Help Manual

Contents






Sigma Magic Help Version 18

Correspondence Analysis

Overview

This analysis can summarize and display in a 2-dimensional graphical form the relationship between row and column variables of a contingency table. The data needs to be entered as a contingency table. An example is shown in the figure below. It is used for categorical rather than continuous data. We can make certain conclusions about the variables by observing where the row and column variables fall on the 2-dimensional graph. We must be cautious about interpreting the distances between row and column variables since these are not strict distance measures in the Euclidean space.

Contingency Table This functionality is provided by the R software using the function ca within the ca package. Note that this functionality requires that RScript software be installed on your computer and linked to the Sigma Magic software within the options menu. The Correspondence Analysis worksheet can be added to your active workbook by clicking on Analytics and then selecting Correspondence Analysis.

Inputs

Click on Analysis Setup to open the menu options for this tool. A sample screenshot of the menu is shown below.
menu 1
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Data Type: You can specify the type of data you use. For this analysis, we require that the data be categorical.
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Graphs: Specify the type of graph you would like to plot.
OptionDescription
SymmetricSymmetric graph will only plot the row and column data points on a 2-dimensional graph.
AsymmetricVectors (columns) are also super-imposed on this graph.
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Num Dimensions: You can specify the number of dimensions kept in the final analysis results. The default is to retain all the dimensions in the analysis.
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Algorithm: Only the CA algorithm is available within Sigma Magic software.
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Additional Options: This field is optional. By typing it here, you can specify any additional options for the R software program.
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Help Button: Click on the Help Button to view the help documentation for this tool.
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Cancel Button: Click on the Cancel Button to discard your changes and exit this menu.
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OK Button: Click on the OK Button to save your changes and try to execute the program. You must specify the required data to complete the analysis and generate outputs. If there are any missing data, the software will remind you to specify the data and click on Compute Outputs to generate analysis results.

Data

You will see the following dialog box if you click the Data button. Here, you can specify the data required for this analysis. Data
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Search Data: The available data displays all the columns of data that are available for analysis. You can use the search bar to filter this list and speed up the search for the right data for analysis. Enter a few characters in the search field, and the software will filter and display the filtered data in the Available Data box.
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Available Data: The available data box contains the list of data available for analysis. If your workbook has no data in tabular format, this box will display "No Data Found.” The information displayed in this box includes the row number, whether the data is Numeric (N) or Text (T), and the name of the column variable. Note that the software displays data from all the tables in the current workbook. Even though data within the same table have unique column names, columns across different tables can have similar names. Hence, it is crucial that you not only specify the column name but also the table name.
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Add or View Data: Click on this button to add more data to your workbook for analysis or to view more details about the data listed in the available data box. When you click on this button, it opens the Data Editor dialog box, where you can import more data to your workbook. You can also switch from the list view to a table view to see the individual data values for each column.
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Required Data: The code for the required data specifies what data can be specified for that box. An example code is N: 2-4. If the code starts with an N, you must select only numeric columns. You can choose numeric and text columns if the code begins with a T. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, you must select a minimum of 2 columns of data and a maximum of 4 columns in this box. If the minimum value is 0, then no data is required to be specified for this box.
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Select Button: Click on this button to select the data for analysis. Any data you choose for the analysis is moved to the right. To select a column, click on the columns in the Available Databox to highlight them and then click on the Select Button. A second method to choose the data is to double-click on the columns in the list of Available Data. Finally, you can drag and drop the columns you are interested in by holding down the select columns using your left mouse key and dragging and dropping them in one of the boxes on the right.
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Selected Data: The list box header will be displayed in black if the right number of data columns is specified. If sufficient data has not been specified, then the list box header will be displayed in red color. Note that you can double-click on any of the columns in this box to remove them from the box.
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View Selection: Click on this button to view the data specified for this analysis. The data can be viewed in a tabular format or a graphical summary of the selected data.

Verify

If you click the Verify button, the software will perform some checks on the data you entered. A sample screenshot of the data is shown in this figure. Pre-Process Inputs 4
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Verify Checks: The objective of this analysis, as well as any checks that are performed, are listed in this dialog box. For example, the software may check if you have correctly specified the input options and if you have specified the data correctly for analysis.
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Check Status: The results of the analysis checks are listed here. If the checks are passed, they are shown as a green checkmark. If the verification checks fail, they are shown as a red 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.
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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 results on the worksheet. A sample screenshot of the worksheet is shown below.
Correspondence Analysis Example
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Notes Section: The notes section provides a summary of the eigenvalue decomposition that can be used to identify how many dimensions are present in your data.
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Graph Section: The graph section shows the correspondence analysis graph. Row points that are closer together have more similar column profiles. Note that you cannot interpret the distance between rows and columns directly. The asymmetric graph shows rows in the principal coordinates and columns as standardized residuals. In addition, mass is represented by points, and arrows represent columns. Point intensity (shading) corresponds to the absolute contribution for the rows. In this example, an eye color of "blue" more closely corresponds to a hair color of "blond" (row 4); similarly, an eye color of "brown" more closely corresponds with a hair color of "black" (row 1).

Notes

Here are a few pointers regarding this analysis:
  • This analysis requires that the R software needs to be installed on your computer. Further, you will need to provide a link to the RScript executable file under Sigma Magic Options so that the software can use the R software to generate analysis results.

Examples

The following examples are in the Examples folder.
  • For the data given in the file, use the correspondence analysis graph to draw inferences between the relationship of the row and column variables. (Correspondence Analysis 1.xlsx)

References

For more information on this topic, please refer to the following articles. Do note that if any external links are mentioned below, they are for reference purposes only.

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