Tufte’s Fundamental Principles of Analytical Design

Carte Figurative des pertes successives en hommes de l’Armée Française dans la campagne de Russie 1812–1813, (M.Minard, 1869)

In his 2006 offering, Edward Tufte highlights his Fundamental Principles of Analytical Design. In this article, I will showcase these principles and provide an illustrating example. (The contrast and comparison with the examples provided in Beautiful Evidence showcase the possible variations in interests and aesthetics).

Throughout, Tufte’s comments and insights are shown in block quotes; our own comments appear as regular text. Whenever possible, examples are sourced and linked to external sources, which may provide more context and detailed information.

Fundamental Principles of Analytical Design

Why do we display evidence in a report, in a newspaper article, online? What’s the fundamental reason or goal of our charts and graphs? Tufte suggests that we present evidence to assist our thinking processes (p. 137). In this regard, his principles are universal – a strong argument can be made that they are dependent neither on technology nor culture. Reasoning and communicating our thoughts are intertwined with our lives in a causal and dynamic multivariate Universe;1 whatever cognitive skills allow us to live and evolve can also be brought to bear on the presentation of evidence.

Tufte also highlights a particular symmetry to visual displays of evidence, that consumers should be seeking exactly what producers should be providing, namely

  • meaningful comparisons;
  • causal networks and underlying structure;
  • multivariate links;
  • integrated and relevant data;
  • honest documentation, and
  • primary focus on content.

Physical science displays tend to be less descriptive and verbal, more visual and quantitative; these trends tend to be reversed when dealing with evidence displays about human behaviour;2 in spite of this, Tufte argues that his principles of analytical design can also be applied to social science and medicine. To demonstrate the universality of his principles, Tufte describes in detail how they are applied in a visual display by Charles Joseph Minard (see figure below).

Carte Figurative des pertes successives en hommes de l'Armée Française dans la campagne de Russie 1812-1813, (M.Minard, 1869).
Carte Figurative des pertes successives en hommes de l’Armée Française dans la campagne de Russie 1812-1813, (M.Minard, 1869).

His lengthy analysis of the image is well worth the read (pp. 122-139) – it will not be repeated here (I must confess that the chart leaves me somewhat … unexcited).

Rather, I will illustrate the principles with the help of the following image from the Gapminder Foundation.

Life expectancy and income per capita in 2012, by nation (Gapminder Foundation).
Life expectancy and income per capita in 2012, by nation (Gapminder Foundation).

It is a bubble chart that plots the 2012 life expectancy, adjusted income per person in USD (log-scaled), population, and continental membership for 193 UN members and 5 other countries, using the latest available data (2011). A high-resolution version of the image can be found on the Gapminder website.


Comparisons

First Principle
Show comparisons, contrasts, differences. (p. 127)

The Fundamental analytical act in statistical reasoning is to answer the question “Compared with what?” Whether we are evaluating changes over space or time, searching big data bases, adjusting and controlling for variables, designing experiments, specifying multiple regressions, or doing just about any kind of evidence-based reasoning, the essential point is to make intelligent and appropriate comparisons [emphasis added]. Thus, visual displays […] should show comparisons. (p. 127)

Comparisons come in varied flavours: for instance, one could compare a

  • unit at a given time against the same unit at a later time;
  • unit’s component against another of its components;
  • unit against another unit,

or any number of combinations of these flavours. Not every comparison will turn out to be insightful, but avoiding comparisons altogether is equivalent to producing displays built from a single datum, and… well, what’s the point, then?


    Health and Wealth of Nations

    Where to begin? First, note that each bubble represents a different country, and that the location of each bubble’s centre is a precise point corresponding to the country’s life expectancy and its GDP per capita. The size of the bubble is correlated with the country’s population, while its colour is linked to continental membership.

    The chart’s compass provides a handy tool for comparison:

    • a bubble to the right (resp. the left) represents a wealthier (resp. poorer) country;
    • a bubble above (resp. below) represents a healthier (resp. sicker) country.

    For instance, a comparison between Japan, Germany and the USA shows that Japan is healthier than Germany, which is itself healthier than the USA (as determined by life expectancy), while the USA are wealthier than Germany, which is itself wealthier than Japan (as determined by GDP per capita) (see below).

    Comparison between Japan, Germany, and the USA, Health and Wealth of Nations, 2012.
    Comparison between Japan, Germany, and the USA, Health and Wealth of Nations, 2012.

    While there is no reason to expect that it should be the case, it is nevertheless possible for two countries to have roughly the same health and the same wealth: consider Indonesia and Fiji, or India and Tuvalu, for instance (see below). In each pair, the centres of both bubbles overlap: any difference in the data must be found in the bubbles’ area or their colour.

