Seeking simplicity in complex data: Bloomberg's dataviz on UK gender pay gap

Bloomberg featured a thought-provoking dataviz that illustrates the pay gap by gender in the U.K. The dataset underlying this effort is complex, and the designers did a good job simplifying the data for ease of comprehension.

U.K. companies are required to submit data on salaries and bonuses by gender, and by pay quartiles. The dataset is incomplete, since some companies are slow to report, and the analyst decided not to merge companies that changed names.

Companies are classified into industry groups. Readers who read Chapter 3 of Numbers Rule Your World (link) should ask whether these group differences are meaningful by themselves, without controlling for seniority, job titles, etc. The chapter features one method used by the educational testing industry to take a more nuanced analysis of group differences.

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The Bloomberg visualization has two sections. In the top section, each company is represented by the percent difference between average female pay and average male pay. Then the companies within a given industry is shown in a histogram. The histograms provide a view of the disparity between companies within a given industry. The black line represents the relative proportion of companies in a given industry that have no gender pay gap but it’s the weight of the histogram on either side of the black line that carries the graphic’s message.

This is the histogram for arts, entertainment and recreation.

Bloomberg_genderpaygap_arts

The spread within this industry is very wide, especially on the left side of the black line. A large proportion of these companies pay women less on average than men, and how much less is highly variable. There is one extreme positive value: Chelsea FC Foundation that pays the average female about 40% more than the average male.

This is the histogram for the public sector.

Bloomberg_genderpaygap_public
It is a much tighter distribution, meaning that the pay gaps vary less from organization to organization (this statement ignores the possibility that there are outliers not visible on this graphic). Again, the vast majority of entities in this sector pay women less than men on average.

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The second part of the visualization look at the quartile data. The employees of each company are divided into four equal-sized groups, based on their wages. Think of these groups as the Top 25% Earners, the Second 25%, etc. Within each group, the analyst looks at the proportion of women. If gender is independent of pay, then we should expect the proportions of women to be about the same for all four quartiles. (This analysis considers gender to be the only explainer for pay gaps. This is a problem I've called xyopia, that frames a complex multivariate issue as a bivariate problem involving one outcome and one explanatory variable. Chapter 3 of Numbers Rule Your World (link) discusses how statisticians approach this issue.)

Bloomberg_genderpaygap_public_pieOn the right is the chart for the public sector. This is a pie chart used as a container. Every pie has four equal-sized slices representing the four quartiles of pay.

The female proportion is encoded in both the size and color of the pie slices. The size encoding is more precise while the color encoding has only 4 levels so it provides a “binned” summary view of the same data.

For the public sector, the lighter-colored slice shows the top 25% earners, and its light color means the proportion of women in the top 25% earners group is between 30 and 50 percent. As we move clockwise around the pie, the slices represent the 2nd, 3rd and bottom 25% earners, and women form 50 to 70 percent of each of those three quartiles.

To read this chart properly, the reader must first do one calculation. Women represent about 60% of the top 25% earners in the public sector. Is that good or bad? This depends on the overall representation of women in the public sector. If the sector employs 75 percent women overall, then the 60 percent does not look good but if it employs 40 percent women, then the same value of 60% tells us that the female employees are disproportionately found in the top 25% earners.

That means the reader must compare each value in the pie chart against the overall proportion of women, which is learned from the average of the four quartiles.

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In the chart below, I make this relative comparison explicit. The overall proportion of women in each industry is shown using an open dot. Then the graphic displays two bars, one for the Top 25% earners, and one for the Bottom 25% earners. The bars show the gap between those quartiles and the overall female proportion. For the top earners, the size of the red bars shows the degree of under-representation of women while for the bottom earners, the size of the gray bars shows the degree of over-representation of women.

Redo_junkcharts_bloombergukgendergap

The net sum of the bar lengths is a plausible measure of gender inequality.

The industries are sorted from the ones employing fewer women (at the top) to the ones employing the most women (at the bottom). An alternative is to sort by total bar lengths. In the original Bloomberg chart - the small multiples of pie charts, the industries are sorted by the proportion of women in the bottom 25% pay quartile, from smallest to largest.

In making this dataviz, I elected to ignore the middle 50%. This is not a problem since any quartile above the average must be compensated by a different quartile below the average.

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The challenge of complex datasets is discovering simple ways to convey the underlying message. This usually requires quite a bit of upfront analytics, data transformation, and lots of sketching.

 

 


The French takes back cinema but can you see it?

I like independent cinema, and here are three French films that come to mind as I write this post: Delicatessen, The Class (Entre les murs), and 8 Women (8 femmes). 

