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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. Reproducability - reproducability 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> <matid> <labid>
                <SUBSET/EXCEPT/FOR qualification>
    where <y> is a response variable;
                <matid> is a material id variable;
                <labid> is a lab id variable;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    E691 INTERLAB Y1 MATID LABID
    E691 INTERLAB Y1 MATID LABID SUBSET LABID > 1
Note:
    The E691 INTERLAB command is typically supplementated with a number of graphs.

    The following graphs are recommended in the above documented:

    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
      MATID = material-id variable
      LABID = lab-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:
    CAPTURE HTML = Generate output in HTML format.
    CAPTURE LATEX = Generate output in Latek format.
    REPLICATED STACK = Convert data to the format required by the E691 INTERLAB command.
    REPEATABILITY STANDARD DEVIATION = Compute the repeatability standard deviation.
    REPRODUCIBILITY STANDARD DEVIATION = Compute the repeatability standard deviation.
    H CONSISTENCY STATISTIC = Compute the h consistency statistic.
    K CONSISTENCY STATISTIC = Compute the k consistency statistic.
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
Program 1: 
     
SKIP 25
READ GLUCOSE.DAT Y LABID MATID
LET STRING E691TIT = Glucose in Serum
.
E691 INTERLAB Y MATID LABID
.
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)
  
  
  
  
 Initial Preparation of Test Result Data for Material:        1
 ================================================================================
 Laboratory            Cell            Cell
   Number              Mean              SD               d          h          k
 ================================================================================
      1             41.2833          0.2230       -106.6567      -1.07       0.51
      2             78.3167          0.1582        -69.6233      -0.70       0.36
      3            133.1967          0.5910        -14.7433      -0.15       1.35
      4            193.6500          0.0600         45.7100       0.46       0.14
      5            293.2533          0.7267        145.3133       1.46       1.66
 ================================================================================
   Average of cell averages             =    147.94000
   Standard deviation of cell averages =     99.55624
   Repeatability standard deviation    =      0.43718
   Reproducability standard deviation  =     99.55688
  
  
 Initial Preparation of Test Result Data for Material:        2
 ================================================================================
 Laboratory            Cell            Cell
   Number              Mean              SD               d          h          k
 ================================================================================
      1             41.4400          0.4851       -108.5807      -1.07       0.10
      2             79.2333          1.3269        -70.7873      -0.70       0.28
      3            135.4067          2.1680        -14.6140      -0.14       0.46
      4            195.1067          4.6824         45.0860       0.44       0.98
      5            298.9167          9.1869        148.8960       1.47       1.93
 ================================================================================
   Average of cell averages             =    150.02066
   Standard deviation of cell averages =    101.50978
   Repeatability standard deviation    =      4.75437
   Reproducability standard deviation  =    101.58398
  
  
 Initial Preparation of Test Result Data for Material:        3
 ================================================================================
 Laboratory            Cell            Cell
   Number              Mean              SD               d          h          k
 ================================================================================
      1             41.4500          1.0608       -106.6907      -1.08       0.62
      2             79.9033          0.8303        -68.2373      -0.69       0.48
      3            134.5900          1.7288        -13.5507      -0.14       1.01
      4            192.0900          1.5932         43.9493       0.44       0.93
      5            292.6700          2.7101        144.5293       1.46       1.58
 ================================================================================
   Average of cell averages             =    148.14067
   Standard deviation of cell averages =     98.79667
   Repeatability standard deviation    =      1.71385
   Reproducability standard deviation  =     98.80658
  
  
 Initial Preparation of Test Result Data for Material:        4
 ================================================================================
 Laboratory            Cell            Cell
   Number              Mean              SD               d          h          k
 ================================================================================
      1             41.4567          1.8118       -109.9140      -1.10       0.53
      2             81.5333          2.7604        -69.8373      -0.70       0.80
      3            140.8300          6.6200        -10.5407      -0.11       1.92
      4            197.2133          1.9365         45.8427       0.46       0.56
      5            295.8200          0.8836        144.4493       1.44       0.26
 ================================================================================
   Average of cell averages             =    151.37067
   Standard deviation of cell averages =    100.04575
   Repeatability standard deviation    =      3.44261
   Reproducability standard deviation  =    100.08523
  
  
 Initial Preparation of Test Result Data for Material:        5
 ================================================================================
 Laboratory            Cell            Cell
   Number              Mean              SD               d          h          k
 ================================================================================
      1             41.4633          0.3667       -106.5433      -1.07       0.32
      2             78.6900          0.7754        -69.3167      -0.70       0.67
      3            133.2667          1.1987        -14.7400      -0.15       1.04
      4            193.0500          1.8826         45.0433       0.45       1.64
      5            293.5633          0.9544        145.5567       1.46       0.83
 ================================================================================
   Average of cell averages             =    148.00667
   Standard deviation of cell averages =     99.48517
   Repeatability standard deviation    =      1.15133
   Reproducability standard deviation  =     99.48961
  