    Comparison between Indonesia and Fiji, and India and Tuvalu, Health and Wealth of Nations, 2012.
    Comparison between Indonesia and Fiji, and India and Tuvalu, Health and Wealth of Nations, 2012.

    Countries can also be compared against world values for life expectancy and GDP per capita (the comparisons for average continental membership or population are less obviously meaningful, in this case). The world’s mean life expectancy and income per person are traced in light blue. Wealthier, healthier, poorer, and sicker are relative terms, but we can also use them to classify the world’s nations with respect to these mean values.3

    Comparison of data points against life expectancy of the world, Health and Wealth of Nations, 2012.
    Comparison of data points against life expectancy of the world, Health and Wealth of Nations, 2012.

    Comparison of data points against GDP per capita of the world, Health and Wealth of Nations, 2012.
    Comparison of data points against GDP per capita of the world, Health and Wealth of Nations, 2012.

Causality, Mechanism, Structure, Explanation

Second Principle
Show causality, mechanism, explanation, systematic structure. (p. 128)

Yet often the reason that we examine evidence is to understand causality, mechanism, dynamics, process, or systematic structure [emphasis added]. Scientific research involves causal thinking, for Nature’s laws are causal laws. […] Reasoning about reforms and making decisions also demands causal logic. To produce the desired effects, we need to know about and govern the causes; thus “policy-thinking is and must be causality-thinking”.4 (p. 128)

Simply collecting data may provoke thoughts about cause and effect: measurements are inherently comparative, and comparisons promptly lead to reasoning about various sources of differences and variability. (p. 128)

In essence, this is the core principle behind data visualization: the display needs to explain something, it needs to provide links between cause and effect, it needs to tell a meaningful story.

If the visualization could be removed at a later stage without changing the underlying message, then that chart should not have been included in the first place, no matter how pretty and modern it looks, nor how costly it was to produce.


    Health and Wealth of Nations

    At a quick glance, the relation between the log of the income per person and life expectancy seems to be increasing roughly linearly. The exact parameter values are not known (and I cannot estimate them analytically as I do not have access to the data), but an approximate line-of-best-fit has been added to the figure below. Charts with this form have been found in other disciplines before.

    Linear relationship in the Health and Wealth of Nations, 2012.
    Linear relationship in the Health and Wealth of Nations, 2012.


    The four quadrants created by the world’s life expectancy and its GDP per capita are not all created equal: naively, we might have expected that each of the quadrants would contain about 25% of the world’s countries (although the large population size of giants like China and India muddle the picture somewhat), however, there is one quadrant which is substantially under-represented (see below). Is it surprising that there should be so few “wealthier” and “sicker” countries? Could it be argued that Russia and Kazakhstan are too near to the separators to really be considered clear-cut members of the quadrant?

    The wealthier and sicker quadrant, Health and Wealth of Nations, 2012.
    The wealthier and sicker quadrant, Health and Wealth of Nations, 2012.


    In the same vein, when we consider the data visualization as a whole, there seems to be one group of outliers below the main trend, to the right (and possibly one group above the main trend, to the left) which cries out for an explanation: South Africa, for instance, has a relatively high GDP per capita but a low life expectancy (potentially, income disparity between a poor majority and a substantially richer minority might help push the dot to the right, while the lower life expectancy of the majority drives the overall life expectancy to the bottom). Could wars, famines, recessions, and epidemics be recovered from the movement of the bubbles over multiple years?

    Outliers in the Health and Wealth of Nations, 2012.
    Outliers in the Health and Wealth of Nations, 2012.

Multivariate Analysis

Third Principle
Show multivariate data; that is, show more than 1 or 2 variables. (p. 130)

Nearly all the interesting worlds (physical, biological, imaginary, human) we seek to understand are inevitably multivariate in nature. (p. 129)

The analysis of cause and effect, initially bivariate, quickly becomes multivariate through such necessary elaborations as the conditions under which the causal relation holds, interaction effects, multiple causes, multiple effects, causal sequences, sources of bias, spurious correlation, sources of measurement error, competing variables, and whether the alleged cause is merely a proxy or a marker variable.5 p. 129)

Reasoning about evidence should not be stuck in 2 dimensions, for the world we seek to understand is profoundly multivariate [emphasis added]. (p. 130)

Alert readers may question the ultimate validity of this principle: after all, doesn’t Occam’s Razor warn us that “it is futile to do with more things that which can be done with fewer”?6 Seen in the right light, that seems like a fairly strong admonition to stay away from multivariate analysis.

