The rule governing which variable to put on which axis, served a la mode

When making a scatter plot, the two variables should not be placed arbitrarily. There is a rule governing this: the outcome variable should be shown on the vertical axis (also called y-axis), and the explanatory variable on the horizontal (or x-) axis.

This chart from the archives of the Economist has this reversed:

The title of the accompanying article is "Ice Cream and IQ"...

In a Trifecta Checkup (link), it's a Type DV chart. It's preposterous to claim eating ice cream makes one smarter without more careful studies. The chart also carries the xyopia fallacy: by showing just two variables, readers are unwittingly led to explain differences in "IQ" using differences in per-capita ice-cream consumption when lots of other stronger variables will explain any gaps in IQ.

In this post, I put aside my objections to the analysis, and focus on the issue of assigning variables to axes. Notice that this chart reverses the convention: the outcome variable (IQ) is shown on the horizontal, and the explanatory variable (ice cream) is shown on the vertical.

Here is a reconstruction of the above chart, showing only the dots that were labeled with country names. I fitted a straight regression line instead of a curve. (I don't understand why the red line in the original chart bends upwards when the data for Japan, South Korea, Singapore and Hong Kong should be dragging it down.)

Note that the interpretation of the regression line raises eyebrows because the presumed causality is reversed. For each 50 points increase in PISA score (IQ), this line says to expect ice cream consumption to raise by about 1-2 liters per person per year. So higher IQ makes people eat more ice cream.

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If the convention is respected, then the following scatter plot results:

The first thing to note is that the regression analysis is different here from that shown in the previous chart. The blue regression line is not equivalent to the black regression line from the previous chart. You cannot reverse the roles of the x and y variables in a regression analysis, and so neither should you reverse the roles of the x and y variables in a scatter plot.

The blue regression line can be interpreted as having two sections, roughly, for countries consuming more than or less than 6 liters of ice cream per person per year. In the less-ice-cream countries, the correlation between ice cream and IQ is stronger (I don't endorse the causal interpretation of this statement).

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When you make a scatter plot, you have two variables for which you want to analyze their correlation. In most cases, you are exploring a cause-effect relationship.

Higher income households cares more on politics.
Less educated citizens are more likely to not register to vote.
Companies with more diverse workforce has better business performance.

Frequently, the reverse correlation does not admit a causal interpretation:

Caring more about politics does not make one richer.
Not registering to vote does not make one less educated.
Making more profits does not lead to more diversity in hiring.

In each of these examples, it's clear that one variable is the outcome, the other variable is the explanatory factor. Always put the outcome in the vertical axis, and the explanation in the horizontal axis.

The justification is scientific. If you are going to add a regression line (what Excel calls a "trendline"), you must follow this convention, otherwise, your regression analysis will yield the wrong result, with an absurd interpretation!

 

Too much of a good thing

Several of us discussed this data visualization over twitter last week. The dataviz by Aero Data Lab is called “A Bird’s Eye View of Pharmaceutical Research and Development”. There is a separate discussion on STAT News.

Here is the top section of the chart:

We faced a number of hurdles in understanding this chart as there is so much going on. The size of the shapes is perhaps the first thing readers notice, followed by where the shapes are located along the horizontal (time) axis. After that, readers may see the color of the shapes, and finally, the different shapes (circles, triangles,...).

It would help to have a legend explaining the sizes, shapes and colors. These were explained within the text. The size encodes the number of test subjects in the clinical trials. The color encodes pharmaceutical companies, of which the graphic focuses on 10 major ones. Circles represent completed trials, crosses inside circles represent terminated trials, triangles represent trials that are still active and recruiting, and squares for other statuses.

The vertical axis presents another challenge. It shows the disease conditions being investigated. As a lay-person, I cannot comprehend the logic of the order. With over 800 conditions, it became impossible to find a particular condition. The search function on my browser skipped over the entire graphic. I believe the order is based on some established taxonomy.

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In creating the alternative shown below, I stayed close to the original intent of the dataviz, retaining all the dimensions of the dataset. Instead of the fancy dot plot, I used an enhanced data table. The encoding methods reflect what I’d like my readers to notice first. The color shading reflects the size of each clinical trial. The pharmaceutical companies are represented by their first initials. The status of the trial is shown by a dot, a cross or a square.

Here is a sketch of this concept showing just the top 10 rows.

Certain conditions attracted much more investment. Certain pharmas are placing bets on cures for certain conditions. For example, Novartis is heavily into research on Meningnitis, meningococcal while GSK has spent quite a bit on researching "bacterial infections."

