DATA607 HW01 Comparison Study of Graphical Displays of Data

Introduction

This report examines four graphical displays of data in order to apply the principles of statistical graphics discussed by Cleveland and McGill (1987) and by Gelman and Unwin (2013). Two of the figures below are effective displays that make an honestly difficult or unfamiliar topic accessible to a general audience, while the other two are ineffective or actively misleading displays. For each figure I have described the source and context of the graphic and explained the specific features that make it effective or ineffective, drawing on Cleveland and McGill’s ranking of elementary perceptual codes and on Gelman and Unwin’s distinction between the discovery and communication goals of a graphic.

Effective Example 1: The White House’s 2016 Interactive Budget Treemap

Source: Obama White House Archives

The first effective example is an interactive treemap titled “President Obama’s 2016 Budget Interactive,” published by the White House Office of Management and Budget in 2015 and preserved today in the Obama White House digital archives. The visualization lets a user click into any area of the proposed federal budget to see the dollar amount and description attached to that program, then zoom back out, and it offers a choice of other tiling data to explore more about. This graphic is also featured in Tableau’s own published collection of notable data visualization examples, which is where I first encountered it.

What makes this treemap effective is less about pure perceptual accuracy and more about the communication goal which is, taking a topic that is notoriously opaque to ordinary citizens i.e., the federal budget, and making it something a person can actually explore and understand in a few clicks. The drill-down interaction lets a reader move from an overview of the whole budget down to a specific program area, which mirrors the kind of guided exploration that Gelman and Unwin argue, is often missing from static infographics. It is worth noting, though, that a treemap encodes the size of each budget category using the area of a rectangle, which Cleveland and McGill rank well below position along a common scale or simple bar length in terms of how accurately readers judge it. A sorted bar chart of the same budget categories would, technically, let a reader compare two program sizes more precisely. That tradeoff does not make the treemap a failure; it simply means its effectiveness rests more on accessibility and engagement than on maximizing perceptual accuracy.

Effective Example 2: “Europe’s Top Economies in 2026 by Projected GDP”

Source: Europe’s Top Economies in 2026 by GDP

The second effective example is a radial, ring-segmented graphic titled “Ranked: Europe’s Top Economies in 2026 by Projected GDP,” published by Visual Capitalist on November 5, 2025, with design credited to Amy Kuo and text to Pallavi Rao, and sourced to the International Monetary Fund’s World Economic Outlook database. Countries are grouped into four regions, Northern, Eastern, Southern, and Western Europe, and within each region every country is sized according to its projected 2026 GDP, with a small central map highlighting geographically, the regions. This graphic also appears in a “best data visualizations” roundup published by the design platform Visme, which is where I found it.

This chart succeeds at conveying, at a glance, both the overall scale of Europe’s economy and the fact that economic output is concentrated in a handful of countries and regions, satisfying the discovery goal that Gelman and Unwin describe of giving a reader a qualitative sense of a dataset’s shape. The color coding by region and the small locator map also help orient a reader who may not already know which countries belong to which part of Europe. As with the treemap above, it is worth briefly noting that the radial, segmented layout encodes each country’s GDP using the angle and area of its wedge rather than position along a single scale, which places it below a plain sorted bar chart on Cleveland and McGill’s accuracy ranking. It also makes it somewhat harder to compare two similarly sized countries. Given that the piece is explicitly framed as a ranking, this is a real tradeoff, though the chart still succeeds admirably at its evident goal of making a 41 country comparison visually inviting rather than a dense table.

Ineffective Example 1: The Reuters “Gun Deaths in Florida” Chart

Source: Florida Gun Deaths

The first ineffective example is a chart titled “Gun Deaths in Florida,” created by Reuters graphic designer C. Chan and published in February 2014 alongside a Reuters article on Florida’s “Stand Your Ground” law. This is a very popular graphic which I even studied in my earlier course of DATA602 - Principles of Data Science. The chart plots the number of murders committed with firearms in Florida from the 1990s through the early 2010s, with a line that starts at 873 deaths, rises, dips sharply after a callout marking the law’s 2005 enactment, and ends at 721 deaths. Critically, the vertical axis is inverted, running from 0 at the top of the chart down to 1,000 at the bottom, a detail documented in a widely circulated writeup on the sociology blog Sociological Images (Wade, reposted 2014) and corroborated by Live Science’s own reporting on the incident.

This inverted axis reverses the ordinary reading of the chart because the line’s downward path on the page actually corresponds to a rising death count, the chart visually implies that gun deaths fell after 2005, when the Florida Department of Law Enforcement data cited on the chart shows they rose substantially. The *Live Science” article cited above even mentioned that the Chan did not appear to intend to mislead, and instead had reused the inverted layout of an unrelated chart depicting Iraq War (as per her tweet) deaths without reconsidering what direction “up” would communicate in this new context. In Cleveland and McGill’s terms, this chart violates the single assumption underlying position along a common scale, namely that increasing position must correspond to increasing value throughout the entire graphic; once that convention is broken, the chart becomes actively misleading regardless of the underlying data’s accuracy and the designer’s personal choice, since readers bring an unstated expectation of standard axis orientation to any chart they read.

