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Dataplot Vol 1 Auxiliary Chapter

E691 INTERLAB

Name:
    E691 INTERLAB
Type:
    Analysis Command
Purpose:
    Generate the tables for an interlab analysis as described by the ASTM E 691 - 99 standard.
Description:
    The following document

      "Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method", ASTM International, 100 Barr Harbor Drive, PO BOX C700, West Conshohoceken, PA 19428-2959, USA.

    describes a methodology for performing an interlab experiment.

    The data consists of:

    1. A response variable
    2. A lab-id variable
    3. A material-id variable

    It is assumed that this is a balanced design. That is, each combination of lab-id and material-id (referred to as a cell in the standard) has an equal number of observations.

    The purpose of the E691 INTERLAB command is to estimate the precision of a test method. Two important concepts in determining the precision are:

    1. Repeatability - repeatability concerns the variability between independent test results obtained within a single laboratory in the shortest practical period of time by a single operator with a specific set of test apparatus using test specimens taken at random from a single quantity of homogeneous material.

    2. Reproducibility - reproducibility is the variability between single test results obtained in different laboratories, each of which has applied the test method to test specimens taken at random from a single quantity of homogeneous material.

    The standard discusses issues regarding the design of the interlaboratory study. We do not dicuss those issues here.

    If your data is stored in a format with each lab in a separate column, you can use the REPLICATED STACK command to save your data in the format needed by the E691 INTERLAB command.

    This command generates the four tables documented in the above document:

    1. For each material:

      • Lab ID, Cell Average, Cell SD,
      • Deviation of Cell Average from Material Average,
      • h-Consistency Statistic, k-Consistency Statistic,

    2. The h-consistency statistic by laboratory and material.

    3. The k-consistency statistic by laboratory and material.

    4. A summary table of precision statistics for each material.

    The following provides some of the quantities that are computed in this command (see the above document for a more detailed discussion of these quantities).

      n = number of test results per cell
      p = number of laboratories
      x = individual test result
      xtilde = cell average
      SUM[i=1 to n][x]/n
      xbar = average of cell averages for one material
      SUM[i=1 to p][xtilde]/p
      s = cell standard deviation
      SQRT(SUM[i=1 to n][(x - xtilde)**2]/(n-1)))
      d = cell deviation
      (xtilde - xbar)
      s(xtilde) = standard deviations of cell averages
      SQRT(SUM[i=1 to p][d**2]/(p-1))
      sr = repeatability standard deviation
      SQRT(SUM[i=1 to p][s**2]/p)
      sR = reproducibility standard deviation
      larger of sr and SQRT((s(xtilde)**2 + s(r)**2*(n-1)/n)
      h = d/s(xtilde) (h is the between-laboratory consistency statistic)
      k = s/sr (k is the within-laboratory consistency statistic)
      r = 2.8*sr
      R = 2.8*sR
Syntax:
    E691 INTERLAB <y> <labid> <matid>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y> is a response variable;
                <labid> is a lab id variable;
                <matid> is a material id variable;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    E691 INTERLAB Y1 LABID MATID
    E691 INTERLAB Y1 LABID MATID SUBSET LABID > 1
Note:
    The E691 INTERLAB command is typically supplementated with a number of graphs.

    The following graphs are recommended in the ASTM document:

    1. h-consistency statistic (materials within labs)
    2. h-consistency statistic (labs within materials)
    3. k-consistency statistic (materials within labs)
    4. k-consistency statistic (labs within materials)
    5. Reproducibility SD and Repeatability SD versus material average

    We also recommend the following graphs:

    1. A graph displaying the lab means and sd's for each material.
    2. A plot of means, sd's, repeatability sd's, and reproducibility sd's for each material.
    3. Dot plots of the h-consistency statistics.
    4. Box plots of the k-consistency statistics.

