
CONSENSUS MEAN PLOTName:
The CONSENSUS MEAN PLOT command performs a consensus means analysis and in addition to the textual output it presents the results in a graphical format. The details of the consensus means analysis are discussed in the documentation for the CONSENSUS MEANS command (enter HELP CONSENSUS MEANS for details). The graph consists of two parts. This plot allows you to compare the consensus values and associated uncertainties obtained by the different methods. It also allows you to compare the consensus values against the lab data. The methods are plotted in the following order:
In most cases, you will probably want only a subset of these methods. You can use the following commands to specify which methods to include in the consensus means analysis. This is demonstrated in the program samples below.
where <y> is the response variable; <tag> is the groupid variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This is used for the raw data case.
<SUBSET/EXCEPT/FOR qualification> where <ymean> is the variable containing the lab means; <ysd> is the variable containing the lab standard deviations; <ni> is the variable containing the lab sample sizes; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This is used for the summary data case.
<SUBSET/EXCEPT/FOR qualification> where <ymean> is the variable containing the lab means; <ysd> is the variable containing the lab standard deviations; <ni> is the variable containing the lab sample sizes; <labid> is the variable containing the labid's (numeric); and where the <SUBSET/EXCEPT/FOR qualification> is optional.
This is used for the summary data case. The
CONSENSUS MEAN PLOT Y TAG CONSENSUS MEAN PLOT Y TAG SUBSET TAG >= 2 CONSENSUS MEAN PLOT Y TAG SUBSET TAG = 1 TO 6 CONSENSUS MEAN PLOT YMEAN YSD NI
To reset the default of showing the lab data on the plot, enter
This is demonstrated in the Program 2 example below.
To reset the default of not sorting the methods, enter
This is demonstrated in the Program 3 example below. The program example shows how to read DPST3F.DAT to retrieve the sorted order of the methods.
In order to specify one or more labs to omit from the plot (but not the analysis), enter the command
where <lab1> ... <labk> is a list of 1 to 10 labs to be omitted from the plot. To reset the default of all labs being plotted, enter
This option was added 12/2016. Similarly, you can omit methods from the plot (but not the analysis) with the commands
SET CONSENSUS MEAN PLOT OMIT METHOD TWO <method> SET CONSENSUS MEAN PLOT OMIT METHOD THREE <method> When extreme outliers are included in the analysis, the results for some methods may distort the plot. This option was added 04/2017.
To reset the default, enter the commnd
This example is demonstrated in the Program 4 example below.
Graybill and Deal (1959), "Combining Unbiased Estimators", Biometrics, 15, pp. 543550. M. S. Levenson, D. L. Banks, K. R. Eberhardt, L. M. Gill, W. F. Guthrie, H. K. Liu, M. G. Vangel, J. H. Yen, and N. F. Zhang (2000), "An ISO GUM Approach to Combining Results from Multiple Methods", Journal of Research of the National Institute of Standards and Technology, Volume 105, Number 4. John Mandel and Robert Paule (1970), "Interlaboratory Evaluation of a Material with Unequal Number of Replicates", Analytical Chemistry, 42, pp. 11941197. Robert Paule and John Mandel (1982), "Consensus Values and Weighting Factors", Journal of Research of the National Bureau of Standards, 87, pp. 377385. Andrew Rukhin (2009), "Weighted Means Statistics in Interlaboratory Studies", Metrologia, Vol. 46, pp. 323331. Andrew Ruhkin (2003), "Two Procedures of Metaanalysis in Clinical Trials and Interlaboratory Studies", Tatra Mountains Mathematical Publications, 26, pp. 155168. Andrew Ruhkin and Mark Vangel (1998), "Estimation of a Common Mean and Weighted Means Statistics", Journal of the American Statistical Association, Vol. 93, No. 441. Andrew Ruhkin, B. Biggerstaff, and Mark Vangel (2000), "Restricted Maximum Likelihood Estimation of a Common Mean and MandelPaule Algorithm", Journal of Statistical Planning and Inference, 83, pp. 319330. Mark Vangel and Andrew Ruhkin (1999), "Maximum Likelihood Analysis for Heteroscedastic OneWay Random Effects ANOVA in Interlaboratory Studies", Biometrics 55, 129136. Susannah Schiller and Keith Eberhardt (1991), "Combining Data from Independent Analysis Methods", Spectrochimica, ACTA 46 (12). Susannah Schiller (1996), "Standard Reference Materials: Statistical Aspects of the Certification of Chemical SRMs", NIST SP 260125, NIST, Gaithersburg, MD. Bimal Kumar Sinha (1985), "Unbiased Estimation of the Variance of the GraybillDeal Estimator of the Common Mean of Several Normal Populations", The Canadian Journal of Statistics, Vol. 13, No. 3, pp. 243247. NienFan Zhang (2006), "The Uncertainty Associated with The Weighted Mean of Measurement Data", Metrologia, 43, PP. 195204. Hagwood and Guthrie (2006), "Combining Data in Small MultipleMethods Studies", Technometrics, Vol. 48, No. 2. Iyer, Wang, and Matthew (2004), "Models and Confidence Intervals for True Values in Interlaboratory Trials", Journal of the American Statistical Association, Vol. 99, No. 468, pp. 10601071. Fairweather (1972), "A Method for Obtaining an Exact Confidence Interval for the Common Mean of Several Normal Populations", Applied Statistics, Vol. 21, pp. 229233. Cox (2002), "The Evaluation of Key Comparison Data", Metrologia, Vol. 39, pp. 589595.
