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Dataplot Vol 2 Vol 1

ISO 13528 DIPERCENTAGE SCORE

Name:
    ISO 13528 DIPERCENTAGE SCORE (LET)
Type:
    Let Subcommand
Purpose:
    Generate a percentage difference score based on the ISO 13528 standard.
Description:
    The ISO 13528 standard for proficiency testing defines the difference between measurement and a reference value as

      \( D_{i} = x_{i} - x_{ref} \)

    The percentage difference score is then defined as

      \( D_{i}\% = 100 \frac{x_{i} - x_{ref}}{x_{ref}} \)

    with xref denoting the "assigned value". The multiplication by 100 is to express the score as a percentage.

    The Di and Di% statistics are performance scores discussed in the ISO 13528 standard (2015 second edition page 25).

    The difference score is typically compared to a \( \delta_{E} \) value such that

      \( D_{i} < -\delta_{E} \) or \( D_{i} > \delta_{E} \)

    indicates an action signal (i.e., unacceptable performance). In terms of the Di% score, this translates to

      \( D_{i}\% < -100 \delta_{E}/x_{ref} \) or \( D_{i}\% > 100 \delta_{E}/x_{ref} \)

    Note that Xref and DELTAe are not computed from the current data. The Xref is considered the "true" value (or the best guess for the true value). The ISO 13528 standard discusses numerous ways of determining this value. The DELTAe is an "acceptable" error. Although the ISO 13258 standard does not define a specific method for determing DELTAe, if estimates for the repeatability and reproducibility are available, then ISO 13528 suggests the following (p. 22)

      \( \sigma_{pt} = \sqrt{\sigma_{R}^2 - \sigma_{r}^2 (1 - 1/m)} \)

    where

      \( \sigma_{pt} \) = standard deviation for proficiency assessment
      \( \sigma_{R} \) = repeatability standard deviation
      \( \sigma_{r} \) = reproducibility standard deviation
      m = number of replicate measurements for each participant

    Then

      \( \delta_{E} = 3 \sigma_{pt} \)

    The justification for this is that this corresponds to an action signal of +/-3 for z-scores.

    In some cases, \( \sigma_{pt} \) may be based on fitness for purpose or data from prior rounds.

    The Di% score is only one of several possible performance scores discussed in the ISO 13528 standard.

Syntax:
    LET <y> = ISO 13528 DIPERCENTAGE SCORE <x> <xref>
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is the response variable;
                <xref> is a parameter that defines the assigned value;
                <y> is a variable where the Di% score values are stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET DIPERC = ISO 13528 DIPERCENTAGE SCORE X XREF DELTAE
Default:
    None
Synonyms:
    ISO 13528 DIPERCENTAGE is a synonym for ISO 13528 DIPERCENTAGE SCORE
    DIPERCENTAGE is a synonym for ISO 13528 PA SCORE
    DI PERCENTAGE is a synonym for DIPERCENTAGE
Related Commands: Reference:
    ISO 13528, Second Edition, Statistical Methods for Use in Proficiency Testing by Interlaboratory Comparisons, 2015, pp. 22, 25.
Applications:
    Proficiency Testing
Implementation Date:
    2016/2
Program:
    . Step 1:   Read the Data
    .
    skip 25
    read e2489a.dat labid y
    .
    . Step 2:   Compute and print the Di percentage values
    .
    let xref   = median y
    .
    let diperc= iso 13528 diperc  y xref
    .
    set write decimals 3
    print y diperc
    .
    . Step 3:   Plot the Di percentage values
    .
    tic mark offset units screen
    tic mark offset 3 3
    case asis
    label case ais
    title case asis
    title offset 2
    .
    y1label D(i) %
    x1label Laboratory
    x2label Assigned Value: ^xref
    title D(i) %  for E2489A.DAT
    line blank solid dash dash
    spike on
    line color black black red red
    .
    let sd = sd y
    let deltae = 3*sd
    let deltae = round(deltae,2)
    let ul = 100*deltae/xref
    let ll = -ul
    .
    let xmax = maximum labid
    let xtemp = data 1 xmax
    let ymax  = data ul ul
    let ymin  = data -ll -ll
    let yzero = data 0 0
    plot diperc labid and
    plot yzero xtemp and
    plot ymax xtemp and
    plot ymin xtemp
        
    The following output is generated
    ------------------------------
                  Y         DIPERC
    ------------------------------
              1.220        -10.949
              1.620         18.248
              1.820         32.847
              0.600        -56.204
              2.750        100.730
              1.550         13.139
              1.170        -14.599
              1.760         28.467
              1.350         -1.460
              1.180        -13.869
              1.190        -13.139
              1.710         24.818
              2.030         48.175
              1.100        -19.708
              1.840         34.307
              1.390          1.460
              1.130        -17.518
              1.660         21.168
              1.280         -6.569
              1.240         -9.489
              0.690        -49.635
              1.540         12.409
              1.430          4.380
              0.840        -38.686
              0.980        -28.467
              1.970         43.796
              4.890        256.934
              1.850         35.036
              1.090        -20.438
              1.070        -21.898
        
    plot generated by sample program

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Date created: 04/11/2016
Last updated: 04/11/2016

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