Wayward legend takes sides in a chart of two sides, plus data woes

Reader Chris P. submitted the following graph, found on Axios:

From a Trifecta Checkup perspective, the chart has a clear question: are consumers getting what they wanted to read in the news they are reading?

Nevertheless, the chart is a visual mess, and the underlying data analytics fail to convince. So, it’s a Type DV chart. (See this overview of the Trifecta Checkup for the taxonomy.)

***

The designer did something tricky with the axis but the trick went off the rails. The underlying data consist of two set of ranks, one for news people consumed and the other for news people wanted covered. With 14 topics included in the study, the two data series contain the same values, 1 to 14. The trick is to collapse both axes onto one. The trouble is that the same value occurs twice, and the reader must differentiate the plot symbols (triangle or circle) to figure out which is which.

It does not help that the lines look like arrows suggesting movement. Without first reading the text, readers may assume that topics change in rank between two periods of time. Some topics moved right, increasing in importance while others shifted left.

The design wisely separated the 14 topics into three logical groups. The blue group comprises news topics for which “want covered” ranking exceeds the “read” ranking. The orange group has the opposite disposition such that the data for “read” sit to the right side of the data for “want covered”. Unfortunately, the legend up top does more harm than good: it literally takes sides!

**

Here, I've put the data onto a scatter plot:

The two sets of ranks are basically uncorrelated, as the regression line is almost flat, with “R-squared” of 0.02.

The analyst tried to "rescue" the data in the following way. Draw the 45-degree line, and color the points above the diagonal blue, and those below the diagonal orange. Color the points on the line gray. Then, write stories about those three subgroups.

Further, the ranking of what was read came from Parse.ly, which appears to be surveillance data (“traffic analytics”) while the ranking of what people want covered came from an Axios/SurveyMonkey poll. As for as I could tell, there was no attempt to establish that the two populations are compatible and comparable.

 

 

 

 

 

Clarifying comparisons in censored cohort data: UK housing affordability

If you're pondering over the following chart for five minutes or more, don't be ashamed. I took longer than that.

The chart accompanied a Financial Times article about inter-generational fairness in the U.K. To cut to the chase, a recently released study found that younger generations are spending substantially higher proportions of their incomes to pay for housing costs. The FT article is here (behind paywall). FT actually slightly modified the original chart, which I pulled from the Home Affront report by the Intergenerational Commission.

One stumbling block is to figure out what is plotted on the horizontal axis. The label "Age" has gone missing. Even though I am familiar with cohort analysis (here, generational analysis), it took effort to understand why the lines are not uniformly growing in lengths. Typically, the older generation is observed for a longer period of time, and thus should have a longer line.

In particular, the orange line, representing people born before 1895 only shows up for a five-year range, from ages 70 to 75. This was confusing because surely these people have lived through ages 20 to 70. I'm assuming the "left censoring" (missing data on the left side) is because of non-existence of old records.

The dataset is also right-censored (missing data on the right side). This occurs with the younger generations (the top three lines) because those cohorts have not yet reached certain ages. The interpretation is further complicated by the range of birth years in each cohort but let me not go there.

TL;DR ... each line represents a generation of Britons, defined by their birth years. The generations are compared by how much of their incomes did they spend on housing costs. The twist is that we control for age, meaning that we compare these generations at the same age (i.e. at each life stage).

***

Here is my version of the same chart:

Here are some of the key edits:

• Vertical blocks are introduced to break up the analysis by life stage. These guide readers to compare the lines vertically i.e. across generations
• The generations are explicitly described as cohorts by birth years
• The labels for the generations are placed next to the lines
• Gridlines are pushed to the back
• The age axis is explicitly labeled
• Age labels are thinned
• A hierarchy on colors
• The line segments with incomplete records are dimmed

The harmful effect of colors can be seen below. This chart is the same as the one above, except for retaining the colors of the original chart:

 

 

Re-thinking a standard business chart of stock purchases and sales

Here is a typical business chart.

A possible story here: institutional investors are generally buying AMD stock, except in Q3 2018.

Let's give this chart a three-step treatment.

STEP 1: The Basics

Remove the data labels, which stand sideways awkwardly, and are redundant given the axis labels. If the audience includes people who want to take the underlying data, then supply a separate data table. It's easier to copy and paste from, and doing so removes clutter from the visual.

The value axis is probably created by an algorithm - hard to imagine someone deliberately placing axis labels  $262 million apart.

The gridlines are optional.

