## What's a histogram?

##### Mar 12, 2024

Almost all graphing tools make histograms, and almost all dataviz books cover the subject. But I've always felt there are many unanswered questions. In my talk this Thursday in NYC, I'll provide some answers. You can reserve a spot here.

***

Here's the most generic histogram:

Even Excel can make this kind of histogram. Notice that we have counts in the y-axis. Is this really a useful chart?

I haven't found this type of histogram useful ever, since I don't do analyses in which I needed to know the exact count of something - when I analyze data, I'm generalizing from the observed sample to a larger group.

Speaking of Excel, I felt that the developers have always hated histograms. Why is it much harder to make histograms than other basic charts?

***

Another question. We often think of histograms as a crude approximation to a probability density function (PDF). An example of a PDF is the famous bell curve. Textbooks sometimes show the concept like this:

This is true of only some types of histograms (and not the one shown in the first section!) Instead, we often face the following situation:

This isn't a trick. The data in the histogram above were generated by sampling the pink bell curve.

***

If you've used histograms, you probably also have run into strange issues. I haven't found much materials out there to address these questions, and they have been lingering in my mind, hidden, for a long time.

My Thursday talk will hopefully fill in some of these gaps.

## My talk next week on histograms

##### Mar 08, 2024

Next Thursday (March 14), I'll be presenting at the Data Visualization New York Meetup, hosted by Naomi and Cameron. The event is in-person at Datadog's office. You can reserve your spot here.

This talk is brand new, based on some work inspired by a blog post by Andrew Gelman. One of Andrew's correspondents asked about a particular type of histogram. While exploring this topic, I filled some of my own gaps in knowledge about this deceptively simple chart form. I'll be sharing this story.

Bits and pieces have appeared before on my blog. See this, this, and this for background.

If you're attending the talk, come up and say hi.

## To a new year of pleasant surprises

##### Jan 01, 2024

Happy new year!

This year promises to be the year of AI. Already last year, we pretty much couldn't lift an eyebrow without someone making an AI claim. This year will be even noisier. Visual Capitalist acknowledged this by making the noisiest map of 2023:

I kept thinking they have a geography teacher on the team, who really, really wants to give us a lesson of where each country is on the world map.

All our attention is drawn to the guiding lines and the random scatter of numbers. We have to squint to find the country names. All this noise drowns out the attempt to make sense of the data, namely, the inset of the top 10 countries in the lower left corner, and the classification of countries into five colored groups.

A small dose of editing helps. Remove most data labels except for the countries for which they have a story. Provide a data table below for those who want details.

***

In the Methodology section, the data analysts (possibly from a third party called ElectronicsHub) indicated that they used Google search volume of "over 90 of the most popular generative AI tools", calculating the "overall volume across all tools per 100k population". Then came a baffling line: "all search volumes were scaled up according to the search engine market share in each country, using figures from statscounter.com." (Note: in the following, I'm calling the data "AI-related search" for simplicity even though their measurement is restricted to the terms described above.)

It took me a while to comprehend what they could have meant by that line. I believe this is what that sentence means: Google is not the only search engine out there so by only researching Google search volume, they undercount the true search volume. How did they deal with the missing data problem? They "scaled up" so if Google is 80% of the search volume in a country, then they divide the Google volume by 80% to "scale up" to 100%.

Whenever we use heuristics like this, we should investigate its foundations. What is the implicit assumption behind this scaling-up procedure? It is that all search engines are effectively the same. The users of non-Google search engines behave exactly as the Google search engine users. If the analysts somehow could get their hands on the data of other search engines, they would discover that the proportion of search volume that is AI-related is effectively the same as seen on Google.

This is one of those convenient, and obviously wrong assumptions – if true, the market would have no need for more than one search engine. Each search engine's audience is just a random sample from the population of all users.

