboratory's estimate of the standard 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, uref and ux, these values will be defined by the user rather than being determined from the data.

    This command is similar to the ISO 13528 ZETA SCORE command. The difference is that the En scores use expanded uncertainties while the zeta-scores use a standard uncertainty.

    When the coverage factor is 2 (i.e., 2 times the standard uncertainty), a critical value of 1 for the En score is equivalent to a critical value of 2 for a z-score (i.e., this generates a "warning signal").

Syntax:
    LET <y> = ISO 13528 EN 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 En 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 EN SCORE X ULAB XREF UREF
Default:
    None
Synonyms:
    EN is a synonym for ISO 13528 EN SCORE
Related Commands: Reference:
    ISO 13528, First Edition, Statistical Methods for Use in Proficiency Testing by Interlaboratory Comparisons, 2005, pp. 27-28.
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 en    = iso 13528 en score y ulab xref uref
    .
    set write decimals 3
    print x y ulab en
        
    The following output is generated.
    ------------------------------------------------------------
                  X              Y           ULAB             EN
    ------------------------------------------------------------
              1.000          1.006          0.008          0.392
              1.000          0.996          0.008         -0.261
              1.000          0.998          0.008         -0.130
              1.000          1.000          0.008          0.000
              1.000          0.992          0.008         -0.523
              1.000          0.993          0.008         -0.458
              1.000          1.002          0.008          0.130
              1.000          0.999          0.008         -0.065
              1.000          0.994          0.008         -0.392
              1.000          1.000          0.008          0.000
              2.000          0.998          0.010         -0.122
              2.000          1.006          0.010          0.367
              2.000          1.000          0.010          0.000
              2.000          1.002          0.010          0.122
              2.000          0.997          0.010         -0.183
              2.000          0.998          0.010         -0.122
              2.000          0.996          0.010         -0.245
              2.000          1.000          0.010          0.000
              2.000          1.006          0.010          0.367
              2.000          0.988          0.010         -0.735
              3.000          0.991          0.007         -0.605
              3.000          0.987          0.007         -0.874
              3.000          0.997          0.007         -0.201
              3.000          0.999          0.007         -0.067
              3.000          0.995          0.007         -0.336
              3.000          0.994          0.007         -0.403
              3.000          1.000          0.007          0.000
              3.000          0.999          0.007         -0.067
              3.000          0.996          0.007         -0.269
              3.000          0.996          0.007         -0.269
              4.000          1.004          0.007          0.339
              4.000          1.002          0.007          0.135
              4.000          0.994          0.007         -0.407
              4.000          1.000          0.007          0.000
              4.000          0.995          0.007         -0.339
              4.000          0.994          0.007         -0.407
              4.000          0.998          0.007         -0.135
              4.000          0.996          0.007         -0.271
              4.000          1.002          0.007          0.135
              4.000          0.996          0.007         -0.271
              5.000          0.998          0.015         -0.101
              5.000          0.998          0.015         -0.101
              5.000          0.982          0.015         -0.914
              5.000          0.990          0.015         -0.508
              5.000          1.002          0.015          0.101
              5.000          0.984          0.015         -0.812
              5.000          0.996          0.015         -0.203
              5.000          0.993          0.015         -0.355
              5.000          0.980          0.015         -1.016
              5.000          0.996          0.015         -0.203
              6.000          1.008          0.019          0.384
              6.000          1.012          0.019          0.555
              6.000          1.008          0.019          0.384
              6.000          0.997          0.019         -0.128
              6.000          0.988          0.019         -0.512
              6.000          1.002          0.019          0.085
              6.000          0.995          0.019         -0.213
              6.000          0.998          0.019         -0.085
              6.000          0.981          0.019         -0.811
              6.000          0.996          0.019         -0.170
              7.000          0.990          0.015         -0.496
              7.000          1.004          0.015          0.198
              7.000          0.996          0.015         -0.198
              7.000          1.000          0.015          0.049
              7.000          0.998          0.015         -0.099
              7.000          1.000          0.015          0.000
              7.000          1.018          0.015          0.893
              7.000          1.010          0.015          0.496
              7.000          0.996          0.015         -0.198
              7.000          1.002          0.015          0.099
              8.000          0.998          0.007         -0.137
              8.000          1.000          0.007          0.000
              8.000          1.006          0.007          0.413
              8.000          1.000          0.007          0.000
              8.000          1.002          0.007          0.137
              8.000          0.996          0.007         -0.275
              8.000          0.998          0.007         -0.137
              8.000          0.996          0.007         -0.275
              8.000          1.002          0.007          0.137
              8.000          1.006          0.007          0.413
              9.000          1.002          0.008          0.132
              9.000          0.998          0.008         -0.132
              9.000          0.996          0.008         -0.265
              9.000          0.995          0.008         -0.332
              9.000          0.996          0.008         -0.265
              9.000          1.004          0.008          0.265
              9.000          1.004          0.008          0.265
              9.000          0.998          0.008         -0.132
              9.000          0.999          0.008         -0.066
              9.000          0.991          0.008         -0.598
             10.000          0.991          0.010         -0.546
             10.000          0.995          0.010         -0.303
             10.000          0.984          0.010         -0.971
             10.000          0.994          0.010         -0.364
             10.000          0.997          0.010         -0.182
             10.000          0.997          0.010         -0.182
             10.000          0.991          0.010         -0.546
             10.000          0.998          0.010         -0.121
             10.000          1.004          0.010          0.242
             10.000          0.997          0.010         -0.182
        

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