STEP 2: Intermediate

Simplify and re-organize the time axis labels; show the quarter and year structure. The years need not repeat.

Align the vocabulary on the chart. The legend mentions "inflows and outflows" while the chart title uses the words "buying and selling". Inflows is buying; outflows is selling.

STEP 3: Advanced

This type of data presents an interesting design challenge. Arguably the most important metric is the net purchases (or the net flow), i.e. inflows minus outflows. And yet, the chart form leaves this element in the gaps, visually.

The outflows are numerically opposite to inflows. The sign of the flow is encoded in the color scheme. An outflow still points upwards. This isn't a criticism, but rather a limitation of the chart form. If the red bars are made to point downwards to indicate negative flow, then the "net flow" is almost impossible to visually compute!

Putting the columns side by side allows the reader to visually compute the gap, but it is hard to visually compare gaps from quarter to quarter because each gap is hanging off a different baseline.

The following graphic solves this issue by focusing the chart on the net flows. The buying and selling are still plotted but are deliberately pushed to the side:

The structure of the data is such that the gray and pink sections are "symmetric" around the brown columns. A purist may consider removing one of these columns. In other words:

Here, the gray columns represent gross purchases while the brown columns display net purchases. The reader is then asked to infer the gross selling, which is the difference between the two column heights.

We are almost back to the original chart, except that the net buying is brought to the foreground while the gross selling is pushed to the background.

 

An exercise in decluttering

My friend Xan found the following chart by Pew hard to understand. Why is the chart so taxing to look at? 

It's packing too much.

I first notice the shaded areas. Shading usually signifies "look here". On this chart, the shading is highlighting the least important part of the data. Since the top line shows applicants and the bottom line admitted students, the shaded gap displays the rejections.

The numbers printed on the chart are growth rates but they confusingly do not sync with the slopes of the lines because the vertical axis plots absolute numbers, not rates. 

The vertical axis presents the total number of applicants, and the total number of admitted students, in each "bucket" of colleges, grouped by their admission rate in 2017. On the right, I drew in two lines, both growth rates of 100%, from 500K to 1 million, and from 1 to 2 million. The slopes are not the same even though the rates of growth are.

Therefore, the growth rates printed on the chart must be read as extraneous data unrelated to other parts of the chart. Attempts to connect those rates to the slopes of the corresponding lines are frustrated.

Another lurking factor is the unequal sizes of the buckets of colleges. There are fewer than 10 colleges in the most selective bucket, and over 300 colleges in the largest bucket. We are unable to interpret properly the total number of applicants (or admissions). The quantity of applications in a bucket depends not just on the popularity of the colleges but also the number of colleges in each bucket.

The solution isn't to resize the buckets but to select a more appropriate metric: the number of applicants per enrolled student. The most selective colleges are attracting about 20 applicants per enrolled student while the least selective colleges (those that accept almost everyone) are getting 4 applicants per enrolled student, in 2017.

As the following chart shows, the number of applicants has doubled across the board in 15 years. This raises an intriguing question: why would a college that accepts pretty much all applicants need more applicants than enrolled students?

Depending on whether you are a school administrator or a student, a virtuous (or vicious) cycle has been realized. For the top four most selective groups of colleges, they have been able to progressively attract more applicants. Since class size did not expand appreciably, more applicants result in ever-lower admit rate. Lower admit rate reduces the chance of getting admitted, which causes prospective students to apply to even more colleges, which further suppresses admit rate. 

 

 

 

Check out the Lifespan of News project

Alberto Cairo introduces another one of his collaborations with Google, visualizing Google search data. We previously looked at other projects here.

The latest project, designed by Schema, Axios, and Google News Initiative, tracks the trending of popular news stories over time and space, and it's a great example of making sense of a huge pile of data.

The design team produced a sequence of graphics to illustrate the data. The top news stories are grouped by category, such as Politics & Elections, Violence & War, and Environment & Science, each given a distinct color maintained throughout the project.

The first chart is an area chart that looks at individual stories, and tracks the volume over time.

To read this chart, you have to notice that the vertical axis measuring volume is a log scale, meaning that each tick mark up represents a 10-fold increase. Log scale is frequently used to draw far-away data closer to the middle, making it possible to see both ends of a wide distribution on the same chart. The log transformation introduces distortion deliberately. The smaller data look disproportionately large because of it.

The time scrolls automatically so that you feel a rise and fall of various news stories. It's a great way to experience the news cycle in the past year. The overlapping areas show competing news stories that shared the limelight at that point in time.

