RANDOM ERROR QUANTITY

RANDOM ERROR QUANTITY (LET)

Let Subcommand

Compute the random error quantity.

In a two sample proficiency study, a laboratory measures two samples. We refer to these as sample X and sample Y. The random error quantity is then defined as
\( \mbox{REQ} = [(X_i - Y_i) - (X_{\mbox{med}} - Y_{\mbox{med}})] \)

with X_med and Y_med denoting the medians of samples X and Y, respectively.

The ASTM E 2489 - 06 standard gives the following rationale for the random error quantity.

1. The medians for each sample define consensus values for each sample.

2. For a given laboratory, X_i contains variation from the consensus value (the median value) due to random error (within-laboratory error) and systematic error (bias). Likewise for Y_i.

3. It is assumed that the systematic error is the same for sample X and sample Y for a given laboratory. Based on this, X_i - Y_i will subtract out the systematic error leaving only random error.

4. Subtracting X_med - Y_med removes any difference that appears for the medians of samplei X and sample Y.

5. The random error quantity should then contain only the laboratories random error. These values can be used to compare the within-laboratory performance of the various laboratories.

LET <yout> = RANDOM ERROR QUANTITY <x> <y>
                        <SUBSET/EXCEPT/FOR qualification>
where <x> is the variable containing the measurements for sample X;
            <y> is the variable containing the measurements for sample Y;
            <yout> is a variable where the computed random error quantities are saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

Note that <x> and <y> are paired so they must be of the same length.

LET RANERR = RANDOM ERROR QUANTITY X Y

None

None

TWO SAMPLE PROFICIENCY TEST	= Perform a two sample proficiency test based on ASTM E 2489.
MEDIAN	= Compute the median of a variable.

"Standard Practice for Statistical Analysis of One-Sample and Two-Sample Proficiency Testing Programs", ASTM International, 100 Barr Harbor Drive, PO BOX C700, West Conshohoceken, PA 19428-2959, USA.

Proficiency Testing

2014/12

skip 25
read e2489b.dat lab y1 y2
.
let ranerr = random error quantity y1 y2
set write decimals 2
print lab ranerr
    

The following output is generated

------------------------------
            LAB         RANERR
------------------------------
           1.00          -0.15
           2.00          -0.40
           3.00           0.51
           4.00          -0.51
           5.00           0.23
           6.00           0.18
           7.00          -0.51
           8.00           0.37
           9.00           0.31
          10.00          -0.14
          11.00          -0.18
          12.00           1.18
          13.00          -0.29
          14.00          -0.34
          15.00          -0.08
          16.00           0.16
          17.00          -0.06
          18.00           0.10
          19.00          -0.03
          20.00           0.42
          21.00          -0.19
          22.00           0.04
          23.00          -0.20
          24.00          -0.54
          25.00          -0.12
          26.00          -0.38
          27.00          -0.50
          28.00          -0.04
          29.00          -0.22
          30.00          -0.28