Let's make up some numbers. Let's say Google has 80% share of search volume in Country A, and AI-related search 10% of the overall Google search volume. The remaining search engines have 20% share. Scaling up here means taking the 8% of Google AI-related search volume, divide by 80%, which yields 10%. Since Google owns 8% of the 10%, the other search engines see 2% of overall search volume attributed to AI searches in Country A. Thus, the proportion of AI-related searches on those other search engines is 2%/20% = 10%.

Now, in certain countries, Google is not quite as dominant. Let's say Google only has 20% share of Country B's search volume. AI-related search on Google is 2%, which is 10% of its total. Using the same scaling-up procedure, the analysts have effectively assumed that the proportion of AI-related search volume in the dominant search engines in Country B to be also 10%.

I'm using the above calculations to illustrate a shortcoming of this heuristic. Using this procedure inflates the search volume in countries in which Google is less dominant because the inflation factor is the reciprocal of Google's market share. The less dominant Google is, the larger the inflation factor.

What's also true? The less dominant Google is, the smaller proportion of the total data the analysts are able to see, the lower the quality of the available information. So the heuristic is the most influential where it has the greatest uncertainty.

***

Hope your new year is full of uncertainty, and your heuristics shall lead you to pleasant surprises.

If you like the blog's content, please spread the word. I'm looking forward to sharing more content as the world of data continues to evolve at an amazing pace.

Disclosure: This blog post is not written by AI.

## Book Review: Visualizing with Text by Richard Brath

##### Nov 03, 2020

The creative process is sometimes described in terms of diverge-converge cycles. The diverge step involves experimentation and rewards suspending disbelief, while excesses are curbed and concepts refined during the converge step. Richard Brath's just-released book Visualizing with Text is an important resource that expands our appreciation for the place of text in visual displays.

Books on data visualization fall into recognizable types, of which two popular ones are the style guide, such as Edward Tufte, Dona Wong, and Alberto Cairo, and the coding manual, such as Ben Fry (processing) and Hadley Wickham (ggplot, Shiny). Brath's volume belongs to neither of those - it reads more like an encyclopedic catalog of how text can be incorporated into charts and graphs. He challenges us to blow up our imaginative space for characters, words, sentences, paragraphs and prose. It is a valuable aid for the diverge step of our creative process.

In modern data visualization, text is treated as an accessory, frequently found in titles, labels, legends, footnotes or surrounding text. Brath wants us to elevate text to the starring attraction. Starting with baby steps, such as direct labeling of lines and objects, and coordinating colors between chart elements and words, he experiments with inserting text into unlikely crannies, not shying away from ideas that even he admits may be somewhat of a dead-end.

One of the more immediately useful examples is the use of text labels that hug the lines on a line chart, similar to how roads and rivers are labeled on maps. I wish all software developers implement this function without delay.

A more esoteric example is to replace these lines with small-size text, as Brath makes an analogy between sentences and lines.

I am still deciding if this is a gold mine or a minefield. It is thought-provoking nonetheless.

Finally, the book includes some flights of fancy, like this one:

The red superscripts are numeric codes for French departments (provinces), arranged in ascending order of a given metric, and placed in proportional distance within the prose!

The converge step is left to the reader, as Brath refrains from bullhorning his opinions about chart types, which is why readers should not expect a style guide. He includes many experimental graphics, and may provide the pros and cons of a form without registering a judgement.

Because many of these ideas have yet to enter the mainstream, we'd need to implement these ideas on our own, which is why readers will not find a coding manual. As mentioned above, even the simplest and least controversial tactic of directly labeling lines is not available in Excel, let alone text that hugs or replaces lines. (This proves Brath's point that our community has done text a disservice.) Other ideas explored in later chapters require such features as italicizing numeric proportions of a word, rather than the entire word.

Recently, text has become a mainstay of Big Data. Visualizing with Text is timely, relevant and provocative. It is also clearly written, and tightly organized. Chapter 13 neatly summarizes the key concepts that have appeared along the way. There are plenty of use cases, primarily derived from research or business. After reading this book, you'll revel in the new sandbox of text, and long to free yourself from the constraints of your tool.

