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Dataplot Vol 2 Vol 1

ISO 13528 ZETA SCORE

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

      Zeta(i) = (X(i) - Xref)/SQRT(u(X)**2 + u(Xref)**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.

    According to the ISO 13528 standard, it is not currently common practice to incorporate the uX information provided by the laboratories in the scores used in the proficiency testing. However, when there is an effective system for validating the laboratories estimates of their uncertainties, zeta-scores may be used instead of z-scores. The zeta-scores have a similar interpretation, i.e., zeta-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 ZETA 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 z-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 ZETA 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. 29-30.
Applications:
    Proficiency Testing
Implementation Date:
    2012/1
Program: 
     
skip 25
read gear.dat y x
.
let xref  = 1.
let uref  = sd y
let ulab  = cross tabulate sd y x
.
let yzeta = iso 13528 zeta score y ulab xref uref
.
set write decimals 3
print x y ulab yzeta
    The following output is generated. 
     
------------------------------------------------------------
              X              Y           ULAB          YZETA
------------------------------------------------------------
          1.000          1.006          0.004          0.785
          1.000          0.996          0.004         -0.523
          1.000          0.998          0.004         -0.261
          1.000          1.000          0.004          0.000
          1.000          0.992          0.004         -1.047
          1.000          0.993          0.004         -0.916
          1.000          1.002          0.004          0.261
          1.000          0.999          0.004         -0.130
          1.000          0.994          0.004         -0.785
          1.000          1.000          0.004          0.000
          2.000          0.998          0.005         -0.245
          2.000          1.006          0.005          0.735
          2.000          1.000          0.005          0.000
          2.000          1.002          0.005          0.245
          2.000          0.997          0.005         -0.367
          2.000          0.998          0.005         -0.245
          2.000          0.996          0.005         -0.490
          2.000          1.000          0.005          0.000
          2.000          1.006          0.005          0.735
          2.000          0.988          0.005         -1.470
          3.000          0.991          0.003         -1.210
          3.000          0.987          0.003         -1.748
          3.000          0.997          0.003         -0.403
          3.000          0.999          0.003         -0.134
          3.000          0.995          0.003         -0.672
          3.000          0.994          0.003         -0.807
          3.000          1.000          0.003          0.000
          3.000          0.999          0.003         -0.134
          3.000          0.996          0.003         -0.538
          3.000          0.996          0.003         -0.538
          4.000          1.004          0.003          0.678
          4.000          1.002          0.003          0.271
          4.000          0.994          0.003         -0.814
          4.000          1.000          0.003          0.000
          4.000          0.995          0.003         -0.678
          4.000          0.994          0.003         -0.814
          4.000          0.998          0.003         -0.271
          4.000          0.996          0.003         -0.542
          4.000          1.002          0.003          0.271
          4.000          0.996          0.003         -0.542
          5.000          0.998          0.007         -0.203
          5.000          0.998          0.007         -0.203
          5.000          0.982          0.007         -1.828
          5.000          0.990          0.007         -1.016
          5.000          1.002          0.007          0.203
          5.000          0.984          0.007         -1.625
          5.000          0.996          0.007         -0.406
          5.000          0.993          0.007         -0.711
          5.000          0.980          0.007         -2.032
          5.000          0.996          0.007         -0.406
          6.000          1.008          0.009          0.768
          6.000          1.012          0.009          1.110
          6.000          1.008          0.009          0.768
          6.000          0.997          0.009         -0.256
          6.000          0.988          0.009         -1.024
          6.000          1.002          0.009          0.170
          6.000          0.995          0.009         -0.426
          6.000          0.998          0.009         -0.170
          6.000          0.981          0.009         -1.622
          6.000          0.996          0.009         -0.341
          7.000          0.990          0.007         -0.992
          7.000          1.004          0.007          0.397
          7.000          0.996          0.007         -0.397
          7.000          1.000          0.007          0.099
          7.000          0.998          0.007         -0.198
          7.000          1.000          0.007          0.000
          7.000          1.018          0.007          1.786
          7.000          1.010          0.007          0.992
          7.000          0.996          0.007         -0.397
          7.000          1.002          0.007          0.198
          8.000          0.998          0.003         -0.275
          8.000          1.000          0.003          0.000
          8.000          1.006          0.003          0.827
          8.000          1.000          0.003          0.000
          8.000          1.002          0.003          0.275
          8.000          0.996          0.003         -0.551
          8.000          0.998          0.003         -0.275
          8.000          0.996          0.003         -0.551
          8.000          1.002          0.003          0.275
          8.000          1.006          0.003          0.827
          9.000          1.002          0.004          0.265
          9.000          0.998          0.004         -0.265
          9.000          0.996          0.004         -0.531
          9.000          0.995          0.004         -0.664
          9.000          0.996          0.004         -0.531
          9.000          1.004          0.004          0.531
          9.000          1.004          0.004          0.531
          9.000          0.998          0.004         -0.265
          9.000          0.999          0.004         -0.132
          9.000          0.991          0.004         -1.196
         10.000          0.991          0.005         -1.092
         10.000          0.995          0.005         -0.607
         10.000          0.984          0.005         -1.942
         10.000          0.994          0.005         -0.728
         10.000          0.997          0.005         -0.364
         10.000          0.997          0.005         -0.364
         10.000          0.991          0.005         -1.092
         10.000          0.998          0.005         -0.242
         10.000          1.004          0.005          0.485
         10.000          0.997          0.005         -0.364

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