User’s Guide to the ‘QDE Toolkit Pro’ Ch 8: 103 Sept 5, 2003 National Research Conseil national Council Canada de recherches User’s Guide to the ‘QDE Toolkit Pro’ Excel Tools for Presenting Metrological Comparisons by B.M. Wood, R.J. Douglas & A.G. Steele Chapter 8. Graphing and Pooling Measurement Distributions (i) In this chapter, the use of some of the QDE Toolkit Pro’s facilities for graphing distributions and pooled distributions is introduced.

QDE Toolkit Pro Graphs - Plotting Pooled Distributions Ch 8: 104 QDE Toolkit Pro Graphs - Plotting Pooled Distributions A superposition of the Labs’ PDFs can be plotted automatically by the Toolkit - Normal and Student PDFs, on linear and logarithmic graphs are available by running the macro tk_pool_PlotBuilder In this section, we use the term “pooling” to refer to the broadest sense of “considering them together” in some way. This is ‘cute’, and its real utility is only revealed when other pooling distributions are included...

QDE Toolkit Pro Graphs - Pooling: Sum of PDFs Ch 8: 105 QDE Toolkit Pro Graphs - Pooling: Sum of PDFs The sum of the PDFs gives a clear description of the range of measurements expected from the pooled group of laboratories. Other than the normalization, it is the PDF of measurement for a Lab chosen at random from the pool, and supports most discussions of “guard-banding”. The facility to easily remove (or readmit) a laboratory to the pool is provided through the Toolkit Pro macro tk_Toggle_Outlier_INvsOUT.

QDE Toolkit Pro Graphs - Pooling: Product of PDFs Ch 8: 106 QDE Toolkit Pro Graphs - Pooling: Product of PDFs The product of the PDFs gives a clear description of the tightest range of measurements expected from the pooled group of laboratories. For Normal distributions, it is the distribution of the inverse-variance weighted mean. Other than the normalization, it is the PDF for agreement of all N Labs within dx. The log graph provides an easy visualization (the log of the product is the sum of the logs) of the contributions to the weighted mean. Below, Lab 9 is shown as a n=15 Student distribution: do you think should it be added to the pool?

QDE Toolkit Pro Graphs - Pooling: Sum of Pair-Difference PDFs Ch 8: 107 QDE Toolkit Pro Graphs - Pooling: Sum of Pair-Difference PDFs The sum of the pair-difference PDFs gives a clear description of the range of possible results expected from a randomly chosen pair in the group of laboratories. Since it includes both (Labi - Labj) and (Labj - Labi), it has a zero mean. It is the first distribution presented here that fully incorporates all known details of the pair difference distributions (degrees of freedom and correlations). Depending on the repeatability properties of the uncertainties, the sum-of-Pair-Difference-PDFs might be expected to be 1.0 to 1.41 times wider than the Sum-of-PDFs distribution.

QDE Toolkit Pro Graphs - Plotting these Pooled Distributions Ch 8: 108 QDE Toolkit Pro Graphs - Plotting these Pooled Distributions By running the macro tk_pool_PlotBuilder, all of these pooled distributions are generated at the same time for all “in-pool” Labs on the active worksheet. The “in-pool” and “out-pool” status of a laboratory can be toggled by selecting its name in column A, and running the QDE Toolkit Pro macro tk_Toggle_Outlier_INvsOUT, which also sets the cell color in Column A: yellow for “out-pool” and white for “in-pool”.

QDE Toolkit Pro Graphs - Plotting these Pooled Distributions Ch 8: 109 QDE Toolkit Pro Graphs - Plotting these Pooled Distributions After running the macro tk_pool_PlotBuilder, all of these pooled distributions are generated at the same time for all “in-pool” Labs on the active worksheet. Other things are output, too, as discussed in Chapter 9. Linear graph Log graph Table of data for plotting and integration (~2000 rows) Supplementary information

QDE Toolkit Pro Graphs - Monte Carlo Histograms Ch 8: 110 QDE Toolkit Pro Graphs - Monte Carlo Histograms Also, the median distribution can be graphed automatically as Monte Carlo histograms, produced by the new Toolkit macro tk_RVisMedianHAddToWorksheet (see also in Chapter 12) The histograms are graphed on a new worksheet, named “Histograms”, added to the active workbook. Histograms of the median, the mean, the weighted mean; and their average (the ARV) are plotted, with the pooled data and pair-difference histograms.