***

I recommend that you get the paper copy of the book. I reviewed the electronic version, and what irony! As you may have guessed, the electronic version ruins the typesetting. On every page, certain paragraphs show up in tiny font that resist all attempts to magnify, making Brath's case that legibility is an important metric for text visualization. Some of the more unusual fonts are dropped. The images are too small, even when popped up.

[P.S. Richard has a webpage where he included larger images and some code.]

## Whither the youth vote

##### Feb 27, 2020

The youth turnout is something that politicians and pundits bring up constantly when talking about the current U.S. presidential primaries. So I decided to look for the data. I found some data at the United States Election Project, a site maintained by Dr. Michael McDonald. The key chart is this one:

This is classic Excel.

***

Here is a quick fix:

The key to the fix is to recognize the structure of the data.

The sawtooth pattern displayed in the original chart does not convey any real trends - it's an artifact that many people only turn out for presidential elections. (As a result, the turnout during presidential election years is driven by the general election turnout.)

The age groups have an order so instead of four different colors, use a progressive color scheme. This is one of the unspoken rules about color usage in data visualization, featured in my Long Read article.

***

What do I learn from this turnout by age group chart?

Younger voters are much more invested in presidential elections than off-year elections. The youth turnout for presidential elections is double that for other years.

Participation increased markedly in the 2018 mid-term elections across all four age groups, reflecting the passion for or against President Donald Trump. This was highly unusual - and in fact, the turnout for that off-year is closer to the turnout of a presidential year election. Whether the turnout will stay at this elevated level is a big question for 2022!

For presidential elections, turnout has been creeping up over time for all age groups. But the increase in 2016 (Hillary Clinton vs Donald Trump) was mild. The growth in participation is more noticable in the younger age groups, including in 2016.

Let's look at the relative jumps in 2018 (right side of the left chart). The younger the age group, the larger the jump. Turnout in the 18-29 group doubled to 32 percent. Turnout in the oldest age group increased by 20%, nothing to sneeze at but less impressive than in the younger age groups.

Why this is the case should be obvious. The 60+ age group has a ceiling. It's already at 60-70%; how much higher can it go? People at that age have many years to develop their preference for voting in elections. It would be hard to convince the holdouts (hideouts?) to vote.

The younger age groups are further from the ceiling. If you're an organizer, will you focus your energy on the 60% non-voting 18-29-years-old, or the 30% non-voting 60+ years-old? [This is the same question any business faces: do you win incremental sales from your more loyal customers, hoping they would spend even more, or your less loyal customers?]

For Democratic candidates, the loss in 2016 is hanging over them. Getting the same people to vote in 2020 as in 2016 is a losing hand. So, they need to expand the base somehow.

If you're a candidate like Joe Biden who relies on the 60+ year old bloc, it's hard to see where he can expand the base. Your advantage is that the core voter bloc is reliable. Your problem is that you don't have appeal to the younger age groups. So a viable path to winning in the general election has to involve flipping older Trump voters. The incremental ex-Trump voters have to offset the potential loss in turnout from younger voters.

If you're a candidate like Bernie Sanders who relies on the youth vote, you'd want to launch a get-out-the-vote effort aimed at younger voters. A viable path can be created by expanding the base through lifting the turnout rate of younger voters. The incremental young voters have to offset the fraction of the 60+ year old bloc who flip to Trump.

## This Excel chart looks standard but gets everything wrong

##### Dec 02, 2019

The following CNBC chart (link) shows the trend of global car sales by region (or so we think).

This type of chart is quite common in finance/business circles, and has the fingerprint of Excel. After examining it, I nominate it for the Hall of Shame.

***

The chart has three major components vying for our attention: (1) the stacked columns, (2) the yellow line, and (3) the big red dashed arrow.

The easiest to interpret is the yellow line, which is labeled "Total" in the legend. It displays the annual growth rate of car sales around the globe. The data consist of annual percentage changes in car sales, so the slope of the yellow line represents a change of change, which is not particularly useful.