Ineffective Example 2: “Our Pool Is Bigger Than Skyscrapers”

Source: Trump’s Statement

The second ineffective example is a bar-style chart titled “Our Pool Is Bigger Than Skyscrapers,” displayed as a physical poster during an Oval Office event on June 3, 2026, celebrating the renovation of the Lincoln Memorial Reflecting Pool. The chart shows four bars, one labeled 2,030 feet for the Reflecting Pool and three others labeled with the heights of the Willis Tower, the Empire State Building, and One World Trade Center, all measured against a shared vertical axis. Coverage of the event by MS NOW noted that the comparison struck several commentators as bizarre, and a subsequent fact check by MEAWW confirmed that the pool’s length figure is roughly accurate against official National Park Service renovation records, while also noting that the chart’s own vertical axis is inconsistently scaled, with the visual distance between 0 and 1,000 feet equal to the distance between 1,000 and 1,500 feet.

This chart is ineffective for several major reasons. First, it compares two fundamentally different kinds of measurement as though they were the same quantity which is, the figure for the Reflecting Pool is a horizontal length, while the figures for the three buildings are vertical heights, a category error that borrows the visual attribute of a legitimate height comparison without the underlying comparison actually being valid. Second, even among the three buildings, the heights are not measured on a consistent basis like, One World Trade Center’s figure of 1,776 feet includes its full spire and antenna, while the Empire State Building’s figure of 1,454 feet reflects only its roof, excluding the antenna that sits atop it. Comparing a spire-inclusive figure to a roof-only figure for two different buildings is itself an inconsistency. Third, and most consequential for a casual reader, the fact-check cited above found that the chart’s vertical axis does not scale consistently, with the visual distance between 0 and 1,000 feet equal to the distance between 1,000 and 1,500 feet. Because the Reflecting Pool’s bar extends well past the 2,000 foot gridline on this distorted scale, its length appears considerably greater than the labeled 2,030 feet, and a reader relying on the bar’s visual proportions rather than its printed label could easily estimate the pool at closer to 2,500 feet.

Final Notes

Taken together, these four examples show that “effective” is not a single fixed standard. The White House treemap and the Visual Capitalist GDP graphic both succeed primarily by satisfying Gelman and Unwin’s communication and discovery goals, making complex or unfamiliar topics approachable and engaging, even though both rely on area or angle encodings that Cleveland and McGill’s own ranking would place below a plain bar chart in terms of raw perceptual accuracy. That tradeoff is worth naming rather than ignoring, though it does not undo the real value either graphic provides. The Reuters gun-deaths chart and the Trump pool-versus-skyscrapers chart, by contrast, each violate a convention that readers rely on without being told, whether that convention is that a chart’s axis runs in a consistent, expected direction, or that a bar’s length always represents the same kind of quantity as every other bar’s length in the same chart. In both of these cases, the visual impression a casual reader takes away actively contradicts the underlying data.

References

Chan, C. (2014, February). Gun deaths in Florida Reuters.

Cleveland, W. S., and McGill, R. (1987). Graphical perception: The visual decoding of quantitative information on graphical displays of data. Journal of the Royal Statistical Society, Series A, 150(3), 192-229.

Gelman, A., and Unwin, A. (2013). Infovis and statistical graphics: Different goals, different looks. Journal of Computational and Graphical Statistics, 22(1), 2-28.

Kuo, A. (designer), and Rao, P. (2025, November 5). Ranked: Europe’s top economies in 2026 by projected GDP. Visual Capitalist. Retrieved from https://www.visualcapitalist.com/ranked-europes-top-economies-in-2026-by-projected-gdp/

MEAWW. (2026, June). Fact check: Is the chart shown by Trump comparing the reflecting pool to US skyscrapers accurate? Retrieved from https://news.meaww.com/fact-check-is-the-chart-shown-by-trump-comparing-the-reflecting-pool-to-us-skyscrapers-accurate

MS NOW. (2026, June 5). Trump’s bizarre chart touting reflecting pool size dismays Nicolle Wallace. Retrieved from https://www.ms.now/news/trump-lincoln-memorial-reflecting-pool-length-brags-nicolle-wallace

Reddit: r/dataisugly. (n.d.). It gets worse the longer you look [Online forum post]. Reddit. Retrieved September 14, 2026, from https://www.reddit.com/r/dataisugly/comments/1tp5q5x/

Reddit: r/dataisugly. (n.d.). The audacity of just putting the graph upside down is incredible [Online forum post]. Reddit. Retrieved September 14, 2026, from https://www.reddit.com/r/dataisugly/comments/1fiaxkn/

Tableau. (n.d.). Data visualization examples. Retrieved September 14, 2026, from https://www.tableau.com/visualization/data-visualization-examples

Visme. (n.d.). Best data visualization examples. Retrieved September 14, 2026, from https://visme.co/blog/best-data-visualizations/

Wade, L. (2014, December 28). How to lie with statistics: Stand your ground and gun deaths. Sociological Images, The Society Pages. Retrieved from https://thesocietypages.org/socimages/2014/12/28/how-to-lie-with-statistics-stand-your-ground-and-gun-deaths/

White House Office of Management and Budget. (2015). President Obama’s 2016 budget interactive [Interactive graphic]. Obama White House Archives. Retrieved from https://obamawhitehouse.archives.gov/node/320071

livescience.com. (2014, April 23). Misleading gun-death chart draws fire. Retrieved from https://www.livescience.com/45083-misleading-gun-death-chart.html