    We have added the following macros to Dataplot's built-in macro library:

    1. E691PLO1.DP - plot of lab means and lab standard deviations for each material
    2. E691PLO2.DP - plot of means, standard deviations, repeatability sd, and reproducibility for each material.
    3. E691PLO3.DP - plot of h-consistency statistic (laboratories within materials)
    4. E691PLO4.DP - plot of k-consistency statistic (laboratories within materials)
    5. E691PLO5.DP - plot of h-consistency statistic (materials within laboratories)
    6. E691PLO6.DP - plot of k-consistency statistic (materials within laboratories)
    7. E691PLO7.DP - plot of repeatability and reproducibility sd versus average for each material
    8. E691DOH1.DP - dot plot of h-consistency statistic (laboratories within materials)
    9. E691DOH2.DP - dot plot of h-consistency statistic (materials within laboratories)
    10. E691DOK1.DP - dot plot of k-consistency statistic (laboratories within materials)
    11. E691DOK2.DP - dot plot of k-consistency statistic (materials within laboratories)
    12. E691BPH1.DP - box plot of h-consistency statistic (laboratories within materials)
    13. E691BPH2.DP - box plot of h-consistency statistic (materials within laboratories)
    14. E691BPK1.DP - box plot of k-consistency statistic (laboratories within materials)
    15. E691BPK2.DP - box plot of k-consistency statistic (materials within laboratories)

    To call one of these macros, define the following values

      Y = response variable
      LABID = lab-id variable
      MATID = material-id variable
      E691TIT = string containing a title for the analysis

    and then use the CALL command to invoke the macro. This is demonstrated in the program example below.

    If you would like to view one of these macros, use the LIST command. For example

      LIST E691PLO1.DP

    If you would like to modify one of these macros, use the COPY command to create a copy of the macro. For example

      COPY E691PLO1.DP C:\E691PLO1_NEW.DP

    You can then edit C:\E691PLO1_NEW.DP to suit your needs.

Note:
    You can use the CAPTURE HTML command to generate these tables in HTML format. You can use the CAPTURE LATEX command to generated these tables in Latex format. You can use the CAPTURE RTF command in Rich Text Format (RTF).

    The second program example demostrates this for Latex.

Default:
    None
Synonyms:
    None
Related Commands: Reference:
    "Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method", ASTM International, 100 Barr Harbor Drive, PO BOX C700, West Conshohoceken, PA 19428-2959, USA.
Applications:
    Interlaboratory Studies
Implementation Date:
    2005/4
    2008/10: Made a number of corrections to the documentation
Program 1:
     
    DIMENSION 100 VARIABLES
    SKIP 25
    READ GLUCOSE.DAT Y LABID MATID
    LET STRING E691TIT = Glucose in Serum
    SET TABLE TITLE ^E691TIT
    .
    E691 INTERLAB Y LABID MATID
    .
    CALL E691PLO1.DP
    CALL E691PLO2.DP
    CALL E691PLO3.DP
    CALL E691PLO4.DP
    CALL E691PLO5.DP
    CALL E691PLO6.DP
    CALL E691PLO7.DP
        
    The following tables are generated
                    INTERLABORATORY ANALYSIS (BASED ON E 691 - 99 STANDARD)
      
      
      
     Glucose
     Initial Preparation of Test Result Data for Material:        1
     ================================================================================
     Laboratory            Cell            Cell
       Number              Mean              SD               d          h          k
     ================================================================================
          1             41.2833          0.2230         -0.2350      -0.39       0.21
          2             41.4400          0.4851         -0.0783      -0.13       0.46
          3             41.4500          1.0608         -0.0683      -0.11       1.00
          4             41.4567          1.8118         -0.0617      -0.10       1.70
          5             41.4633          0.3667         -0.0550      -0.09       0.34
          6             42.0200          1.4081          0.5017       0.83       1.32
          7             40.4567          1.2478         -1.0617      -1.75       1.17
          8             42.5767          0.8225          1.0583       1.75       0.77
     ================================================================================
       Average of cell averages             =     41.51833
       Standard deviation of cell averages =      0.60613
       Repeatability standard deviation    =      1.06322
       Reproducibility standard deviation  =      1.06322
      