  
 Initial Preparation of Test Result Data for Material:        6
 ================================================================================
 Laboratory            Cell            Cell
   Number              Mean              SD               d          h          k
 ================================================================================
      1             42.0200          1.4081       -108.1260      -1.08       0.63
      2             79.8933          1.6366        -70.2527      -0.70       0.73
      3            136.6167          1.2870        -13.5293      -0.14       0.57
      4            197.2433          1.6496         47.0973       0.47       0.73
      5            294.9567          4.0343        144.8107       1.45       1.79
 ================================================================================
   Average of cell averages             =    150.14600
   Standard deviation of cell averages =     99.99750
   Repeatability standard deviation    =      2.25008
   Reproducability standard deviation  =    100.01437
  
  
 Initial Preparation of Test Result Data for Material:        7
 ================================================================================
 Laboratory            Cell            Cell
   Number              Mean              SD               d          h          k
 ================================================================================
      1             40.4567          1.2478       -106.3167      -1.08       0.47
      2             79.5200          2.0605        -67.2533      -0.68       0.77
      3            132.4933          2.1243        -14.2800      -0.15       0.79
      4            191.2600          3.8177         44.4867       0.45       1.43
      5            290.1367          3.3042        143.3633       1.46       1.23
 ================================================================================
   Average of cell averages             =    146.77333
   Standard deviation of cell averages =     98.18639
   Repeatability standard deviation    =      2.67611
   Reproducability standard deviation  =     98.21071
  
  
 Initial Preparation of Test Result Data for Material:        8
 ================================================================================
 Laboratory            Cell            Cell
   Number              Mean              SD               d          h          k
 ================================================================================
      1             42.5767          0.8225       -107.9053      -1.07       0.56
      2             80.3467          0.5065        -70.1353      -0.70       0.35
      3            134.7433          0.9774        -15.7387      -0.16       0.67
      4            198.1233          2.4638         47.6413       0.47       1.69
      5            296.6200          1.6479        146.1380       1.45       1.13
 ================================================================================
   Average of cell averages             =    150.48199
   Standard deviation of cell averages =    100.54382
   Repeatability standard deviation    =      1.46110
   Reproducability standard deviation  =    100.55090
  
  
  
 =======================================================================
                                     Material
 Laboratory        1         2         3         4         5         6
 =======================================================================
      1          -1.07     -1.07     -1.08     -1.10     -1.07     -1.08
      2          -0.70     -0.70     -0.69     -0.70     -0.70     -0.70
      3          -0.15     -0.14     -0.14     -0.11     -0.15     -0.14
      4           0.46      0.44      0.44      0.46      0.45      0.47
      5           1.46      1.47      1.46      1.44      1.46      1.45
 =======================================================================
   CRITICAL VALUE =    1.74
  
  
  
 ===============================
                 Material
 Laboratory        7         8
 ===============================
      1          -1.08     -1.07
      2          -0.68     -0.70
      3          -0.15     -0.16
      4           0.45      0.47
      5           1.46      1.45
 ===============================
   CRITICAL VALUE =    1.74
  
  
  
                                     Material
  
 Laboratory        1         2         3         4         5         6
 =======================================================================
      1           0.51      0.10      0.62      0.53      0.32      0.63
      2           0.36      0.28      0.48      0.80      0.67      0.73
      3           1.35      0.46      1.01      1.92      1.04      0.57
      4           0.14      0.98      0.93      0.56      1.64      0.73
      5           1.66      1.93      1.58      0.26      0.83      1.79
 =======================================================================
  
  
  
                 Material
  
 Laboratory        7         8
 ===============================
      1           0.47      0.56
      2           0.77      0.35
      3           0.79      0.67
      4           1.43      1.69
      5           1.23      1.13
 ===============================
   CRITICAL VALUE =    1.92
  
  
  
 ========================================================================================
 Material            Xbar            s(x)            s(r)            s(R)       r       R
 ========================================================================================
     1           147.9400         99.5562          0.4372         99.5569    1.22  278.76
     2           150.0207        101.5098          4.7544        101.5840   13.31  284.44
     3           148.1407         98.7967          1.7138         98.8066    4.80  276.66
     4           151.3707        100.0458          3.4426        100.0852    9.64  280.24
     5           148.0067         99.4852          1.1513         99.4896    3.22  278.57
     6           150.1460         99.9975          2.2501        100.0144    6.30  280.04
     7           146.7733         98.1864          2.6761         98.2107    7.49  274.99
     8           150.4820        100.5438          1.4611        100.5509    4.09  281.54
 ========================================================================================
  
    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: 
     
SKIP 25
READ MANDEL6.DAT Y LABID MATID
LET STRING E691TIT = Pentosans in Wood Pulp
.
. DEMONSTRATE HOW TO SAVE OUTPUT IN A LATEX FILE
. WITH GRAPHICS
CAPTURE LATEX E691.TEX
E691 INTERLAB Y MATID LABID
.
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: 4/19/2005
Please email comments on this WWW page to alan.heckert@nist.gov.