2011/10: Redesigned plot to incorporate the lab data 2016/12: Support for SET CONSENSUS MEAN PLOT OMIT LABS 2017/03: Support for SET CONSENSUS MEAN PLOT OMIT METHOD 2017/07: Changed the default for SchillerEberhardt, Fairweather, and Bayesian consensus procedure to OFF 2019/08: Added the command SET CONSENSUS MEAN PLOT DATA . Step 1: Read the data . SKIP 25 READ STUTZ86.DAT ALITE JUNK2 JUNK3 JUNK4 JUNK5 LABID . . Step 2: Specify methods to include on the plot and define . strings containing method id's. Define settings . for DerSimonianLaird bootstrap. . set write decimals 5 set modified mandel paule off set schiller eberhardt off set mean of means off set grand mean off set graybill deal off set generalized confidence interval off set fairweather off set bayesian consensus procedure off set dersimonian laird minmax off set dersimonian laird bootstrap on . let string sx1 = MP let string sx2 = VR let string sx3 = DSLcr()Original let string sx4 = DSLcr()HHD let string sx5 = DSLcr()Bootstrap let string sx6 = BOB let nmeth = 6 . seed 21307 set random number generator fibonacci congruential bootstrap samples 100000 . . Step 3: Set plot control features . . Settings for plot characters/lines . line solid all character blank all character fill on character hw 1 0.75 character circle line blank . . Settings for labels . case asis title asis title offset 2 tic mark label case asis title Consensus Means Plot y1label Response . let nlab = unique labid loop for k = 1 1 nlab let icnt = k + nmeth let string sx^icnt = ^k end of loop . let ntot = nmeth + nlab xlimits 1 ntot major xtic mark number ntot minor xtic mark number 0 tic mark offset units data xtic mark offset 0.5 0.5 x1tic mark label format group label let igx = group label sx1 to sx^ntot x1tic mark label content igx . . Step 4: Generate the plot . set consensus mean plot error two standard errors feedback off consensus mean plot alite labid . . Step 5: Post plot labelling . line dotted drawdsds 6.5 20 6.5 90 justification center moveds 3.5 5 text Consensus Method: Two Standard Errors moveds 9 5 text Laboratorycr()meansp()+/2*sd/sqrt(n)Program 2: . This version suppresses the lab data portion of the plot . . Step 1: Read the data . SKIP 25 READ STUTZ86.DAT ALITE JUNK2 JUNK3 JUNK4 JUNK5 LABID . . Step 2: Specify methods to include on the plot and define . strings containing method id's. Define settings . for DerSimonianLaird bootstrap. . set write decimals 5 set modified mandel paule off set schiller eberhardt off set mean of means off set grand mean off set graybill deal off set generalized confidence interval off set fairweather off set bayesian consensus procedure off set dersimonian laird minmax off set dersimonian laird bootstrap on . let string sx1 = MP let string sx2 = VR let string sx3 = DSLcr()Original let string sx4 = DSLcr()HHD let string sx5 = DSLcr()Bootstrap let string sx6 = BOB let nmeth = 6 . seed 21307 set random number generator fibonacci congruential bootstrap samples 100000 . . Step 3: Set plot control features . . Settings for plot characters/lines . line solid all character blank all character fill on character hw 1 0.75 character circle line blank . . Settings for labels . case asis title asis title offset 2 tic mark label case asis title Consensus Means Plot y1label Response . xlimits 1 nmeth major xtic mark number nmeth minor xtic mark number 0 tic mark offset units data xtic mark offset 0.5 0.5 x1tic mark label format group label let igx = group label sx1 to sx^nmeth x1tic mark label content igx x1label Consensus Method: Two Standard Errors x1label displacement 15 . title Consensus Means Plot  Lab Data Omitted set consensus mean plot data off feedback off consensus mean plot alite labidProgram 3: . Step 1: Read the data . SKIP 25 READ STUTZ86.DAT ALITE JUNK2 JUNK3 JUNK4 JUNK5 LABID . . Step 2: Specify methods to include on the plot and define . strings containing method id's. Define settings . for DerSimonianLaird bootstrap. . set write decimals 5 set modified mandel paule off set schiller eberhardt off set mean of means off set grand mean off set graybill deal off set generalized confidence interval off set fairweather off set bayesian consensus procedure off set dersimonian laird minmax off set dersimonian laird bootstrap on . let string sx1 = MP let string