     Glucose
     Initial Preparation of Test Result Data for Material:        2
     ================================================================================
     Laboratory            Cell            Cell
       Number              Mean              SD               d          h          k
     ================================================================================
          1             78.3167          0.1582         -1.3629      -1.36       0.11
          2             79.2333          1.3269         -0.4463      -0.45       0.89
          3             79.9033          0.8303          0.2238       0.22       0.56
          4             81.5333          2.7604          1.8538       1.85       1.85
          5             78.6900          0.7754         -0.9896      -0.99       0.52
          6             79.8933          1.6366          0.2138       0.21       1.09
          7             79.5200          2.0605         -0.1596      -0.16       1.38
          8             80.3467          0.5065          0.6671       0.67       0.34
     ================================================================================
       Average of cell averages             =     79.67958
       Standard deviation of cell averages =      1.00275
       Repeatability standard deviation    =      1.49485
       Reproducibility standard deviation  =      1.57963
      
     Glucose
     Initial Preparation of Test Result Data for Material:        3
     ================================================================================
     Laboratory            Cell            Cell
       Number              Mean              SD               d          h          k
     ================================================================================
          1            133.1967          0.5910         -1.9462      -0.73       0.22
          2            135.4067          2.1680          0.2637       0.10       0.79
          3            134.5900          1.7288         -0.5529      -0.21       0.63
          4            140.8300          6.6200          5.6871       2.14       2.41
          5            133.2667          1.1987         -1.8763      -0.71       0.44
          6            136.6167          1.2870          1.4738       0.55       0.47
          7            132.4933          2.1243         -2.6496      -1.00       0.77
          8            134.7433          0.9774         -0.3996      -0.15       0.36
     ================================================================================
       Average of cell averages             =    135.14291
       Standard deviation of cell averages =      2.65595
       Repeatability standard deviation    =      2.74827
       Reproducibility standard deviation  =      3.47698
      
     Glucose
     Initial Preparation of Test Result Data for Material:        4
     ================================================================================
     Laboratory            Cell            Cell
       Number              Mean              SD               d          h          k
     ================================================================================
          1            193.6500          0.0600         -1.0671      -0.41       0.02
          2            195.1067          4.6824          0.3896       0.15       1.78
          3            192.0900          1.5932         -2.6271      -1.01       0.61
          4            197.2133          1.9365          2.4962       0.96       0.74
          5            193.0500          1.8826         -1.6671      -0.64       0.72
          6            197.2433          1.6496          2.5262       0.97       0.63
          7            191.2600          3.8177         -3.4571      -1.33       1.45
          8            198.1233          2.4638          3.4063       1.31       0.94
     ================================================================================
       Average of cell averages             =    194.71709
       Standard deviation of cell averages =      2.59500
       Repeatability standard deviation    =      2.62506
       Reproducibility standard deviation  =      3.36571
      
     Glucose
     Initial Preparation of Test Result Data for Material:        5
     ================================================================================
     Laboratory            Cell            Cell
       Number              Mean              SD               d          h          k
     ================================================================================
          1            293.2533          0.7267         -1.2387      -0.46       0.18
          2            298.9167          9.1869          4.4246       1.64       2.33
          3            292.6700          2.7101         -1.8221      -0.68       0.69
          4            295.8200          0.8836          1.3279       0.49       0.22
          5            293.5633          0.9544         -0.9287      -0.34       0.24
          6            294.9567          4.0343          0.4646       0.17       1.03
          7            290.1367          3.3042         -4.3554      -1.62       0.84
          8            296.6200          1.6479          2.1279       0.79       0.42
     ================================================================================
       Average of cell averages             =    294.49207
       Standard deviation of cell averages =      2.69314
       Repeatability standard deviation    =      3.93497
       Reproducibility standard deviation  =      4.19233
      