This interpretation depends, of course, on what it means to “do with fewer”: are we attempting to “do with fewer“, or to “do with fewer”?. If it’s the former, then we can produce any number of univariate and bivariate charts to represent the data (which in itself starts to border on a multivariate display, although the number of such charts can balloon quite quickly), but any significant link between 3 and more variables is unlikely to be shown, which drastically reduces the explanatory power of the charts. If it’s the latter, the difficulty evaporates: we simply retain as much features as necessary to maintain the desired explanatory power.


    Health and Wealth of Nations

    Only 4 variables are represented in the display, which we could argue just barely qualifies the data as multivariate. The population size seems uncorrelated with both of the axes’ variates, unlike continental membership: there is a clear divide between the West, most of Asia, and Africa (see below). This “clustering” of the world’s nations certainly fits with common wisdom about the state of the planet, which provides some level of validation for the display.

    Clusters in the Health and Wealth of Nations, 2012.
    Clusters in the Health and Wealth of Nations, 2012.

    Other variables could also be considered or added, notably the year, allowing for bubble movement: one would expect that life expectancy and GDP per capita have both been increasing over time. The Gapminder Foundation’s online tool can build bubble charts with other variates, leading to interesting inferences and conclusions.


Integration of Evidence

Fourth Principle
Completely integrate words, numbers, images, diagrams. (p. 131)

The evidence doesn’t care what it is – whether word, number, image. In reasoning about substantive problems, what matters entirely is the evidence, not particular modes of evidence [emphasis added]. (p. 130)

Words, numbers, pictures, diagrams, graphics, charts, tables belong together [emphasis added]. Excellent maps, which are the heart and soul of good practices in analytical graphics, routinely integrate words, numbers, line-art, grids, measurement scales. (p. 131)

Tables of data might be thought of as paragraphs of numbers, tightly integrated with the text for convenience of reading rather than segregated at the back of a report. […] Images and tables used in public presentations should be annotated with words explaining what is going on. In exploratory data analysis, however, the integration of data needs to be thought through. Perhaps the number of data points may stand alone for a while, so we can get a clean look at the data, although techniques of layering and separation may simultaneously allow a clean look as well as bringing other information into the scene. (p. 131)

When authors and researchers select a single specific method or mode of information during the inquiries, the focus switches from “can we explain what’s happening?” to “can the method we selected explain what’s happening?”. There is an art to selecting methods, and experience and expertise can often suggest relevant methods, but “when all one has is a hammer, everything looks like a nail”, as the saying goes: the goal should be to use whatever (and all) evidence is necessary to explain “what’s happening”. If that goal is met, it makes no difference which modes of evidence were used.


    Health and Wealth of Nations

    The various details attached to the chart (such as country names, font sizes, axes scale, grid, and world landmarks) provide substantial benefits when it comes to consuming the display. They may become lost in the background, with the effect that they are taken for granted. Compare the display obtained from (nearly) the same data, but without integration of evidence (see below).

    Health and Wealth of Nations, 2012, without integration of evidence.
    Health and Wealth of Nations, 2012, without integration of evidence.

    Not nearly as compelling, eh? What’s missing?


Documentation

Fifth Principle
Thoroughly describe the evidence. Provide a detailed title, indicate the authors and sponsors, document the data sources, show complete measurement scales, point out relevant issues. (p. 133)

The credibility of an evidence presentation depends significantly on the quality and integrity of the authors and their data sources. Documentation is an essential mechanism of quality control for displays of evidence. Thus authors must be named, sponsors revealed, their interests and agenda unveiled, sources described, scales labeled, details enumerated [emphasis added]. (p. 132)

Depending on the context, questions and items to address could include:

  • What is the title/subject of the visualization?
  • Who did the analysis?
  • Who created the visualization? (if distinct from analyst(s))
  • When was the visualization published?
  • Which version of the visualization is rendered here?
  • Where did the underlying data come from?
  • Who sponsored the display?
  • What assumptions were made during data processing and clean-up?
  • What colour schemes, legends, scales are in use in the chart?

It’s not obvious whether all this information can fit inside a single chart in some cases. But, keeping in mind the Principle of Integration of Evidence, charts should not be presented in isolation in the first place, and some of the relevant information can be provided in the text, on the webpage, or in an accompanying document. This is especially important when it comes to discussing the methodological assumptions used for data collection, processing, and analysis. An honest assessment may require sizable amounts of text, and it may not be reasonable to include that information with the display (in that case, a link to the accompanying documentation should be provided).

Publicly attributed authorship indicates to readers that someone is taking responsibility for the analysis; conversely, the absence of names signals an evasion of responsibility. […] People do things, not agencies, bureaus, departments, divisions [emphasis added]. (pp. 132-133)


    Health and Wealth of Nations
    • What is the title/subject of the visualization?
    • The health and wealth of nations in 2012, using the latest available data (2011).

