bar charts

Communicating data effectively with data visualizations - Part 6 (Tornado diagram)

BACKGROUND

Suppose you had some results and you were interested in whether or not these findings were sensitive to change. You can illustrate these effects using a tornado diagram, which uses bar charts to compare the change from the original findings. In other words, tornado diagrams are useful to illustrate a sensitivity analysis.

In this tutorial, we will provide you with a step-by-step guide on how to graph a tornado diagram from a sensitivity analysis.

 

MOTIVATING EXAMPLE

Imagine that you are planning a vacation, and you allocated $6,000 for the trip. You perform some cost estimates and find a vacation package that costs $5,050, which is within your budget. But then you see some deals and some extra luxuries that you want to add to your current vacation package. Some of these will change the cost of your original cost estimates. In order to see which of these additional deals or luxuries would impact your cost estimates, you decide to perform a one-way sensitivity analysis. That is, you change the cost of one variable at a time to see how it effects your original cost estimates (e.g., base-case).

Table 1 summarizes your base-case vacation costs and the possible changes due to the additions of deals and luxuries.

Table 1.png

The “Low input” or “deals” reduce the total cost of your vacation. The “High input” or luxuries increase the cost of your vacation.

You want to visualize if any of these adjustments will change your original cost estimates (e.g., $5,050).

 

BUILDING A TORNADO DIAGRAM

A tornado diagram can be used to visualize these additional changes to the variables.

Step 1: Open Excel and insert a clustered bar chart

Figure 1.png

Step 2: Enter date for the “Low input”

Right-click on the empty chart area and select “Name” and enter “Low input.” Then in the “Y values:” box, select all the values in the “Low result” column of your table. In the Horizontal (Category) axis labels:” highlight the variable names under the “Base-case results” column. The figure below illustrates the correct selections for each input box.

Figure 2.png

Step 3: Enter data for the “High input”

Repeat same steps for the “High input” data range.

Figure 3.png

Step 4: Center the axis at the estimated cost

Right-click on the X-axis and go to the Format Axis > Vertical Axis Crosses > Axis Value and enter “5050.” This will center the axis at the estimated cost of $5,050.

Figure 4.png

Step 5: Move the variable names to the left side of the plot

After centering the axis on the estimate cost of $5,050, you can start to see the beginnings of a tornado diagram. However, the variable names are in the way. To relocate these, Right-click on the Y-axis and select the Axis Options > Interval Between Labels and select “Low.” This will move the variable names to the left side so that it doesn’t interfere with the bars in the middle of the chart.

Figure 5.png

Step 6: Align the bars so that they are next to each other

The bars are not aligned with each other. You can align them using the series overlap option. Right-click on one of the bars and go to Series Options > Plot Series On and enter 100 on the “Series Overlap” widget. After you press Enter, the bars should be aligned with each other.

Figure 6.png

Step 7: Sort and change fonts

To complete the tornado diagram, you can sort the bars so that the largest change is at the top and the smallest change is at the bottom (looks like a tornado). Right-click on the Y-axis and got to Format Axis > Axis Options > Axis Position and check the box “Categories in reverse order.” This will order your diagram to look more like a tornado.

Figure 7.png

Step 8: Final changes and edits

The last steps improve the aesthetics. Changing the fonts and colors can improve the tornado diagram.

Figure 8.png

CONCLUSIONS

The tornado diagram tells us that paying for an additional “luxury” for the cost of the flight will exceed our budget of $6,000 (indicated by dotted red line). As a result, we will not spend extra capital to upgrade our seats! However, we can splurge a little when it comes to other elements of our trip (e.g., expensive meals, luxury vehicle rental, or additional excursions).

 

REFERENCES

I used the following guide developed by Excel Champs to develop this this blog.

