Issue 61

Comparing Data Sets Using Radar Plots

Grapher 8's new Radar Plot allows you to graph multivariate data in a way that makes their relationships simple to discern. The Radar Plot does this by creating an axis for each variable, and then drawing polygons whose vertices lie along the axes. Each polygon represents a data group. They can be customized with colors and fills that make them easy to distinguish.

Radar Graphs are known by several different names, including web plots, spider plots and star plots, because the graph's shape resembles a spider's web or a star. It can also be called an irregular polygon, polar chart, or kiviat diagram.

This article describes how to create and format data for a radar plot, create the radar plot, and details how to customize the radar plot to highlight the important information that the graph is portraying.

Formatting the Data
The spreadsheet format for radar plots is fairly simple to create. Each variable should be placed in a separate column. In this sample radar plot graph, there are potentially four variables: mass, charge, spin, and names. Because names contains no numeric data, it is not included as a variable in the graph. It can be used for labels, though. Each row contains a single data group, with a data value listed in each column. For instance, the data group named "Up Quark" has a value of 2.4 for the mass variable. Each row generates a separate radar line plot. The line connects all of the data values in the row.

A matrix of groups and values is ideal for charting with a Radar Graph.

Generating the Plot
To create a radar plot, open a new plot window using the File | New command. Select Plot and click the OK button. A new blank plot window is created. Now, choose Graph | Polar Graphs | Radar Plot. Select a worksheet that contains your data and click the Open button. Grapher automatically creates a graph with three axes and a separate line for each row of data.

The default Radar Graph uses three axes and all available data rows.

The default Radar Graph has three axes, created from the first three columns of numeric data. Grapher will add axes to the plot based on the settings on the Graph tab of the Property Inspector. Each column in the data file that is plotted corresponds to a new axis on the graph. To add or remove axes:

1. Click on the Graph 1 object in the Object Manager.
2. In the Property Inspector, click on the Graph tab.
3. Click the Columns command.
4. Check or uncheck the data columns in the drop-down list. All checked columns will appear in the graph. After checking the desired columns, click anywhere in the Property Inspector to update the graph.

Check the columns that you want to display on the radar plot.

The Worksheet rows command on the Graph tab controls the number of plots in the graph. By default, all rows with data are used. Changing the First row and Last row values allows you to limit or expand the number of plots in the graph.

Set the first and last rows to the range containing the data.

Customizing the Axes
Columns are shown on the radar plot as axes. The columns are assigned an axis in the order they appear in the worksheet. Radar Axis 1 corresponds to column A, Radar Axis 2 corresponds to column B, and so on. Axes are ordered clockwise, with the first axis vertical and pointing to the top of the page. If you would like the first axis to be located at another position, select the entire graph and choose Arrange | Rotate. Type in the number of degrees to rotate the graph. Positive numbers rotate the graph the specified number of degrees in the counter-clockwise direction. Negative numbers rotate the graph the specified number of degrees in the clockwise direction.

By default the axes are synched. This means that the minimum and maximum values for each axis are the same. The automatic range for the axes covers the minimum and maximum of the entire data set, with slight padding to produce regular tick mark intervals. If this does not suit your data, the axes are easy to adjust. Some axis customizations are listed below.

One item you may want to change is to format the axes so each axis uses its own data range. To do so:

1. Select the Graph 1 object in the Object Manager.
2. In the Property Inspector, click on the Graph tab.
3. Uncheck the Keep axes synched command. Each axis will now use its own limits.

The graph on the left shows synched axes, all axes have the same minimum and maximum values.
The graph on the right shows independent axes, each axis is scaled according to only that data.

If you would like to display grid lines that connect the axis tick marks, you have the option of using either a linear or radial set of grid lines. To change between the linear and radial grid:

1. Click on the Graph 1 object in the Object Manager.
2. In the Property Inspector, click on the Graph tab.
3. To display linear grid lines, check the Use linear grid option. To display radial grid lines, uncheck the Use linear grid option.
4. Click on any axis in the Object Manager or in the plot window to select it.
5. In the Property Inspector, open the Grid Lines tab.
6. Check the At major ticks box to display grid lines at each major tick mark.
7. Check the At minor ticks box to display grid lines at each minor tick mark.

The graph on the left shows linear grid lines.
The graph on the right shows radial, or circular, grid lines.

Note that if you are using independently scaled axes, the grid lines will not always correspond with the tick mark location for each axis. The axis that you have selected in step 4 above will have the tick marks and grid lines aligned. The grid lines will not necessarily align with the major tick marks on the other axes.

The radar axes can be further customized, in a similar manner to other axis types in Grapher. Altering the properties of an axis was previously discussed in another newsletter article, available at Easy Axis Edits to Enhance a Graph. Most of the items in this article are also relevant to radar axes.