sx2 = VR let string sx3 = DSLcr()Original let string sx4 = DSLcr()HHD let string sx5 = DSLcr()Boot let string sx6 = BOB let nmeth = 6 . seed 21307 set random number generator fibonacci congruential bootstrap samples 100000 . . Step 3: Set plot control features . . Settings for plot characters/lines . line solid all character blank all character fill on character hw 1 0.75 character circle line blank . . Settings for labels . case asis title asis title offset 2 tic mark label case asis y1label Response . let nlab = unique labid loop for k = 1 1 nlab let icnt = k + nmeth let string sx^icnt = ^k end of loop . let ntot = nmeth + nlab xlimits 1 ntot major xtic mark number ntot minor xtic mark number 0 tic mark offset units data xtic mark offset 0.5 0.5 x1tic mark label format group label let igx = group label sx1 to sx^ntot x1tic mark label content igx . . Step 4: Generate the plot . loop for k = 1 1 ntot let string sxnew^k = ^sx^k end of loop . . Generate dummy plot, read dpst3f.dat to obtain . sorted labels . set consensus mean plot sorted on set consensus mean plot error two standard errors . device 1 off device 2 off print off consensus mean plot alite labid skip 0 read dpst3f.dat indx loop for k = 1 1 nmeth let icnt = indx(k) let string sxnew^k = ^sx^icnt end of loop let igx = group label sxnew1 to sxnew^ntot x1tic mark label content igx device 1 on device 2 on printing on . . Now generate plot with sorted labels . title Consensus Means Plot  Method Sorted by Width of Expanded Uncertainty feedback off consensus mean plot alite labid . . Step 5: Post plot labelling . line dotted drawdsds 6.5 20 6.5 90 justification center moveds 3.5 5 text Consensus Method: Two Standard Errors moveds 9 5 text Laboratorycr()meansp()+/2*sd/sqrt(n)Program 4: . Step 1: Read the data . SKIP 25 READ STUTZ86.DAT ALITE JUNK2 JUNK3 JUNK4 JUNK5 LABID . . Step 2: Define consensus means options . set write decimals 5 set bob on set dersimonian laird bootstrap on set dersimonian laird minmax off set modified mandel paule off set schiller eberhardt off set mean of means off set grand mean off set graybill deal off set generalized confidence interval off set fairweather off set bayesian consensus procedure off set random number generator fibonacci congruential seed 55631 bootstrap samples 100000 . . iflagm = 1 => 95% Confidence Interval . = 2 => Two Standard Errors Confidence Interval . = 3 => One Standard Errors Confidence Interval . let iflagm = 2 if iflagm = 1 set consensus mean plot error confidence intervals else if iflagm = 2 set consensus mean plot error two standard errors else if iflagm = 3 set consensus mean plot error one standard errors end of if . . . Step 3: Define strings containing Method id's . let nlab = unique labid loop for k = 1 1 nlab let string sx^k = ^k end of loop . let icnt = nlab + 1 let string sx^icnt = MP let icnt = icnt + 1 let string sx^icnt = VR let icnt = icnt + 1 let string sx^icnt = DSLcr()Original let icnt = icnt + 1 let string sx^icnt = DSLcr()HHD let icnt = icnt + 1 let string sx^icnt = DSLcr()Bootstrap let icnt = icnt + 1 let string sx^icnt = BOB let nmeth = 6 . . Step 4: Set plot control options . line solid all character blank all character fill on character hw 1 0.75 character circle line blank . case asis title case asis label case asis tic mark label case asis title offset 2 title Consensus Means Plot  With Data, Unsorted y1label Percentage of Alite . let ntot = nmeth + nlab xlimits 1 ntot major xtic mark number ntot minor xtic mark number 0 tic mark offset units data xtic mark offset 0.5 0.5 x1tic mark label format group label let igx = group label sx1 to sx^ntot x1tic mark label content igx . . Step 5: Generate the consensus mean plot . set consensus mean plot data left . printing off capture screen on capture cmplot.out consensus mean plot alite labid end of capture . printing on . line dotted drawdsds 5.5 20 5.5 90 . justification center moveds 8.5 8 if iflagm = 1 text Consensus Method:cr()95% Confidence Limits else if iflagm = 2 text Consensus Method:cr()Two Standard Errors else if iflagm = 3 text Consensus Method:cr()One Standard Error end of if moveds 2.5 8 text Method/Laboratorycr()meansp()+/2*sd/sqrt(n)  
Date created: 08/17/2001 Last updated: 12/04/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 