ISO 13528 EN SCORE

ISO 13528 EN SCORE (LET)

Let Subcommand

Generate a E_n score based on the ISO 13528 standard.

The ISO 13528 standard for proficiency testing defines the following E_n score

with X_ref, u_ref and u_x 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 X_ref, u_ref and u_x, 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 E_n 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 E_n score is equivalent to a critical value of 2 for a z-score (i.e., this generates a "warning signal").

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 E_n 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.

LET Z = ISO 13528 EN SCORE X ULAB XREF UREF

None

EN is a synonym for ISO 13528 EN SCORE

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, First Edition, Statistical Methods for Use in Proficiency Testing by Interlaboratory Comparisons, 2005, pp. 27-28.

Proficiency Testing

2012/01

 
.  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          0.009          0.393
           1.000          0.996          0.009         -0.262
           1.000          0.998          0.009         -0.131
           1.000          1.000          0.009          0.000
           1.000          0.992          0.009         -0.524
           1.000          0.993          0.009         -0.458
           1.000          1.002          0.009          0.131
           1.000          0.999          0.009         -0.065
           1.000          0.994          0.009         -0.393
           1.000          1.000          0.009          0.000
           2.000          0.998          0.010         -0.123
           2.000          1.006          0.010          0.368
           2.000          1.000          0.010          0.000
           2.000          1.002          0.010          0.123
           2.000          0.997          0.010         -0.184
           2.000          0.998          0.010         -0.123
           2.000          0.996          0.010         -0.245
           2.000          1.000          0.010          0.000
           2.000          1.006          0.010          0.368
           2.000          0.988          0.010         -0.735
           3.000          0.991          0.008         -0.605
           3.000          0.987          0.008         -0.874
           3.000          0.997          0.008         -0.202
           3.000          0.999          0.008         -0.067
           3.000          0.995          0.008         -0.336
           3.000          0.994          0.008         -0.404
           3.000          1.000          0.008          0.000
           3.000          0.999          0.008         -0.067
           3.000          0.996          0.008         -0.269
           3.000          0.996          0.008         -0.269
           4.000          1.005          0.008          0.339
           4.000          1.002          0.008          0.136
           4.000          0.994          0.008         -0.407
           4.000          1.000          0.008          0.000
           4.000          0.995          0.008         -0.339
           4.000          0.994          0.008         -0.407
           4.000          0.998          0.008         -0.136
           4.000          0.996          0.008         -0.271
           4.000          1.002          0.008          0.136
           4.000          0.996          0.008         -0.271
           5.000          0.998          0.015         -0.102
           5.000          0.998          0.015         -0.102
           5.000          0.982          0.015         -0.914
           5.000          0.990          0.015         -0.508
           5.000          1.002          0.015          0.102
           5.000          0.984          0.015         -0.813
           5.000          0.996          0.015         -0.203
           5.000          0.993          0.015         -0.356
           5.000          0.980          0.015         -1.016
           5.000          0.996          0.015         -0.203
           6.000          1.009          0.020          0.384
           6.000          1.013          0.020          0.555
           6.000          1.009          0.020          0.384
           6.000          0.997          0.020         -0.128
           6.000          0.988          0.020         -0.512
           6.000          1.002          0.020          0.085
           6.000          0.995          0.020         -0.213
           6.000          0.998          0.020         -0.085
           6.000          0.981          0.020         -0.811
           6.000          0.996          0.020         -0.171
           7.000          0.990          0.016         -0.496
           7.000          1.004          0.016          0.199
           7.000          0.996          0.016         -0.199
           7.000          1.001          0.016          0.050
           7.000          0.998          0.016         -0.099
           7.000          1.000          0.016          0.000
           7.000          1.018          0.016          0.893
           7.000          1.010          0.016          0.496
           7.000          0.996          0.016         -0.199
           7.000          1.002          0.016          0.099
           8.000          0.998          0.007         -0.138
           8.000          1.000          0.007          0.000
           8.000          1.006          0.007          0.414
           8.000          1.000          0.007          0.000
           8.000          1.002          0.007          0.138
           8.000          0.996          0.007         -0.276
           8.000          0.998          0.007         -0.138
           8.000          0.996          0.007         -0.276
           8.000          1.002          0.007          0.138
           8.000          1.006          0.007          0.414
           9.000          1.002          0.008          0.133
           9.000          0.998          0.008         -0.133
           9.000          0.996          0.008         -0.266
           9.000          0.995          0.008         -0.332
           9.000          0.996          0.008         -0.266
           9.000          1.004          0.008          0.266
           9.000          1.004          0.008          0.266
           9.000          0.998          0.008         -0.133
           9.000          0.999          0.008         -0.066
           9.000          0.991          0.008         -0.598
          10.000          0.991          0.011         -0.546
          10.000          0.995          0.011         -0.304
          10.000          0.984          0.011         -0.971
          10.000          0.994          0.011         -0.364
          10.000          0.997          0.011         -0.182
          10.000          0.997          0.011         -0.182
          10.000          0.991          0.011         -0.546
          10.000          0.998          0.011         -0.121
          10.000          1.004          0.011          0.243
          10.000          0.997          0.011         -0.182