 

Communicating data effectively with data visualizations - Part 1 (Principles of Data Viz)

Introduction

Data visualization is a form of visual communication that takes quantitative information and displays it as a graphic, an abstraction of the real world. Effective data communication makes complex statistical analysis accessible without excessive mental burden. It is also used to identify patterns through data exploration. Unlike information visualization which includes catch-phrases such as “Infoviz” and “Infographics,” data visualization is intuitive, informative, and “pretty” while simultaneously focused on scientifically structured comparisons, analytic precision, and statistical inference. The challenge is compressing all the quantitative information into a single chart or graphic that provides a narrative or purpose that can be synthesized and acted on with very little mental effort.

There are a variety of data visualizations that can be used such as choropleths, heatmaps, scatter plots, and dot plots (this list is not all inclusive). The selection is dependent on the data, audience, and narrative. How complex is the analysis? Who are you presenting this information to? Why should the audience care?

The best way to present data effectively is with a good story. Your graphic should be able to tell a story based on the quantitative information. Every graphic you create should be a self-contained narrative of the data. This can be achieved using simple tools, but the creation of effective data visualization depends more on your ability to tell a good story. The purpose of this article is to highlight some important principles of data visualization, review common data visualizations, and develop a mechanism to select the most effective data visualization.

Principles of data visualization

Data visualization can be traced to several different schools of thought (e.g., Edward Tufte and William S. Cleveland), but the fundamental principles are similar and often overlap. Edward Tufte identified several key principles when developing data visualizations (Table 1).

Table 1. Tufte's principles for graphical integrity. *

Principle**

Description

Avoid chart junk

Inventive displays seldom generate interest. Rather, they generate visual noise.

 

Data-ink ratio

Use ink to show the data. Ink that does not contribute to the reporting of the data should be removed.

 

Numbers should be directly proportional to the numerical quantities represented

The "Lie Factor" is a proportion of the Size of the effect shown in the graphing / Size of the effect in the data. The graphic should not inflate the actual magnitude of the change.

 

Use small multiples and repeat

High quality information graphic portrays many numbers per square inch. Small multiple, comparative images work especially well for this. Examples include sparklines.

 

Avoid graphical distortions and ambiguity

Avoid distortions of numbers by graphic devices. Show data variation in context, and label them. Write out explanation of the data on the graphic itself. Properly label events in the data.

 

Multifunction

Information layers and architecture emerge best when data display elements serve multiple functions. Different readings at different levels of detail (micro-macro) serve this goal well. For example, the y-axis can be used to provide scale while calling out to important values by either coloring that value differently or enlarging it.

 

Show data variation, not design variation

Use scales that are similar and do not generate ambiguity. Be consistent in the data when displaying them as a graphic.

 

In time-series displays of money, deflated and standardized units of monetary measurement are nearly always better than nominal units

Properly adjust current due to inflation or population growth. We want to the currency in real purchasing power (value) rather than nominal purchasing power.

 

The number of information-carrying (variable) dimensions depicted should not exceed the number of dimensions in the data

Using graphics to show the proportional change of a metric can bias our perception due to the number of dimensions that are changing. If we look at a single metric such as budget, then we are only looking at a one-dimensional scale, meaning that when the budget increase, it only changes in one dimension. However, it is easy to use a display such as a 2-dimensional picture and scale it up according to the one-dimensional scale. For example, if we have a 2-dimensional graphic and we scale it according to an increase on a one-dimensional metric, the actual proportional increase in 4 times (2^2 = 4). If this was a 3-dimensional object, then the proportional increase in 8 (2^3 = 8).

 

Graphics must not quote data out of context

An accurate picture must report the totality of the effect. Showing only one piece of the data with graphics is just as bad as the data. Context is critical. In time-series analysis, it is imperative that the researcher provides an illustration of the overall trend including any changes in seasonality. Therefore, apply rational judgement when presenting data visualization. The use of comparison groups helps to answer any secular impacts that may not be captured when looking at data at a single point in time.

 

* From Tufte ER. (2001) The Visual Display of Quantitative Information. Second Edition. Cheshire, CT. Graphics Press, LLC.

