Dataplot Vol 2 Vol 1

# RANDOM ERROR QUANTITY

Name:
RANDOM ERROR QUANTITY (LET)
Type:
Let Subcommand
Purpose:
Compute the random error quantity.
Description:
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 Xmed and Ymed 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, Xi contains variation from the consensus value (the median value) due to random error (within-laboratory error) and systematic error (bias). Likewise for Yi.

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

4. Subtracting Xmed - Ymed 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.
Syntax:
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.

Examples:
LET RANERR = RANDOM ERROR QUANTITY X Y
Default:
None
Synonyms:
None
Related Commands:
 TWO SAMPLE PROFICIENCY TEST = Perform a two sample proficiency test based on ASTM E 2489. MEDIAN = Compute the median of a variable.
Reference:
"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.
Applications:
Proficiency Testing
Implementation Date:
2014/12
Program:
skip 25
.
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


NIST is an agency of the U.S. Commerce Department.

Date created: 12/31/2014
Last updated: 12/31/2014