E691 INTERLAB

E691 INTERLAB

Analysis Command

Generate the tables for an interlab analysis as described by the ASTM E 691 - 99 standard.

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
\( \tilde{x} \)	=	cell average \( \sum_{i=1}^{n}{x}/n \)
\( \bar{X} \)	=	average of cell averages for one material \( \sum_{i=1}^{p}{\tilde{x}}/p \)
s	=	cell standard deviation \( \sum_{i=1}^{n}{(x - \tilde{x})^2}/(n-1) \)
d	=	cell deviation \( \tilde{x} - \bar{X} \)
\( s_{\tilde{x}} \)	=	standard deviations of cell averages \( \sum_{i=1}^{p}{d^2}/(p-1) \)
sr	=	repeatability standard deviation \( \sqrt{\sum_{i=1}^{p}{s^2}/p} \)
sR	=	reproducibility standard deviation larger of sr and \( \sqrt{s_{\tilde{x}}^2 + s_{r}^2(n-1)/n} \)
h	=	\( d/s_{\tilde{x}} \) (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

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.

E691 INTERLAB Y1 LABID MATID
E691 INTERLAB Y1 LABID MATID SUBSET LABID > 1

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.

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.

In some cases, you may not want to generate all of the tables for the E691 analysis. You can specify which tables to generate with the commands
SET E692 DATA SUMMARY TABLE <ON/OFF>
SET E692 TEST RESULTS TABLE <ON/OFF>
SET E692 H CONSISTENCY TABLE <ON/OFF>
SET E692 K CONSISTENCY TABLE <ON/OFF>
SET E692 PRECISION STATISTICS TABLE <ON/OFF>

By default, materials are identified with the numeric code given in the material id variable on the E691 INTERLAB command.

If you have defined a group label variable (HELP GROUP LABEL for details) that defines alphabetic codes for the material names, you can use the command

SET E691 MATERIAL ID GROUP LABEL <group-id variable>

where <group-id variable> is the name of a group-id variable.

To restore the use of numeric codes, enter

SET E691 MATERIAL ID GROUP LABEL NONE

The 2023 version of the standard was updated to support unbalanced data. Note that the E691 standard still recommends that the study be designed as a balanced design. Support for unbalanced data is incorporated so that if a laboratory has a bad measurement, that laboratory does not have to be removed from the study.

The 2024/05 version updated the E691 command to support unbalanced data. The formulas for the unbalanced data are given in section A2 of the 2023 version of the standard and are not given here.

None

None

PROFICIENCY TEST	= Perform one-sample or two-sample proficiency analysis.
CAPTURE HTML	= Generate output in HTML format.
CAPTURE LATEX	= Generate output in LaTek format.
CAPTURE RTF	= Generate output in Rich Text Format (RTF) format.
REPLICATED
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.

"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.

Interlaboratory Studies

2005/04
2008/10: Made a number of corrections to the documentation
2015/03: SET commands to allow user control over which tables will be printed
2015/03: Added table to print raw data
2024/05: Added support for unbalanced data

 
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)


Test Result Data
-------------------------------------------------------------------------------------
                                           Material
Laboratory              1              2              3              4              5
-------------------------------------------------------------------------------------
     1            41.0300        78.2800       132.6600       193.7100       292.7800
     1            41.4500        78.1800       133.8300       193.5900       294.0900
     1            41.3700        78.4900       133.1000       193.6500       292.8900
 
     2            41.1700        77.7800       132.9200       190.8800       292.2700
     2            42.0000        80.3800       136.9000       200.1400       309.4000
     2            41.1500        79.5400       136.4000       194.3000       295.0800
 
     3            41.0100        79.1800       132.6100       192.7100       295.5300
     3            40.6800        79.7200       135.8000       193.2800       290.1400
     3            42.6600        80.8100       135.3600       190.2800       292.3400
 
     4            39.3700        84.0800       138.5000       195.8500       295.1900
     4            42.3700        78.6000       148.3000       196.3600       295.4400
     4            42.6300        81.9200       135.6900       199.4300       296.8300
 
     5            41.8800        78.1600       131.9000       192.5900       293.9300
     5            41.1900        79.5800       134.1400       191.4400       292.4800
     5            41.3200        78.3300       133.7600       195.1200       294.2800
 
     6            43.2800        78.6600       137.2100       195.3400       297.7400
     6            40.5000        79.2700       135.1400       198.2600       296.8000
     6            42.2800        81.7500       137.5000       198.1300       290.3300
 
     7            41.0800        79.7600       130.9700       194.6600       287.2900
     7            41.2700        81.4500       131.5900       191.9900       293.7600
     7            39.0200        77.3500       134.9200       187.1300       289.3600
 
     8            43.3600        80.4400       135.4600       197.5600       298.4600
     8            42.6500        80.8000       135.1400       195.9900       295.2800
     8            41.7200        79.8000       133.6300       200.8200       296.1200
  
  
 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.
    

 
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).