A good strategy when exploring a data set is to begin by examining each variable one at a time, then progress to bivariate and then multivariate visualizations to understand the relationships between variables.

Visualizing the distributions of key variables is a good first step. In this case, the backlogs, bed capacity, location, and patient satisfaction scores are key variables. A histogram is a good choice to show the range of observed values and the shape of the distribution. We begin by creating histograms for the 2015 and 2016 backlogs. Select Distribution and enter “Appts May 1 2015 31-60 days” and “Appts May 1 2016 31-60 days” in the Y field. Check the Histograms only box. The resulting histograms are shown in Figure 9.4 Histograms for 2015 and 2016 Appointment Backlogs.

The two histograms should have the same x-axis scale to facilitate comparison. Select Uniform Scale from the Options menu next to Distributions. Figure 9.5 Histograms for 2015 and 2016 Appointment Backlogs with Uniform Scaling shows the appointment backlogs on the same scale. Use caution when comparing the shapes of these two distributions as the histograms were created from only 16 observations.

These histograms show the magnitude and variation of the backlogs.

Figure 9.6 Histograms for Backlog Difference, Bed Capacity, and Patient Satisfaction shows the histograms for the backlog difference, in-patient bed capacity, and the patient overall satisfaction scores.

The Backlog Difference histogram shows that only four of the 16 medical centers (25%) reduced the number of veterans waiting 31-60 days for an appointment. This histogram only shows the change in the backlog, not the magnitude of the backlog. The bed capacity of these hospitals spans almost an order of magnitude. The histogram for patient satisfaction shows two of the 16 hospitals (12.5%) with relatively high ratings.

Figure 9.7 Histograms for State and VISN shows the geographic distribution of the 16 medical centers by state and VISN.

Since the research question focuses on the change in appointment backlogs from 2015 to 2016, we next visualize the relationships between Backlog Difference and other variables in the data set. We begin by looking at Backlog Difference by City.State (our shortened identifier for the medical center name) using a horizontal needle chart. To create this graph select Graph > Chart and complete the dialog as shown in Figure 9.8 Dialog to Create a Horizontal Needle Chart

The resulting horizontal needle chart is shown in Figure 9.9 Horizontal Needle Chart: Backlog Difference by City.State.

A vertical point chart is a good way to visualize the relationship between Backlog Difference and State. In the Chart dialog, highlight Backlog Difference and in the Statistics drop-down choose Data, enter State into the Categories, X, Levels field, and for the Options choose Vertical and Point Chart. The result is shown in Figure 9.10 Vertical Point Chart: Backlog Difference by State. A reference line on the y-axis has been added by right clicking anywhere over the y-axis scale and select Axis Settings. Add the value 0 to the Reference Lines dialog. The vertical point chart is shown in Figure 9.10 Vertical Point Chart: Backlog Difference by State.

This chart shows the variability of the change in backlog by state. The Chart platform is useful for plotting a continuous variable by a nominal or ordinal variable.

Overlay graphs are appropriate for visualizing the relationship between two continuous variables. Select Graph > Overlay and enter Beds in the X field and Backlog Difference in the Y field. The X-Y plot is shown in Figure 9.11 Overlay Plot: Backlog Difference by Beds.

This X-Y plot shows no apparent relationship between bed capacity and backlog difference.

Other bivariate relationships can be explored using the Chart or Overlay Plot options from the Graph platform.

A bubble plot is an effective multivariate data visualization. Bubble plots allow up to five variables to be visualized simultaneously with variables plotted on the x- and y-axes, bubble size and color can represent two more variables, and animation allows a fifth variable to be included. Animation is useful for time dependent variables.

Bubble plots can be created from the JMP Graph menu. Figure 9.12 Bubble Plot Dialog shows the completed dialog needed to create a bubble plot with four variables from the VHA data table. The change in backlog is shown on the y-axis and the hospital location (city and state) appears on the x-axis. The size of the bubbles indicates the magnitude of the backlog in May 2016 and the color scale represents the size of the hospital as measured by the number of in-patient beds.

The rendered bubble plot is shown in Figure 9.13 Bubble Plot for VHA Appointment Backlogs.

The plot can be enhanced by adding a reference line at 0 on the y-axis to clearly delineate those hospitals whose backlog has increased and those whose backlog has decreased. This can be done by right clicking over any of the numbers on the y-axis scale and selecting Axis Settings. Type 0 into the Value field in the Reference Lines portion of the dialog and click Add. Note that a preview of the reference line appears to the right. The bubble plot with the added reference line is shown in Figure 9.14 Bubble Plot for VHA Appointment Backlogs with Reference Line.

In this plot we see that the Fayetteville, NC facility has experienced a considerable reduction in backlog and that in 2016 it has a relatively small backlog of appointments over 31-60 days. Fayetteville has one of the smallest in-patient capacities. Six of the larger facilities appear to have had small changes in their backlogs relative to 2015. These facilities are generally, although not exclusively, larger sized facilities. Not surprisingly, large backlogs in 2016 are associated with increases in backlog over the previous year as shown by the larger circles at the top of the bubble plot.

Figure 9.15 Bubble Plot Showing Bed Capacity and Patient Satisfaction shows another view of the data by changing the size of the bubbles to indicate bed capacity and the color scale to indicate patient satisfaction ratings.

In this visualization we see that while the Fayetteville, NC facility appears to have improved their backlog performance over the year, it has one of the lowest patient satisfaction ratings. The two red-shaded bubbles are the hospitals with the highest patient satisfaction but had large increases in their backlog.

Presenting the 2016 backlog levels on a map allows the reader to interpret the data in geographic context. This can be done with the JMP Graph Builder. Drag Longitude to the X drop zone and Latitude to the Y drop zone. Select the Points button on the control panel. Right click over any one of the points and choose Graph > Background Map. Complete the Set Background Map dialog as shown in Figure 9.16 Set Background Map Dialog.

This will show US state borders on the map. Drag Beds to the Color drop zone and Appts May 1 2016 31-60 days to the Size drop zone. The dots over the location of each VA medical center will be sized to the magnitude of the backlog and the color scale will indicate the hospital’s bed capacity. The map is shown in Figure 9.16 Set Background Map Dialog.

An additional variable can be visualized by dragging it to the Overlay drop zone. This additional variable will be rendered using symbols.