Notched box-and-whisker diagram:

A notched box plot compares the difference among median values. In Grapher, you can create a notched box diagram and display a confidence interval for the median by following the steps below:

1. Click the Home | New Graph | Statistical | Notched Vertical Box Plot () command or the Home | New Graph | Statistical | Notched Horizontal Box Plot () command.
   
   
2. In the Open Worksheet dialog, select the data file and click Open. The default notched box-whisker plot is created.
   
   
3. Click on the box plot layer in the Object Manager to select the box plot (underneath Graph 1).
   
4. In the Property Manager, click on the Plot tab.
   
   
5. If desired, you can adjust the notch Factor.

   • The notch Factor determines the degree of confidence among median values. To increase the degree of confidence in the median values, increase the notch Factor.

   • The notch Factor is the value multiplied by the standard deviation of the median. The default notch Factor is 1.5.

   • In most cases, a notch Factor value of 1.96 would show approximately 99% confidence in the median. A smaller notch Factor will produce a more conservative test of the confidence.

   • An appropriate range for notch Factor values is between 1.3 and 1.96.

     
     To edit the value, highlight the existing value and type the desired value. Press ENTER on the keyboard to make the change.
     
     

A Vertical and Horizontal Notched Box-Whisker Plot with
the notch Factor set to 1.7.

Set Adjustable or Variable Box Widths

If you'd like to layer box plots, or represent the size of data populations in each sample dataset, you can control the width of box plots in Grapher. To change the width of a boxes in a box plot:

1. Select the Box Plot in the Object Manager. 
2. In the Property Manager, click the Plot tab. 
3. Expand the Width section. 
4. Change the Box width (percentage) to change the width for all boxes at the same time. 
5. Set the Type field to Variable, Fixed, or leave it set to Auto. 
   • Variable to vary the size based on the number of sample entries in each set of data. When using the Variable option the width of each box is determined via the sample count in that box vs the sum of the sample counts of all boxes. 
   • Fixed to choose a set width for each box plot. 
   • Auto to have Grapher automatically determine an appropriate box width

Box plot with Variable Width applied. 

Use Data Filter to Clip Box Plot Limits

The data filter makes it possible to exclude or include specific criteria from your data without removing these data from your file. You can use the data filter with Box Plots in Grapher. 

1. In the Object Manager, select the Box Plot. 
2. In the Property Manager, click the Data Limits tab. 
3. Click Set in the Criteria Filter section. 
4. Delete the existing values in the Clipping section and replace with desired values. Learn more about Clipping in Grapher's Help. 
5. Fill out the Exclude data or Include data fields for your desired results and click OK. 

Note

Removing data from a Box Plot using Data Filter may affect the statistical shape or distribution of that box, depending on the chosen settings for Box Edges and Whiskers.

Learn more in Grapher's Help.

Create Irregularly Spaced Box Plots

Follow the steps below to space box plots at irregular intervals along the axis.

1. Click the Home | New Graph | Statistical | Vertical Box Plot () command.
2. Click on the box plot in the Object Manager to select it.
3. In the Property Manager, click on the Plot tab.
4. Change the Last variable to be the same as the First variable. Only one box is now plotted.
5. In the Object Manager, click on the Box Plot Axis 1 to select it.
6. In the Property Manager, click on the Axis tab.
7. Change the Length to twice the desired width of the bar. If the box should be 0.5 inches wide, make the Length equal to 1.0 inches.
8. Click the Graph Tools | Add to Graph | Plot command.
9. In the dropdown menu, select Box Plot - Vertical Plot.
10. Click OK in the Choose Axes dialog to create a new X axis.
11. Select the data file and click Open.
12. Repeat steps 2 through 4 for the new box plot.
13. In the plot window, click and drag the new box plot axis to move it to the desired location.
14. Repeat steps 8-13 for each additional box plot.
    
    1. 1. If the labels are incorrect on the box plot axes, you can uncheck the boxes in the Object Manager next to each Box Plot Axis name. Then, add a new axis by clicking the Graph Tools | Add to Graph | Axis command. Label the new axis as desired.
15. To move keep your boxes relatively positioned so that they move with other plot changes, link your boxes to the appropriate axis in the Link Axis tab of the Property Manager.

Create variable spaced box plots using multiple box-plot axes.

Updated August 2023