Help Manual

Contents






Sigma Magic Help Version 19

Pairwise Comparison Matrix

Overview

A pairwise comparison matrix is a structured tool used to compare multiple options, criteria, or alternatives two at a time, to establish priorities, preferences, or relative importance. It's often used in decision-making, especially in methods like the Analytic Hierarchy Process (AHP). This process can be used for product feature prioritization, supplier selection, risk assessment, and strategy planning.

The purpose of using the matrix is:
  • Prioritize features, criteria, or options.
  • Assign weights to decision criteria.
  • Structure subjective judgements in a quantifiable way.
Use the following steps to create the matrix:
  • List all items to compare (criteria, options, etc.).
  • Compare each pair, rating which item in the pair is more important (or preferred) and by how much.
  • Fill the matrix with the comparison values.
  • Normalize the matrix and calculate weights or priorities.
This tool can be added to your active workbook by clicking on Project and then selecting Pairwise Comparison.

Inputs

Click on Analysis Setup to open the menu options for this tool. A sample screenshot of the menu is shown below. inputs
1
Template Type: Specify the format of the template. The following options are available:
OptionDescription
Upper TriangleSpecify the values of the matrix in the upper quadrant. The values in the lower quadrant are automatically derived by the software.
Lower TriangleSpecify the values of the matrix in the lower quadrant. The values in the upper quadrant are automatically derived by the software.
2
Num Items: Specify the number of items you want to compare and rate to derive the weights. You can pick from 2 to 100 items.
3
Rating Scale: Specify the rating scale you want to use to compare the items. The following options are available:
OptionDescription
0,1Rate the items on a 0, 1 scale. Use 0 if the item is worse than the other option and use 1 if the item is better than the other option.
1-9Use a granular scale 1-9. Use 1 if both items are equal, use 2 if the item is two times better than the other option, 3 if the item is three times better than the other option and so on.
4
Sort Items: Specify if the final results need to be sorted based on the weights. The available options are:
OptionDescription
NoneDo not sort the items - leave it the way they are entered.
SortThis option to sort the items based on weights is not currently enabled.
5
Example: Click on this button to open an example workbook.
6
Help Button: Click on this button to open the help file for this topic.
7
Cancel Button: Click on this button to discard any changes and close the dialog box.
8a
Create Button: Click this button to save any changes and reformat the worksheet layout.
8b
OK Button: If possible, click this button to save any changes and compute the analysis outputs.

Charts

You will see the following dialog box if you click the Charts button. Charts
1
Title: The system will automatically pick a title for your chart. However, if you want to override that with your title, you can specify a title for your chart here. Note that this input is optional.
2
Sub Title: The system will automatically pick a subtitle for your chart. However, if you want to override that with your subtitle, specify a subtitle for your chart here. Note that this input is optional.
3
X Label: The system will automatically pick a label for the x-axis. However, if you would like to override that with your label for the x-axis, you can specify a different label here. Note that this input is optional.
4
Y Label: The system will automatically pick a label for the y-axis. However, if you would like to override that with your label for the y-axis, you can specify a different label here. Note that this input is optional.
5
X Axis: The system will automatically pick a scale for the x-axis. This option is not currently enabled.
6
Y Axis: The system will automatically pick a scale for the y-axis. This option is not currently enabled.
7
Horizontal Lines: You can specify the values here if you want to add a few extra horizontal reference lines on top of your chart. The format for this input is numeric values separated by semi-colon. For example, if you specify 12;15, two horizontal lines are plotted at Y = 12 and Y = 15, respectively. Note that this input is optional.
8
Vertical Lines: You can specify the values here if you want to add a few extra vertical reference lines on top of your chart. The format for this input is numeric values separated by semi-colon. For example, if you specify 2;5, two vertical lines are plotted at X = 2 and X = 5, respectively. Note that this input is optional.

Optional Chart Formating

If a chart has already been created earlier and you have made any changes to the chart format directly on the chart, it is possible to copy the settings and save them to memory. The next time you regenerate the chart, the same settings will be applied by the software, and you won't have to reapply them manually. The following image appears in the Charts tab if a valid chart exists on the worksheet. If no charts are found on the worksheet, the image shown below is hidden and will not appear in your dialog box. Chart Format
1
Copy Format: Click on this button to copy the chart settings to memory. The chart settings will be saved and reapplied the next time you regenerate the chart.
2
Clear Format: Click on this button to clear any existing settings you have made to the chart. The default software settings will be applied to your chart.

Verify

If you click the Verify button, the software will perform some checks on the data you entered. A sample screenshot of the dialog box is shown in the figure below. Verify The software checks if you have correctly specified the input options and entered the required data on the worksheet. The results of the analysis checks are listed on the right. If the checks are passed, they are shown as green-colored checkmarks. If the verification checks fail, they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange exclamation mark. Finally, any checks that are required to be performed by the user are shown as blue info icons.
1
Section: The left-hand side shows the major tabs and the items checked within each section
2
Item: The left-hand side shows the major tabs and the items checked within each section
3
Status: The right-hand side shows the status of the checks.
4
Overall Status: The overall status of all the checks for the given analysis is shown here. The overall status check shows a green thumps-up sign if everything is okay and a red thumps-down sign if any checks have not passed. Note that you cannot proceed with generating analysis results for some analyses if the overall status is not okay.

Outputs

Click on Compute Outputs to update the output calculations. A sample screenshot of the worksheet is shown below. outputs
>
Notes: The text output of the analysis contains a table which contains the count of the raw data, the overall score, and the relative rank of the item.
>
Graphs: The graph output contains the Pareto chart of the scores. The Pareto chart contains the ordered bar chart and the cumulative frequency line (shown in red). The Pareto chart can be used to identify a few vital causes. Draw an imaginary line on the red cumulative graph at 80%, and this will indicate how many causes contribute to 80% of the problems.
outputs

Notes

Here are a few pointers regarding this analysis:
  • If you do not have summarized data, then specify that your data is in a single column in the dialog box. Sigma Magic software will automatically determine the frequencies by reading this column. It does this by counting the number of times the group name is repeated in this column.

Examples

The following examples are in the Examples folder.
  • Create a relative weighting matrix for all the factors you want to consider for choosing a new product (Pairwise 1. xlsx).


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