
TWO FACTOR PLOTName:
This plot is motivated by the desire to plot residuals for the "phase 3" analysis related to the ASTM E691 standard. The phase 3 analysis is a rowlinear model for the data in a E691 study and was proposed by John Mandel (see the References below) as an additional step in the E691 analysis. In particular, Mandel recommended a plot of the standardized residuals from the rowlinear model (specific plots for the h and kstatistics are implemented with the H CONSISTENCY PLOT and K CONSISTENCY PLOT commands). Although motivated by the E691 analysis, this plot can be used for any two factor data set from a full factorial design (i.e., all combinations of levels from the two factors are included). If there is replication within a cell, the mean of the replicates will be used.
<SUBSET/EXCEPT/FOR qualification> where <y> is a response variable; <labid> is a variable that specifies the labid; <matid> is a variable that specifies the materialid; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET YSD = CROSS TABULATE SD Y X1 X2 LET X1D = CROSS TABULATE GROUP ONE X1 X2 LET X2D = CROSS TABULATE GROUP TWO X1 X2 TWO FACTOR PLOT YSD X1D X2D
LAB: 1 2 3 1 2 3 1 2 3 MAT: 1 1 1 2 2 2 3 3 3 X: 1 2 3 4 5 6 7 8 9 Alternatively, you can stack the lab values so that the xaxis is laid out as
LAB: 1 1 1 2 2 2 3 3 3 MAT: 1 2 3 X: 1 2 3 To specify the stacked alternative, enter the command
To reset the line linear option, enter the command
To define the xaxis as "materials within laboratories", enter the command
To reset the default, enter
We find it useful to generate both versions of the plot. Although the information being displayed is the same, different types of patterns may be clearer in one or the other of these plots.
where <value> is a nonnegative integer. So in the above example,
yields LAB: 1 2 3 1 2 3 1 2 3 MAT: 1 1 1 2 2 2 3 3 3 X: 1 2 3 5 6 7 9 10 11Note:
To address this, the following commands were added
SET TWO FACTOR PLOT LABORATORY LAST <value> SET TWO FACTOR PLOT MATERIAL FIRST <value> SET TWO FACTOR PLOT MATERIAL LAST <value> These commands allow you to specify the range of laboratories (or materials) to be displayed. Note that these commands limit you to contiguous ranges of laboratories or materials.
Mandel (1994), "Analyzing Interlaboratory Data According to ASTM Standard E691", Quality and Statistics: Total Quality Management, ASTM STP 1209, Kowalewski, Ed., American Society for Testing and Materials, Philadelphia, PA 1994, pp. 5970. Mandel (1993), "Outliers in Interlaboratory Testing", Journal of Testing and Evaluation, Vol. 21, No. 2, pp. 132135. Mandel (1995), "Structure and Outliers in Interlaboratory Studies", Journal of Testing and Evaluation, Vol. 23, No. 5, pp. 364369. Mandel (1991), "Evaluation and Control of Measurements", Marcel Dekker, Inc.
. Step 1: Read the data . dimension 40 columns skip 25 read mandel7.dat y x1 x2 . let nlab = unique x1 let nmat = unique x2 let ntot = nlab*nmat . variable label y Stress variable label x1 LabID variable label x2 Rubber let nlab = unique x1 let ncol = unique x2 . . Step 2: Define some default plot control settings . case asis title case asis title offset 2 label case asis tic mark offset units screen tic mark offset 3 3 . . Step 3: Generate the two way row plot . x1label Column Average character blank all line dash all loop for k = 1 1 nlab let kindex = (k1)*2 + 1 let plot character kindex = ^k let plot line kindex = blank end of loop . set two way plot factor label value set two way plot factor decimal 4 set two way plot anova table on set two way plot anova table decimals 4 set write decimals 4 title Stress in Kg/cm**2 at 100% Elongation for Natural Rubber Vulcaizates y1label Data by Laboratory . two way row plot y x1 x2 . . Step 4: Now generate the two factor plot of the residuals . skip 1 read dpst3f.dat labid matid junk1 junk2 junk3 resstd skip 0 y1label Standardized Residuals x1label LabID/RubberID legend 1 MATERIAL: legend 2 LAB: legend 1 justification right legend 2 justification right legend 1 coordinates 14 15 legend 2 coordinates 14 12 legend 1 size 1.7 legend 2 size 1.7 . x1label x1tic mark label off xlimits 1 ntot major x1tic mark number ntot minor x1tic mark number 0 x1tic mark offset 1 1 . line blank character blank spike on spike base 0 two factor plot resstd labid matid line solid drawdata 1 0 ntot 0 . . Step 5: Draw lines separating the labs and add tic labels . to identify labs/materials . let ycoorz = 16 let xcoor = 1 justification center height 0.7 . loop for k = 1 1 ntot moveds xcoor ycoorz let ktemp = mod(k1,nmat) + 1 text ^ktemp let xcoor = xcoor + 1 end of loop . height 1.5 let ycoorz = 12 let xcoor = (nmat/2)+0.5 line color red line dash loop for k = 1 1 nlab moveds xcoor ycoorz let ival = k text ^ival if k < nlab let xcoor2 = xcoor + (nmat/2) drawdsds xcoor2 20 xcoor2 90 end of if let xcoor = xcoor + nmat end of loop line color black line blankThe following output is generated Parameters of RowLinear Fit for Stress  Standard Error Correlation LabID Height Slope RESSD of Slope Coefficient  1.0000 4.9300 1.0909 0.1168 0.0268 0.9985 2.0000 4.5957 1.0990 0.0851 0.0195 0.9992 3.0000 4.8043 1.0613 0.1547 0.0355 0.9972 4.0000 5.5200 0.9777 0.1818 0.0417 0.9955 5.0000 5.0671 0.8575 0.1844 0.0423 0.9940 6.0000 4.8657 0.8960 0.1289 0.0296 0.9973 7.0000 4.7729 0.8063 0.1784 0.0409 0.9936 8.0000 4.8543 1.0869 0.1006 0.0231 0.9989 9.0000 5.2386 1.0304 0.2197 0.0504 0.9941 10.0000 4.8571 1.0696 0.1045 0.0240 0.9987 11.0000 4.8457 1.0244 0.1773 0.0407 0.9961 Standard Deviation of Slopes: 0.1024 Pooled Standard Deviation of Fit: 0.1616 Column Averages  Column Rubber Average  1.0000 3.2291 2.0000 3.5927 3.0000 4.0418 4.0000 4.4273 5.0000 5.0791 6.0000 5.7345 7.0000 8.4827 Mean of Column Means: 4.9410 ANOVA Table for RowLinear Fit  Degrees of Sum of Mean Source Freedom Squares Square  Total 76 216.8951 2.8539 Rows 10 4.4471 0.4447 Column 6 209.1488 34.8581 Error 60 3.2991 0.0550 Residuals 50 1.3054 0.0261 Slopes 10 1.9937 0.1994 Concurrence 1 0.0496 0.0496 NonConcurrence 9 1.9441 0.2160
 
Date created: 07/08/2015 Last updated: 12/04/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 