1. User’s Guide to the ‘QDE Toolkit Pro’ National ResearchConseil national Council Canadade recherches Excel Tools for Presenting Metrological Comparisons by B.M. Wood, R.J. Douglas & A.G. Steele Chapter 3. Tables of Equivalence (i) This chapter presents the simple use of a Toolkit macro to build Equivalence Tables. May 2, 2002 Ch 3: 30

2. Tables of Equivalence - Input Data In preparing to choose the KCRV and its uncertainty, the table detailing the bilateral inter-laboratory degrees of equivalence can be created, along with equivalence to several candidate Reference Values (RVs). The input data for this table requires three pieces of information for each laboratory: name (or acronym, or pseudonym), deviation from one RV (or from zero), and claimed uncertainty. The block of Lab data is ended by the first name with an ‘RV’ in it. This starts the block of reference value data, where the equivalence consequences of different choices for the KCRV and its uncertainty can be explicitly examined. The reference values are terminated by a blank in the name column (column A). The input data must be listed in columns A,B, and C in an Excel worksheet; the first row of each column must be used to label the data: Name, Deviation, Uncertainty. Ch 3: 31

3. Recall the input data was placed in columns A,B, and C of an Excel spreadsheet; the first row of each column was used to label the data: Name, Deviation, Uncertainty. Tables of Equivalence - Toolkit V1 Input Data leave a blank row to denote the end of the data put column titles in the first row put comparison data in the next rows put lab names in first column, deviation in second column, uncertainty in third column Ch 3: 32

4. The required input data: Name, Deviation and Uncertainty are entered as for our earlier toolkits. Tables of Equivalence - ‘Toolkit Pro’ Input Data leave a blank row to denote the end of the data put column titles in the first row put comparison data in the next rows put lab names in first column, deviation in second column, uncertainty in third column The first row with an ‘RV’ in its name starts the block of candidate KCRVs: 0,1... or n of them. Ch 3: 33

5. Tables of Equivalence - Input Constraints  The first row must contain the column labels (in A1, B1, C1).  The data must start in the next row (A2, B2, C2). All data in columns B and C must be in the same units.  Toolkit macros adapt to any number of laboratories and RVs, and the first blank row indicates the end of the data list.  The RV block is optional. It starts with the first name in A that contains an “RV” (case insensitive), and is terminated by a blank name. Multiple candidate KCRVs can be included. We recommend but do not require that these names contain “RV”.  The uncertainties are listed as standard (k=1) uncertainties as recommended by the MRA.  Effective degrees of freedom and correlation coefficients can be incorporated as described below. Ch 3: 34

6. Tables of Equivalence - Run the Macro Perhaps surprisingly, the next step in entering degrees of freedom and correlation coefficients is to run one of the macros: most will automatically write the defaults of normal uncorrelated uncertainties: you will be able to edit them later.  Begin by selecting a cell corresponding to the upper left hand corner of the equivalence table to be created.  Select the Tools menu, which drops down.  In the drop down menu, select Macro, which cascades.  In the cascaded menu, select Macros…, which opens a dialog box containing the available macros for your worksheet. The next slides show what this looks like in Excel. Ch 3: 35

7. Tables of Equivalence - Run the Macro Secondly, run the macro from the “Tools” drop-down menu list First, click-select the top left ‘anchor’ cell for table output, initially below the input data rows. Ch 3: 36

8. Tables of Equivalence - Run the Macro …then Run it. If you are running it in an established Toolkit Pro workbook, it will fill in the defaults, and produce a table of equivalences... Select the macro from the list… tk_mraCCQM_TableBuilder is a good start Ch 3: 37

9. Tables of Equivalence - after Running the Macro The table is “anchored” with the top left corner in the cell which you selected. A pop-up comment gives the time, date and Toolkit version for the table. The table extends beyond what is shown, and includes all of the 10x10 bilateral degrees of equivalence for this example data set of nine labs + KCRV The table output format is determined by the input data format of B2 and C2 Ch 3: 38

10. Tables of Equivalence - after Running the Macro The macro has tried reading a 9 column by 10 row matrix of correlation coefficients. A valid matrix must have an all-1’s diagonal. Not finding one, it has been automatically written, along with 0’s in the other elements for the default: uncorrelated results. Aside: Where did the title and units come from? They came from another Excel worksheet, named TK Title, in your Toolkit Pro workbook. If it cannot be found by a macro that needs it, one is created and you are nagged to fill it out. There will be more about this later, in Chapter 10. The macro has tried reading the degrees of freedom in Column D, and has not found valid numbers or strings, so it has assumed normal distributions as its default, which it wrote into Column D. Ch 3: 39

11. Tables of Equivalence - after first Running the Macro The correlation coefficient matrix is symmetric about its diagonal. The elements above the diagonal are only for show: edit the cell below the diagonal and the matching cell above will magically show the same change. If you have information about any effective degrees of freedom, or correlation coefficients, you simply edit the appropriate cells. TIP: Editable cells have a double line at the bottom. Ch 3: 40

12. Tables of Equivalence - The Output  The tables can be re-formatted differently after they have been generated by the macro. These formatting changes include cell background color, font name, font size, font color, number of displayed digits*, etc.  The table, or parts of it, can be ‘cut and pasted’ onto other Excel worksheets or into other documents.  To change the order of the laboratories, to add other labs or to change the input values the macro must be run again after editing the input. Simply select the output anchor cell, and repeat the steps to run the macro. Unless merged cells conflict, you can usually overwrite the old table if you wish. * Note: some tables of strings require re-running the macro to modify the number of digits displayed. Ch 3: 41

13. Tables of Equivalence - ‘The’ KCRV and ‘The’ U KCRV  The promotion of a candidate KCRV to ‘the’ KCRV can have many subtle consequences that your CC and WG may wish to consider. Deciding on the variation to be attributed to any ‘reasonable’ variation in the KCRV method (both creation and use) is not a job for a general Excel macro, and the Toolkit does not try to do it for you.  The Toolkit’s output Tables of Equivalence need your judgement as a particular Table is given its final editing that will usually include finalizing the method for determining the KCRV and finalizing the uncertainty budget for U KCRV. Final editing is a good time for final review, for example as you move a candidate KCRV column from the right to the left of the Table. Ch 3: 42

14. Tables of Equivalence - The Macros The Toolkit includes four Table-building macros: tk_mraCCQM_TableBuilder CCQM format for MRA Degree of Equivalence tk_mraDOE_TableBuilder MRA Degree of Equivalence (DOE) with (D  U) formatting tk_mraDOEandQDE_TableBuilder DOE and QDE 0.95 95% confidence interval in one table tk_mraQDC_MatrixBuilder Demonstrated confidence for agreement within  CMC, default: 2 u lab Ch 3: 43