Just bear in mind that you have to mentally reverse the distortion introduced by the log scale.

***

In the second part of the project, they tackle regional patterns. Now you see a map with proportional symbols. The top story in each locality is highlighted with the color of the topic. As time flows by, the sizes of the bubbles expand and contract.

Sometimes, the entire nation was consumed by the same story, e.g. certain obituaries. At other times, people in different regions focused on different topics.

***

In the last part of the project, they describe general shapes of the popularity curves. Most stories have one peak although certain stories like U.S. government shutdown will have multiple peaks. There is also variation in terms of how fast a story rises to the peak and how quickly it fades away.

The most interesting aspect of the project can be learned from the footnote. The data are not direct hits to the Google News stories but searches on Google. For each story, one (or more) unique search terms are matched, and only those stories are counted. A "control" is established, which is an excellent idea. The control gives meaning to those counts. The control used here is the number of searches for the generic term "Google News." Presumably this is a relatively stable number that is a proxy for general search activity. Thus, the "volume" metric is really a relative measure against this control.

 

 

 

 

This chart advises webpages to add more words

A reader sent me the following chart. In addition to the graphical glitch, I was asked about the study's methodology.

I was able to trace the study back to this page. The study uses a line chart instead of the bar chart with axis not starting at zero. The line shows that web pages ranked higher by Google on the first page tend to have more words, i.e. longer content may help with Google ranking.

On the bar chart, Position 1 is more than 6 times as big as Position 10, if one compares the bar areas. But it's really only 20% larger in the data.

In this case, even the line chart is misleading. If we extend the Google Position to 20, the line would quickly dip below the horizontal axis if the same trend applies.

The line chart includes too much grid, one of Tufte's favorite complaints. The Google position is an integer and yet the chart's gridlines imply that 0.5 rank is possible.

Any chart of this data should supply information about the variance around these average word counts. Would like to see a side-by-side box plot, for example.

Another piece of context is the word counts for results on the second or third pages of Google results. Where are the short pages?

***

Turning to methodology, we learn that the research team analyzed 1 million pages of Google search results, and they also "removed outliers from our data (pages that contained fewer than 51 words and more than 9999 words)."

When you read a line like this, you have to ask some questions:

How do they define "outlier"? Why do they choose 51 and 9,999 as the cut-offs?

What proportion of the data was removed at either end of the distribution?

If these proportions are small, then the outliers are not going to affect that average word count by much, and thus there is no point to their removal. If they are large, we'd like to see what impact removing them might have.

In any case, the median is a better number to use here, or just show us the distribution, not just the average number.

It could well be true that Google's algorithm favors longer content, but we need to see more of the data to judge.

 

 

GDPR: justice for data visualization

Reader LG found the following chart, tweeted by @EU_Justice.

This chart is a part of a larger infographic, which is found here.

The following points out a few issues with this effort:

The time axis is quite embarrassing. The first six months or so are squeezed into less than half the axis while the distance between Nov and Dec is not the same as that between Dec and Jan. So the slope of each line segment is what the designer wants it to be!

The straight edges of the area chart imply that there were only three data points, with straight lines drawn between each measurement. Sadly, the month labels are not aligned to the data on the line.

Lastly, the dots between May and November intended to facilitate reading this chart backfire. There are 6 dots dividing the May-Nov segment when there should only be five.

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The chart looks like this when not distorted:

 

Labels, scales, controls, aggregation all in play

JB @barclaysdevries sent me the following BBC production over Twitter.

He was not amused.

This chart pushes a number of my hot buttons.

First, I like to assume that readers don't need to be taught that 2007 and 2018 are examples of "Year".

Second, starting an area chart away from zero is equally as bad as starting a bar chart not at zero! The area is distorted and does not reflect the relative values of the data.

Third, I suspect the 2007 high point is a local peak, which they chose in order to forward a sky-is-falling narrative related to China's growth.

So I went to a search engine and looked up China's growth rate, and it helpfully automatically generated the following chart:

Just wow! This chart does a number of things right.

First, it confirms my hunch above. 2007 is a clear local peak and it is concerning that the designer chose that as a starting point.

Second, this chart understands that the zero-growth line has special meaning.

Third, there are more year labels.

Fourth, and very importantly, the chart offers two "controls". We can look at China's growth relative to India's and relative to the U.S.'s. Those two other lines bring context.

JB's biggest complaint is that the downward-sloping line confuses the issue, which is that slowing growth is still growth. The following chart conveys a completely different message but the underlying raw data are the same: