H CONSISTENCY STATISTIC

H CONSISTENCY STATISTIC (LET)

Let Subcommand

Compute the h-consistency statistic of a variable as defined by the ASTM E691 standard.

The h-consistency statistic is defined in the ASTM E691 standard as
\( h = d/s_{\tilde{x}} \) (between laboratory consistency statistic)

with

d = cell deviation (cell average - average of cell averages)
\( s_{\tilde{x}} \) = standard deviations of cell averages

Essentially, h is a standardized deviation from the grand averages.

LET <h> = H CONSISTENCY STATISTIC <y> <labid>
            <SUBSET/EXCEPT/FOR qualification>
where <y> is a response variable;
            <labid> is a lab-id variable;
            <h> is a variable where the h-consistency statistic values are saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax is used to compute the h-consistency statistic for a single material. The number of h-values is equal to the number of laboratories.

LET <h> <labtag> <mattag>= H CONSISTENCY STATISTIC <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;
            <h> is a variable where the h-consistency statistic values are saved;
<labtag> is a variable where the corresponding lab-id values are saved;
<mattag> is a variable where the corresponding material-id values are saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax is used to compute the h-consistency statistic for multiple materials. The number of h-values is equal to the number of materials times the number of laboratories.

LET A = H CONSISTENCY STATISTIC Y LAB
LET HVAL = H CONSISTENCY STATISTIC Y LAB MAT
LET HVAL = H CONSISTENCY STATISTIC Y LAB MAT SUBSET MAT > 2

The 2023 version of the E691 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

E691 INTERLAB	= Perform an E691 interlab analysis.
H CONSISTENCY PLOT	= Generate an h consistency plot.
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 Analysis

2005/04
2024/05: Added support for unbalanced data

SKIP 25
READ GLUCOSE.DAT Y MATID LABID
.
LET HVAL LABTAG MATTAG = H CONSISTENCY STATISTIC Y LABID MATID
.
SET WRITE DECIMALS 4
PRINT HVAL LABTAG MATTAG
    

The following output is generated

---------------------------------------------
           HVAL         LABTAG         MATTAG
---------------------------------------------
        -0.3877         1.0000         1.0000
        -0.1292         2.0000         1.0000
        -0.1127         3.0000         1.0000
        -0.1017         4.0000         1.0000
        -0.0907         5.0000         1.0000
         0.8277         6.0000         1.0000
        -1.7516         7.0000         1.0000
         1.7461         8.0000         1.0000
        -1.3592         1.0000         2.0000
        -0.4450         2.0000         2.0000
         0.2231         3.0000         2.0000
         1.8487         4.0000         2.0000
        -0.9869         5.0000         2.0000
         0.2132         6.0000         2.0000
        -0.1591         7.0000         2.0000
         0.6653         8.0000         2.0000
        -0.7328         1.0000         3.0000
         0.0993         2.0000         3.0000
        -0.2082         3.0000         3.0000
         2.1413         4.0000         3.0000
        -0.7064         5.0000         3.0000
         0.5549         6.0000         3.0000
        -0.9976         7.0000         3.0000
        -0.1504         8.0000         3.0000
        -0.4112         1.0000         4.0000
         0.1501         2.0000         4.0000
        -1.0124         3.0000         4.0000
         0.9619         4.0000         4.0000
        -0.6424         5.0000         4.0000
         0.9735         6.0000         4.0000
        -1.3322         7.0000         4.0000
         1.3126         8.0000         4.0000
        -0.4600         1.0000         5.0000
         1.6429         2.0000         5.0000
        -0.6766         3.0000         5.0000
         0.4931         4.0000         5.0000
        -0.3449         5.0000         5.0000
         0.1725         6.0000         5.0000
        -1.6172         7.0000         5.0000
         0.7901         8.0000         5.0000