Customizing the Plots
The lines that connect the data points on each axis in the radar plot form polygons. Radar Plot 1 will correspond to row 1, Radar Plot 2 will correspond to row 2, and so on. These plots have customizable properties similar to other Grapher plots. Usually, radar graphs are used to compare relationships between multiple similar data groups. So, the Fill property is useful in distinguishing between similar lines. Using multiple fill colors will also produce an attractive, informative radar graphs. To fill in the interior area of a plot:

1. Click once on the Radar Plot 1 name in the Object Manager to select it.
2. In the Property Inspector, click on the Fill tab to open it.
3. Next to the Pattern command, click the None sample. In the drop-down, select Solid. The plot is automatically filled with a solid black color, by default.
4. Next to the Foreground command, click the Black sample color. Because we will be adding multiple overlapping colors, lighter colors tend to work better for radar plots. In the drop-down color list, click on the desired new color, such as Pastel Blue. The plot automatically updates to show the new color.
5. To make the color partially transparent, change the 100% next to the Foreground Opacity command. You can either scroll to a new value or highlight the existing value and type in a new value. When the desired transparency percentage is shown, press the Enter key on the keyboard or click anywhere else in the property inspector for the change to be made.
6. Repeat the above steps for each additional radar plot listed in the object manager. Each plot can have different fill colors, percentage opacity, and fill pattern, if desired.

In addition to the fill properties, each radar plot can have different line and symbol properties, as well. To change these:

1. Click once on the Radar Plot 1 name in the Object Manager to select it.
2. In the Property Inspector, click on the Line tab to open it.
   1. Next to the Style command, click the Solid line sample. In the drop-down, you can select any other line type, such as the 0.3 in. Dash. The plot is automatically updated to show the dashed line.
   2. Next to the Color command, click the Black sample color. You can select the same color as the fill or any desired color. The plot automatically updates to show the new color.
   3. Next to the Width command, scroll up or down to change the line thickness. You can also highlight the existing thickness and type in a new value. When the desired width is shown, press the Enter key on the keyboard or click anywhere else in the property inspector for the change to be made.
   4. If desired, the line can be made partially transparent, as well. If desired, change the 100% next to the Opacity command. You can either scroll to a new value or highlight the existing value and type in a new value. When the desired transparency percentage is shown, press the Enter key on the keyboard or click anywhere else in the property inspector for the change to be made.
3. In the Property Inspector, click on the Symbol tab to open it.
   1. Next to the Symbol frequency command, change the zero to a one to show symbols at every data point.
   2. Change the Symbol by clicking the existing default symbol and selecting a new symbol from the drop-down list.
   3. The Fill color and Line color can be changed to match the fill or line colors of the plot.
   4. The Size can be changed to make the symbol smaller or larger.
   5. Additional symbol changes can be made, if desired.
4. Repeat the above steps for each additional radar plot listed in the object manager. Each plot can have different line styles, colors, widths and symbol sizes, shapes, and frequencies, if desired.

Comparing radar plots is easier when using filled partially transparent colors.

Finalizing the Graph
Our radar plot is almost finished, but it is still missing some critical plot elements. For instance, you probably want it to be easy for your reader to know which axis goes with which variable. And, it is equally as important to know which colored polygon goes with which data group. Adding axis titles and legends makes this graph much easier to read. Adding titles, legends, and other items is the same with radar plots as it is for other graph types. These steps explain the process of adding an axis title, a legend, and a graph title.

1. Click on the Radar Axis 1 in the Object Manager to select it.
   1. Click on the Axis tab in the Property Inspector.
   2. Open the Axis title section.
   3. Next to the Title command, click the words <Click here to edit text>.
   4. In the Text Editor, type the name of the first variable, such as Mass (MeV).
   5. If desired, highlight the text and change the font size, color, or other properties. When all text changes have been made, click the OK button. The axis title is added to the graph.
   6. To move the axis title so that it does not overwrite your plots, you can change the X offset and Y offset values in the Axis title section of the Property Inspector. You can also rotate the title by changing the value next to the Angle command.
2. To add a graph title, click on the Graph 1 object in the Object Manager.
   1. Click on the Title tab in the Property Inspector.
   2. Next to the Titlecommand, click the words <Click here to edit text>.
   3. In the Text Editor, type the graph name, such as Properties of 1st Generation Fermions.
   4. If desired, highlight the text and change the font size, color, or other properties. When all text changes have been made, click the OK button. The graph title is added to the graph.
3. To add a legend, click on any portion of the radar graph.
   1. Choose Graph | Add to Graph | Legend. The legend is automatically added to the graph.
   2. To change the properties of the legend, click on the Legend 1 object in the Object Manager to select it. In the Property Inspector, make any desired changes. For instance, you may want to change the text associated with each plot. Click on the Entries command where it says <Click here to edit entries>. Make any changes and click OK to update the graph.
   3. To move the legend, click on the legend in the plot window. Hold down the left mouse button and drag it to a new location. When it is positioned correctly, release the mouse button.
4. Make any further customizations to the graph, as desired.

Radar plots can be useful when comparing similar data groups,
such as these properties of First Generation Fermions.