The big red arrow is making the point that the projected decline in global car sales in 2019 will return the world to the slowdown of 2008-9 after almost a decade of growth.

The stacked columns appear to provide a breakdown of the global growth rate by region. Looked at carefully, you'll soon learn that the visual form has hopelessly mangled the data.

What is the growth rate for Chinese car sales in 2006? Is it 2.5%, the top edge of China's part of the column? Between 1.5% and 2.5%, the extant of China's section? The answer is neither. Because of the stacking, China's growth rate is actually the height of the relevant section, that is to say, 1 percent. So the labels on the vertical axis are not directly useful to learning regional growth rates for most sections of the chart.

Can we read the vertical axis as global growth rate? That's not proper either. The different markets are not equal in size so growth rates cannot be aggregated by simple summing - they must be weighted by relative size.

The negative growth rates present another problem. Even if we agree to sum growth rates ignoring relative market sizes, we still can't get directly to the global growth rate. We would have to take the total of the positive rates and subtract the total of the negative rates.

***

At this point, you may begin to question everything you thought you knew about this chart. Remember the yellow line, which we thought measures the global growth rate. Take a look at the 2006 column again.

The global growth rate is depicted as 2 percent. And yet every region experienced growth rates below 2 percent! No matter how you aggregate the regions, it's not possible for the world average to be larger than the value of each region.

For 2006, the regional growth rates are: China, 1%; Rest of the World, 1%; Western Europe, 0.1%; United States, -0.25%. A simple sum of those four rates yields 2%, which is shown on the yellow line.

But this number must be divided by four. If we give the four regions equal weight, each is worth a quarter of the total. So the overall average is the sum of each growth rate weighted by 1/4, which is 0.5%. [In reality, the weights of each region should be scaled to reflect its market size.]

***

tldr; The stacked column chart with a line overlay not only fails to communicate the contents of the car sales data but it also leads to misinterpretation.

I discussed several serious problems of this chart form:

• stacking the columns make it hard to learn the regional data

• the trend by region takes a super effort to decipher

• column stacking promotes reading meaning into the height of the column but the total height is meaningless (because of the negative section) while the net height (positive minus negative) also misleads due to presumptive equal weighting

• the yellow line shows the sum of the regional data, which is four times the global growth rate that it purports to represent

***

PS. [12/4/2019: New post up with a different visualization.]

## Webinar Wednesday

##### Oct 29, 2018

I'm delivering a quick-fire Webinar this Wednesday on how to make impactful data graphics for communication and persuasion. Registration is free, at this link.

***

In the meantime, I'm preparing a guest lecture for the Data Visualization class at Yeshiva University Sims School of Management. The goal of the lecture is to emphasize the importance of incorporating analytics into the data visualization process.

Here is the lesson plan:

1. Introduce the Trifecta checkup (link) which is the general framework for effective data visualizations
2. Provide examples of Type D data visualizations, i.e. graphics that have good production values but fail due to issues with the data or the analysis
3. Hands-on demo of an end-to-end data visualization process
4. Lessons from the demo including the iterative nature of analytics and visualization; and sketching
5. Overview of basic statistics concepts useful to visual designers

## Steel tariffs, and my new dataviz seminar

##### Mar 12, 2018

I am developing a new seminar aimed at business professionals who want to improve their ability to communicate using charts. I want any guidance to be tool-agnostic, so that attendees can implement them using Excel if that’s their main charting software. Over the 12+ years that I’ve been blogging, certain ideas keep popping up; and I have collected these motifs and organized them for the seminar. This post is about a recent chart that brings up a few of these motifs.

This chart has been making the rounds in articles about the steel tariffs.

The chart shows the Top 10 nations that sell steel to the U.S., which together account for 78% of all imports.