The French people are taking back cinema. Even though they purchased more tickets to U.S. movies than French movies, the gap has been narrowing in the last two decades. How do I know? It's the subject of this infographic

DataCinema

How do I know? That's not easy to say, given how complicated this infographic is. Here is a zoomed-in view of the top of the chart:

Datacinema_top

 

You've got the slice of orange, which doubles as the imagery of a film roll. The chart uses five legend items to explain the two layers of data. The solid donut chart presents the mix of ticket sales by country of origin, comparing U.S. movies, French movies, and "others". Then, there are two thin arcs showing the mix of movies by country of origin. 

The donut chart has an usual feature. Typically, the data are coded in the angles at the donut's center. Here, the data are coded twice: once at the center, and again in the width of the ring. This is a self-defeating feature because it draws even more attention to the area of the donut slices except that the areas are highly distorted. If the ratios of the areas are accurate when all three pieces have the same width, then varying those widths causes the ratios to shift from the correct ones!

The best thing about this chart is found in the little blue star, which adds context to the statistics. The 61% number is unusually high, which demands an explanation. The designer tells us it's due to the popularity of The Lion King.

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The one donut is for the year 1994. The infographic actually shows an entire time series from 1994 to 2014.

The design is most unusual. The years 1994, 1999, 2004, 2009, 2014 receive special attention. The in-between years are split into two pairs, shrunk, and placed alternately to the right and left of the highlighted years. So your eyes are asked to zig-zag down the page in order to understand the trend. 

To see the change of U.S. movie ticket sales over time, you have to estimate the sizes of the red-orange donut slices from one pie chart to another. 

Here is an alternative visual design that brings out the two messages in this data: that French movie-goers are increasingly preferring French movies, and that U.S. movies no longer account for the majority of ticket sales.

Redo_junkcharts_frenchmovies

A long-term linear trend exists for both U.S. and French ticket sales. The "outlier" values are highlighted and explained by the blockbuster that drove them.

 

P.S.

1. You can register for the free seminar in Lyon here. To register for live streaming, go here.
2. Thanks Carla Paquet at JMP for help translating from French.


Two nice examples of interactivity

Janie on Twitter pointed me to this South China Morning Post graphic showing off the mighty train line just launched between north China and London (!)

Scmp_chinalondonrail

Scrolling down the page simulates the train ride from origin to destination. Pictures of key regions are shown on the left column, as well as some statistics and other related information.

The interactivity has a clear purpose: facilitating cross-reference between two chart forms.

The graphic contains a little oversight ... The label for the key city of Xian, referenced on the map, is missing from the elevation chart on the left here:

Scmp_chinalondonrail_xian

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I also like the way New York Times handled interactivity to this chart showing the rise in global surface temperature since the 1900s. The accompanying article is here.

Nyt_surfacetemp

When the graph is loaded, the dots get printed from left to right. That's an attention grabber.

Further, when the dots settle, some years sink into the background, leaving the orange dots that show the years without the El Nino effect. The reader can use the toggle under the chart title to view all of the years.

This configuration is unusual. It's more common to show all the data, and allow readers to toggle between subsets of the data. By inverting this convention, it's likely few readers need to hit that toggle. The key message of the story concerns the years without El Nino, and that's where the graphic stands.

This is interactivity that succeeds by not getting in the way. 

 

 

 


Using a bardot chart for survey data

Aleks J. wasn't amused by the graphs included in Verge's report about user attitudes toward the major Web brands such as Google, Facebook, and Twitter.

Let's use this one as an example:

Verge_survey_fb

Survey respondents are asked to rate how much they like or dislike the products and services from each of six companies, on a five-point scale. There is a sixth category for "No opinion/Don't use."

In making this set of charts, the designer uses six different colors for the six categories. This means he/she thinks of these categories as discrete so that the difference between categories carries no meaning. In a bipolar, five-point scale, it is more common to pick two extreme colors and then use shades to indicate the degree of liking or disliking. The middle category can be shown in a neutral color to express the neutrality of opinion.

The color choice baffles me. The two most prominent colors, gray and dark blue, correspond to two minor categories (no opinion and neutral) while the most important category - "greatly like" - is painted the modest yellow, paling away.

Verge sees the popularity of Facebook as the key message, which explains its top position among the six brands. However, readers familar with the stacked bar chart form are likely looking to make sense of the order, and frustrated.

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In revising this chart, I introduce a second level of grouping: the six categories fit into three color groups: red for dislike, gray for no opinion/neutral, and orange for like. The like and dislike groups are plotted at the left and right ends of the chart while the two less informative categories are lumped toward the middle.

Redo_vergesurveyfb_1

I take great pleasure in dumping the legend box.

