1. Users 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 4. Tables of Equivalence (ii) This chapter presents some of the refinements that are in the QDE Toolkit Pro for creating Tables of Equivalence. April 16, 2002 Ch 4: 44

2. The Toolkit includes: tk_mraCCQM_TableBuilder It creates a table in the format circulated by C.Thomas of BIPM who is in charge of the database. This format was proposed by the CCQM to meet the needs of chemical metrology. It is a full, anti-symmetric table of ordered pairs of data with row minus column differences in the first cell and expanded (k 0.95 ) uncertainties in the second cell. The choice of the particular cell bolding and cell outlines reflect our understanding of their most recent format. Tables of Equivalence - CCQM Format Ch 4: 45

3. Tables of Equivalence - CCQM Format tk_mraCCQM_TableBuilder : output is row-column difference D 12 and expanded uncertainty U 12 = k 12 (0.95)(u 1 2 +u 2 2 - 2 r 12 u 1 u 2 ) 0.5 as values in each double element of the table. Each 95% confidence coverage factor k 12 (0.95) is calculated by numerically integrating the Student distribution with a pair effective degrees of freedom (not truncated to an integer) calculated using the Welch-Satterthwaite formula. Ch 4: 46

4. Tables of Equivalence - CCQM Format: Pop-up Comments Pop-up Comments: the macro has automatically added an explanatory pop-up comment to each number in the table. As your mouse pointer hovers over a cell, its comment pops-up. The comments can be managed and edited with Excel. Ch 4: 47

5. Tables of Equivalence - Formatting Precision and Fonts The format of the columns in the equivalence tables use the format of the input data. In particular, the number of decimal places used in cells B2 and C2 for the input data is used in the output tables. This is also true for the font typeface and size (although bolding is forced on for differences and off for uncertainties). Toolkit comments use a fixed 8 point font, and other parts use 8 and 10 point fixed fonts. We suggest using 10 point fonts for your input data, and using Excels Zoom to adjust the on-screen size. We prefer the way Windows Small Fonts interacts with the Excel Zoom to the way Windows Large Fonts interacts with the Excel Zoom feature. Ch 4: 48

6. Tables of Equivalence - Formatting cell sizes and colors Individual or groups of table cells can still be formatted using Excels standard features which allow you to change cell height and width, colors, borders, etc. The width and height of cell A2 is read by many macros which use them for scaling some non-critical sizes: comment box sizes and the initial size of graphs. The background color of the Lab name cells (column A) is set (by tk_Toggle_Outlier_INvsOUT) to yellow for out-of- pool Labs, and to white for in-pool Labs. Ch 4: 49

7. Multiple Tables of Equivalence Multiple tables each have a comment in its anchor cell, identifying the date and time of output. This may help you to correlate notebook and workbook, and to validate the order of tables as subtle changes are made. Multiple tables can be created on the same worksheet. Simply select a new output anchor cell and run (or re-run) a macro. The consequences of different degrees of freedom or correlation coefficients can be easily explored in this way. Multiple versions of input data (outlier identification, degrees of freedom, correlation coefficients, or conjectured corrections to values or uncertainties…) can be comfortably accommodated on different worksheets of the workbook. Ch 4: 50

8. Where to Put Multiple Tables of Equivalence Each worksheet has a safe zone which macros do not try to clear. If there is a total of N labs and RVs, then columns to the right of N+5, and rows below N+5, are safe. A new table can overwrite an old matching table of the same position, type and size. Conflicting merged cells can cause problems in some other cases. Tip: copying one blank cell and pasting it to the entire region of the old table will remove any troubling formatting. Ch 4: 51

9. Adjusting Column Widths with Multiple Tables If columns need to be widened, Excels Format | Columns | AutoFit Selection can often help. With columns from other equivalence tables sharing the same column, this process can create problems in other tables. Tip: Select the table and run the Toolkit Pro macro tk_Widen_Columns_to_Fit, which operates like Excels AutoFit except that it only widens and does not contract column widths. Ch 4: 52

10. Multiple Candidate KCRVs Multiple candidate KCRVs can be accommodated on one worksheet, and even in one Equivalence Table: just add them at the bottom of the input table, below the first name with an RV in it. Some automated RV macros are available. They use outlier status and weights stored on worksheet TK Title, and will be discussed later. The first row with an RV in its name starts the block of candidate KCRVs (here 3 RVs). Ch 4: 53

11. Multiple Candidate KCRVs Multiple input candidate KCRVs give rise to multiple outputs in the Degrees of Equivalence Tables: Ch 4: 54

12. Tables of Equivalence - Different Data Sets The macro works in the same fashion with other comparison data sets. The Toolkit Pro works best with a separate Excel workbook for each separate Comparison. A new workbook can be started from an old workbook. To avoid overwriting the old workbook, simply Save the old workbook, and then Save As a new workbook file. Next you should edit the just-copied worksheet TK Title. Enter, or copy-and-paste the new data into the first three columns of a new worksheet and run the tk_mraCCQM_TableBuilder macro to create the editable defaults for i and r ij, and the output equivalence table. Ch 4: 55

13. Other Tables of Equivalence The Toolkit offers several other tables of equivalence for use by metrologists and others to more fully communicate the equivalence relationships.These include tables which present: the MRA Degree Of Equivalence (DOE) in a format commonly used for physical measurements, (D ± U), the single parameter QDE 0.95 description, and the single probability parameter, Quantified Demonstrated Confidence for agreement in a specified interval, QDC. Reference: Wood and Douglas, Metrologia 35, 187-196 (1998) This paper covers the essentials of probability calculus for computing confidence in an interval centered on the concept of equivalence. Ch 4: 56

14. The Toolkit includes : tk_mraDOE_TableBuilder creates a table: row-column difference D ± k 12 (0.95)(u 1 2 +u 2 2 - 2 r 12 u 1 u 2 ) 0.5 as a string in each element of the table MRA Degree Of Equivalence Table again, there are lots of pop-up comments automatically added Ch 4: 57

15. Degree of Equivalence and QDE 0.95 The Toolkit includes : tk_mraDOEandQDE_TableBuilder creates a table: row-column difference ± k 12 (0.95)(u 1 2 +u 2 2 - 2 r 12 u 1 u 2 ) 0.5 as a string in the above-diagonal elements of the table and in the below-diagonal elements it places the 95% confidence interval for agreement, QDE 0.95. again, there are lots of pop-up comments automatically added Ch 4: 58