The chart shows a few signs of design. These things caught my eye:

1. the pie chart on the left delivers the top-line message that 10 countries account for almost 80% of all U.S. steel imports
2. the callout gives further information about which 10 countries and how much each nation sells to the U.S. This is a nice use of layering
3. on the right side, progressive tints of blue indicate the respective volumes of imports

On the negative side of the ledger, the chart is marred by three small problems. Each of these problems concerns inconsistency, which creates confusion for readers.

1. Inconsistent use of color: on the left side, the darker blue indicates lower volume while on the right side, the darker blue indicates higher volume
2. Inconsistent coding of pie slices: on the right side, the percentages add up to 78% while the total area of the pie is 100%
3. Inconsistent scales: the left chart carrying the top-line message is notably smaller than the right chart depicting the secondary message. Readers’ first impression is drawn to the right chart.

Easy fixes lead to the following chart:

***

The central idea of the new dataviz seminar is that there are many easy fixes that are often missed by the vast majority of people making Excel charts. I will present a stack of these motifs. If you're in the St. Louis area, you get to experience the seminar first. Register for a spot here.

Send this message to your friends and coworkers in the area. Also, contact me if you'd like to bring this seminar to your area.

***

I also tried the following design, which brings out some other interesting tidbits, such as that Canada and Brazil together sell the U.S. about 30% of its imported steel, the top 4 importers account for about 50% of all steel imports, etc. Color is introduced on the chart via a stylized flag coloring.

## The state of the art of interactive graphics

##### Mar 10, 2016

Scott Klein's team at Propublica published a worthy news application, called "Hell and High Water" (link) I took some time taking in the experience. It's a project that needs room to breathe.

The setting is Houston Texas, and the subject is what happens when the next big hurricane hits the region. The reference point was Hurricane Ike and Galveston in 2008.

This image shows the depth of flooding at the height of the disaster in 2008.

The app takes readers through multiple scenarios. This next image depicts what would happen (according to simulations) if something similar to Ike plus 15 percent stronger winds hits Galveston.

One can also speculate about what might happen if the so-called "Mid Bay" solution is implemented:

This solution is estimated to cost about \$3 billion.

***

I am drawn to this project because the designers liberally use some things I praised in my summer talk at the Data Meets Viz conference in Germany.

Here is an example of hover-overs used to annotate text. (My mouse is on the words "Nassau Bay" at the bottom of the paragraph. Much of the Bay would be submerged at the height of this scenario.)

The design has a keen awareness of foreground/background issues. The map uses sparse static labels, indicating the most important landmarks. All other labels are hidden unless the reader hovers over specific words in the text.

I think plotting population density would have been more impactful. With the current set of labels, the perspective is focused on business and institutional impact. I think there is a missed opportunity to highlight the human impact. This can be achieved by coding population density into the map colors. I believe the colors on the map currently represent terrain.

***

This is a successful interactive project. The technical feats are impressive (read more about them here). A lot of research went into the articles; huge amounts of details are included in the maps. A narrative flow was carefully constructed, and the linkage between the text and the graphics is among the best I've seen.

## Enhanced tables, and supercharged spreadsheets with in-cell tech

##### Dec 04, 2015

Old-timer Chris P. sent me to this Bloomberg article about Vanguard ETFs and low-cost funds (link). The article itself is interesting, and I will discuss it on the sister blog some time in the future.

Chris is impressed with this table included with the article:

This table indeed presents the insight clearly. Those fund sectors in which Vanguard does not compete have much higher costs than the fund sectors in which Vanguard is a player. The author calls this the "Vanguard effect."

This is a case where finding a visual design to beat this table is hard.

For a certain type of audience, namely financial, the spreadsheet is like rice or pasta; you simply can't live without it. The Bloomberg spreadsheet does one better: the bands of blue contrast with the white cells, which neatly divides those funds into two groups.

If you use spreadsheets a lot, you should definitely look into in-cell charts. Perhaps Tufte's sparkline is the most famous but use your imagination. I also wish vendors would support in-cell charts more eagerly.

Here is a vision of what in-cell technology can do with the above spreadsheet. (The chart is generated in R.)