** This table provides fundamental principles on graphical integrity and data graphics and is not all inclusive.

Figure 1. Box plots of MLB wins in the 2017 season. [click to enlarge]

Dot plots are simple graphics that use points (filled in circles) instead of line or bars on a simple scale. They convey the same information as bar charts, but use less ink to do so. The advantage they provide is that they reduce the junk of the bar charts which contain useless space that are uninformative. In Figure 2a, the dot plot provides the same information from the previous bar charts; however, there is a better sense of scale with the removal of the clutter introduced by the bar charts. Like the bar charts, use pastel colors to dampen the effect of the teams that are not the focus of the chart and use solid colors to bring out the teams with the most and least wins (Figure 2b). The minor grid lines do not provide any information about the data and should be removed (Figure 2c). Finally, Figure 2d takes the dot plots and use data values to provide the audience with the actual number of wins. This is also reinforced by the pastel and solid colors, which provide good contrast between the teams that have the most and least wins.

Figure 2. Dot plots of MLB wins in the 2017 season. [click to enlarge]

Line plots are graphics that use lines to illustrate a trend. A line plot would not be appropriate for the baseball wins example because the x-axis does not have any continuous scale, which is needed for line plots. Table 2 provides data on MLB players’ batting averages from 2013 to 2017. The table provides us with information across five years, but the order and rankings are difficult to determine.

Table 2. Batting averages of Major League Baseball players (2013-2017).

Players

2013

2014

2015

2016

2017

Yasiel Puig

0.319

0.296

0.255

0.263

0.260

Justin Turner

0.280

0.340

0.294

0.275

0.332

Michael Trout

0.323

0.287

0.299

0.315

0.329

Ichiro Suzuki

0.262

0.284

0.229

0.291

0.250

The table doesn’t do a good job illustrating the trends over time. Instead, it is a good reference that is searchable. When it comes to visually telling a story, the table doesn’t do a good job. Converting this table to several line plots can help illustrate the changes in each players’ batting averages over time. Figure 3a trends each player’s batting averages, but the clutter makes it difficult to identify any important patterns. For graphics that use a time interval (or continuous interval) on the x-axis, it is useful to truncate the y-axis to see any incremental changes in the trend.

Figure 3b truncates the batting average from 0 to 0.360 to 0.200 to 0.360. Now the changes in batting average is more discernable from this truncated y-axis. It’s clear that Yasiel Puig’s batting average declined from 2013, but Justin Turner’s batting average improved. However, this still feels cluttered. The different lines and colors make it hard tell that Justin Turner was improving. In fact, it seems like all the players except for Yasiel Puig were improving. To make sense of the clutter, let’s assume that we were interested in the player who had the most improvement from 2013. Calculating the percent change between 2013 and 2017 and then putting it on the graphic provides us with some metric to distinguish Justin Turner from the rest of the other players.

Figure 3c adds the percent change in batting averages from 2013 to 2017 with the player’s name. The legend was removed because it didn’t contribute much to the graphic once the names were adjacent to each line. Despite these modifications, it’s not easy to distinguish the improvement in batting averages for Justin Turner. There are too many competing colors, which distract the focus from Justin Turner’s improvement.

Figure 3d dampens the non-critical lines using a single pastel color and matching the to the trend lines, which highlights Justin Turner’s trend line, the only one with color. This technique draws your attention to Justin Turner’s trend while providing details about the change in trend and the player associated with that change.

Figure 3. Line plots of MLB players’ batting averages (2013-2017). [click to enlarge]

Summary

So far, basic principles and examples of data visualization were presented in this article, which is part of an on-going series on data visualization. Since this is a primer on data visualizations, you should review existing graphics and try to apply some of these principles. Web-based data visualizations are prevalent and can be found in places such as the R-Shiny gallery and Tableau gallery. As you start to explore different data visualizations, you’ll discover many creative and useful tools. Next issue, we’ll discuss other data visualization graphics that will reflect the Tufte’s principles for graphical integrity and excellence.

References

Tufte ER. (2001) The Visual Display of Quantitative Information. Second Edition. Cheshire, CT. Graphics Press, LLC.

Knaflic CN. (2015) Storytelling with Data: A Data Visualization Guide for Business Professionals. Hoboken, New York. John Wiley & Sons, Inc.