    • Who did the analysis? Who sponsored the display? Who created the visualization?
    • The analysis was done by the Gapminder Foundation; the map layout was created by Paulo Fausone. No data regarding the sponsor is found on the chart or in the documentation. The relevant Wikipedia article states that “the Gapminder Foundation is a non-profit venture registered in Stockholm, Sweden, that promotes sustainable global development and achievement of the United Nations Millennium Development Goals by increased use and understanding of statistics and other information about social, economic and environmental development at local, national and global levels.” It seems plausible that there is no external sponsor, but that is no certainty.

    • When was the visualization published? Which version of the visualization is rendered here?
    • The 11th version of this chart was published in September 2012. It is the latest available version as of October 2016.

    • Where did the underlying data come from? What assumptions were made during data processing and clean-up?
    • Typically, the work that goes into preparing the data is swept under the carpet in favour of the visualization itself; there are no explicit source of data on this chart, for instance. However, there is a URL in the legend box that leads to detailed information.
      gap42For most countries, life expectancy data was collected from the Human Mortality database, the UN Population Division World Population Prospects, files from historian James C. Riley, the Human Life Table database, data from diverse national statistical agencies, the CIA World Fact book, the World Bank, and the South Sudan National Bureau of Statistics.

      Benchmark 2005 GDP data was derived via regression analysis from International Comparison Program data for 144 countries, and extended to other jurisdictions using another regression against data from the UN Statistical Division, Maddison Online, the CIA World Fact book, and estimates from the World Bank. The 2012 values were then derived from the 2005 benchmarks using long-term growth rates estimate from Maddison Online, Barro & Ursua, the United Nations Statistical Division, the Penn World Table (mark 6.2), the International Monetary Fund’s World Economic Outlook database, the World Development Indicators, Eurostat, and national statistical offices or some other specific publications.
      Population estimates were collated from the United Nations Population Division World Population Prospects, Maddison Online, Mitchell’s International Historical Statistics, the United Nations Statistical Division, the US Census Bureau, national sources, undocumented sources, and “guesstimates”. Exact figures for countries with a population below 3 million inhabitants were not needed as this marked the lower end of the chart resolution.

    • What colour schemes, legends, scales are in use in the chart?
    • The Legend Inset is fairly comprehensive:

      Legend, Health and Wealth of Nations, 2012.
      Legend, Health and Wealth of Nations, 2012.

      Perhaps the last item of note is that the scale of the axes differs: life expectancy is measured linearly, whereas GDP per capita is measured on a logarithmic scale.


    Content Counts Most of All

    Sixth Principle
    Analytical presentations ultimately stand of fall depending on the quality, relevance, and integrity of their content. (p. 136)

    The most effective way to improve a presentation is to get better content [emphasis added] […] design devices and gimmicks cannot salvage failed content. (p. 136)

    The first questions in constructing analytical displays are not “How can this presentation use the color purple?” Not “How large must the logotype be?” Not “How can the presentation use the Interactive Virtual Cyberspace Protocol Display Technology?” Not decoration, not production technology. The first question is “What are the content-reasoning tasks that this display is supposed to help with?” (p. 136)

    A compelling narrative, which may not be the one that was initially expected to emerge from a solid analysis of sound data, is the name of the game. Simply speaking, the visual display should assist in explaining the situation at hand and at answering the original questions.


      Health and Wealth of Nations

      How would we answer the following questions:

      • Do we observe similar patterns every year?
      • Does the shape of the relationship between life expectancy and log-GDP per capita vary continuously over time?
      • Do countries ever migrate large distances in the display over short periods?
      • Do exceptional events affect all countries similarly?
      • What are the effects of secession or annexation?

      The 2012 Health and Wealth of Nations data represent a single datum in the general space of data visualizations; better content means getting data for more than just 2012.

      Health and Wealth of Nations, 2013.
      Health and Wealth of Nations, 2013.

About Dr. Idlewyld 8 Articles
As a youth, Dr. Idlewyld used to read everything he could lay his hands on and he was in a band. For years, he believed that the NHL would have come calling if he hadn't broken his leg as a kid in a hilarious skiing mishap. Nowadays, whatever's left of his hair is slowly turning grey, and that can only mean one thing: he's had the chance to work on plenty of quantitative projects, providing expertise in operations research methods, data science and predictive analytics, stochastic and statistical modeling, and simulations. So he's got that going for him, which is nice. He's not keen on buzzwords, but overall he's glad to see interest in analytical endeavours grow. In the final analysis, he thinks that insights and discoveries are within everyone's reach, and that he would have made a great goalie.