ISO 13528 DIPERCENTAGE SCORE

ISO 13528 DIPERCENTAGE SCORE (LET)

Let Subcommand

Generate a percentage difference score based on the ISO 13528 standard.

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

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

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.

LET DIPERC = ISO 13528 DIPERCENTAGE SCORE X XREF DELTAE

None

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

ISO 13528 PA SCORE	= Compute the percentage of allowed deviation-score as defined by the ISO 13528 standard.
ISO 13528 EN SCORE	= Compute the En-score as defined by the ISO 13528 standard.
ISO 13528 ZETA SCORE	= Compute the zeta-score as defined by the ISO 13528 standard.
ISO 13528 ZPRIME SCORE	= Compute the z'-score as defined by the ISO 13528 standard.
ISO 13528 ZSCORE	= Compute the z-score as defined by the ISO 13528 standard.
ISO 13528 EZMINUS SCORE	= Compute the Ez- score as defined by the ISO 13528 standard.
ISO 13528 EZPLUS SCORE	= Compute the Ez+ score as defined by the ISO 13528 standard.

ISO 13528, Second Edition, Statistical Methods for Use in Proficiency Testing by Interlaboratory Comparisons, 2015, pp. 22, 25.

Proficiency Testing

2016/2

. 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