ISO 13528 PA SCORE

ISO 13528 PA SCORE (LET)

Let Subcommand

Generate a percentage of allowed deviation (PA) score based on the ISO 13528 standard.

The ISO 13528 standard for proficiency testing defines the following PA score
\( Pa_{i} = \frac{x_{i} - x_{ref}}{\delta_{E}} 100 \)

with x_ref and \(\delta_{E}\) denoting the "assigned value" and the pre-defined allowance for measurement error, respectively. The multiplication by 100 is to express the score as a percentage.

The Pa statistic is a performance score discussed in the ISO 13528 standard (2015 second edition pp. 25-26). Values of Pa ≤ -100 and Pa ≥ 100 indicate an action signal (i.e., unacceptable performance).

Note that x_ref and \(\delta_{E}\) are not computed from the current data. The x_ref 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 \( \delta_{E} \) is an "acceptable" error.

Although the ISO 13258 standard does not define a specific method for determing \( \delta_{E} \), 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 Pa score is only one of several possible performance scores discussed in the ISO 13528 standard.

LET <y> = ISO 13528 PA SCORE <x> <xref> <deltae>
                        <SUBSET/EXCEPT/FOR qualification>
where <x> is the response variable;
            <xref> is a parameter that defines the assigned value;
            <deltae> is a parameter that defines the DELTAe value;
            <y> is a variable where the Pa score values are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET PA = ISO 13528 PA SCORE X XREF DELTAE

None

ISO 13528 PA is a synonym for ISO 13528 PA SCORE
PA is a synonym for ISO 13528 PA SCORE

ISO 13528 DIPERC SCORE	= Compute the percentage difference-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, 25-26.

Proficiency Testing

2016/2

 
. Step 1:   Read the Data
.
skip 25
read e2489a.dat labid y
.
. Step 2:   Compute and print the Pa values
.
let xref   = median y
let sd     = sd y
let deltae = 3*sd
let deltae = round(deltae,2)
.
let pa    = iso 13528 pa  y xref deltae
.
set write decimals 3
print y pa
.
. Step 3:   Plot the Pa values
.
tic mark offset units screen
tic mark offset 3 3
case asis
label case ais
title case asis
title offset 2
.
y1label Percentage of Allowed Deviation (Pa)
x1label Laboratory
x2label Assigned Value: ^xref
x3label DeltaE: ^deltae
title Pa for E2489A.DAT
line blank solid dash dash
spike on
line color black black red red
.
let xmax = maximum labid
let xtemp = data 1 xmax
let ymax  = data 100 100
let ymin  = data -100 -100
let yzero = data 0 0
plot pa labid and
plot yzero xtemp and
plot ymax xtemp and
plot ymin xtemp
    

The following output is generated

------------------------------
              Y             PA
------------------------------
          1.220         -6.466
          1.620         10.776
          1.820         19.397
          0.600        -33.190
          2.750         59.483
          1.550          7.759
          1.170         -8.621
          1.760         16.810
          1.350         -0.862
          1.180         -8.190
          1.190         -7.759
          1.710         14.655
          2.030         28.448
          1.100        -11.638
          1.840         20.259
          1.390          0.862
          1.130        -10.345
          1.660         12.500
          1.280         -3.879
          1.240         -5.603
          0.690        -29.310
          1.540          7.328
          1.430          2.586
          0.840        -22.845
          0.980        -16.810
          1.970         25.862
          4.890        151.724
          1.850         20.690
          1.090        -12.069
          1.070        -12.931