      
     Glucose-h
     =============================================================
                                    Material
     Laboratory        1         2         3         4         5
     =============================================================
          1          -0.39     -1.36     -0.73     -0.41     -0.46
          2          -0.13     -0.45      0.10      0.15      1.64
          3          -0.11      0.22     -0.21     -1.01     -0.68
          4          -0.10      1.85      2.14      0.96      0.49
          5          -0.09     -0.99     -0.71     -0.64     -0.34
          6           0.83      0.21      0.55      0.97      0.17
          7          -1.75     -0.16     -1.00     -1.33     -1.62
          8           1.75      0.67     -0.15      1.31      0.79
     =============================================================
       CRITICAL VALUE =    2.15
      
      
     Glucose-k
                                    Material
      
     Laboratory        1         2         3         4         5
     =============================================================
          1           0.21      0.11      0.22      0.02      0.18
          2           0.46      0.89      0.79      1.78      2.33
          3           1.00      0.56      0.63      0.61      0.69
          4           1.70      1.85      2.41      0.74      0.22
          5           0.34      0.52      0.44      0.72      0.24
          6           1.32      1.09      0.47      0.63      1.03
          7           1.17      1.38      0.77      1.45      0.84
          8           0.77      0.34      0.36      0.94      0.42
     =============================================================
       CRITICAL VALUE =    2.06
      
      
     Glucose-Precision Statistics
     ========================================================================================
     Material            Xbar            s(x)            s(r)            s(R)       r       R
     ========================================================================================
         1            41.5183          0.6061          1.0632          1.0632    2.98    2.98
         2            79.6796          1.0028          1.4949          1.5796    4.19    4.42
         3           135.1429          2.6559          2.7483          3.4770    7.70    9.74
         4           194.7171          2.5950          2.6251          3.3657    7.35    9.42
         5           294.4921          2.6931          3.9350          4.1923   11.02   11.74
     ========================================================================================
      
        The following graphs are generated.
        
    plot generated by sample program

    plot generated by sample program

    plot generated by sample program

    plot generated by sample program

    plot generated by sample program

    plot generated by sample program

    plot generated by sample program

Program 2:
     
    DIMENSION 100 VARIABLES
    SKIP 25
    READ MANDEL6.DAT Y LABID MATID
    LET STRING E691TIT = Pentosans in Wood Pulp
    SET TABLE TITLE ^E691TIT
    .
    . DEMONSTRATE HOW TO SAVE OUTPUT IN A LATEX FILE
    . WITH GRAPHICS
    CAPTURE LATEX E691.TEX
    E691 INTERLAB Y LABID MATID
    .
    SET IPL1NA E691PLO1.PS
    DEVICE 2 POSTSCRIPT
    CALL E691PLO1.DP
    DEVICE 2 CLOSE
    SET IPL1NA E691PLO2.PS
    DEVICE 2 POSTSCRIPT
    CALL E691PLO2.DP
    DEVICE 2 CLOSE
    SET IPL1NA E691DOH1.PS
    DEVICE 2 POSTSCRIPT
    CALL E691DOH1.DP
    DEVICE 2 CLOSE
    SET IPL1NA E691DOH2.PS
    DEVICE 2 POSTSCRIPT
    CALL E691DOH2.DP
    DEVICE 2 CLOSE
    SET IPL1NA E691DOK1.PS
    DEVICE 2 POSTSCRIPT
    CALL E691DOK1.DP
    DEVICE 2 CLOSE
    SET IPL1NA E691DOK2.PS
    DEVICE 2 POSTSCRIPT
    CALL E691DOK2.DP
    DEVICE 2 CLOSE
    SET IPL1NA E691PLO7.PS
    DEVICE 2 POSTSCRIPT
    CALL E691PLO7.DP
    DEVICE 2 CLOSE
    END OF CAPTURE
        
    This program will generate the E691 tables and graphs in a Latex file (E691.TEX).

Date created: 4/19/2005
Last updated: 10/16/2005
Please email comments on this WWW page to alan.heckert@nist.gov.