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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: 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
    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
        

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

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