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Now, when a five-point scale is used, many analysts like to analyze the Top 2, or Bottom 2 boxes. The choice of colors in the above chart facilitates this analysis. Adding some subtle dots makes it even better!

Redo_vergesurveyfb_2

Because this chart is a superposition of a stacked bar chart and a dot plot, I am calling this a bardot chart.

Also notice that the brands are re-ordered by Top 2 box popularity.

 

 


Let's not mix these polarized voters as the medians run away from one another

Long-time follower Daniel L. sent in a gem, by the Washington Post. This is a multi-part story about the polarization of American voters, nicely laid out, with superior analyses and some interesting graphics. Click here to see the entire article.

Today's post focuses on the first graphic. This one:

Wpost_friendsparties1

The key messages are written out on the 2017 charts: namely, 95% of Republicans are more conservative than the median Democrat, and 97% of Democrats are more libearl than the median Republicans.

This is a nice statistical way of laying out the polarization. There are a number of additional insights one can draw from the population distributions: for example, in the bottom row, the Democrats have been moving left consistently, and decisively in 2017. By contrast, Republicans moved decisively to the right from 2004 to 2017. I recall reading about polarization in past elections but it is really shocking to see the extreme in 2017.

A really astounding but hidden feature is that the median Democrat and the median Republican were not too far apart in 1994 and 2004 but the gap exploded in 2017.

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I like to solve a few minor problems on this graphic. It's a bit confusing to have each chart display information on both Republican and Democratic distributions. The reader has to understand that in the top row, the red area represents Republican voters but the blue line shows the median Democrat.

Also, I want to surface two key insights: the huge divide that developed in 2017, and the exploding gap between the two medians.

Here is the revised graphic:

  Redo_wpost_friendsparties1

On the left side, each chart focuses on one party, and the trend over the three elections. The reader can cross charts to discover that the median voter in one party is more extreme than essentially all of the voters of the other party. This same conclusion can be drawn from the exploding gap between the median voters in either party, which is explicitly plotted in the lower right chart. The top right chart is a pretty visualization of how polarized the country was in the 2017 election.

 


Reorientation in the French election

Financial Times has this chart up about the voters for the National Front, which is Marie Le Pen's party.

FT_France_FN_C97-rl3WsAMb2aA

I find the chart very hard to decipher, even though I usually like the dot plot format.

The first thing to figure out is not visual. It's a definition of the data. The average voter represents those who voted in the 2015 regional election. The National Front voters are those who intended to vote in 2015, and these are sub-divided into "loyal" and "new" voters. All it takes one to be "loyal" is to have voted for the National Front in 2012; all others are "new."

All of the above information you pick up primarily from the footnotes, combined with various parts of the title, and legend. Similarly, you also learn that FN is the acronym for National Front.

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 This following version is clearer:

Jc_ft_frenchnationalfront

The new version mostly just re-orients the original chart, turning it on its side. It's quite surprising how much better I feel about it. I think it's because the message is primarily about the relative ages, and in the original chart, aging is portrayed downwards, which is not natural.


Story within story, bar within bar

This Wall Street Journal offering caught my eye.

Wsj_gender_workforce_sm

It's the unusual way of displaying proportions.

Your first impression is to interpret the graphic as a bar chart. But it really is a bar within a bar: the crux of the matter - gender balance - is embedded in individual bars.

Instead of pie charts or stacked bar charts, we see  stacked columns within each bar.

I see what the designer is attempting to accomplish. The first message is the sharp decline in gender equality at higher job titles. The next message is the sharp drop in the frequency of higher job titles.

This chart is a variant of the "Marimekko" chart (beloved by management consultants), also called the mosaic chart. The only difference being how the distribution of jobs in the work force is coded.

The Marimekko is easier to understand:

Redo_wsjgenderworkforce_mekko2

A key advantage of this version is to be found in the thin columns.

Here is another way to visualize this data, drawing attention to the gender gap.

Redo_wsjgenderworkforce_lines

In the other versions, the reader must do subtractions to figure out the size of the gaps.


Lining up the dopers and their medals

The Times did a great job making this graphic (this snapshot is just the top half):

Nyt_olympicdopers_top

A lot of information is packed into a small space. It's easy to compose the story in our heads. For example, Lee Chong Wai, the Malaysian badminton silver medalist, was suspended for doping for a short time during 2015, and he was second twice before the doping incident.

They sorted the athletes according to the recency of the latest suspension. This is very smart as it helps make the chart readable. Other common ordering such as alphabetically by last name, by sport, by age, and by number of medals will result in a bit of a mess.

I'm curious about the athletes who also had doping suspensions but did not win any medals in 2016.


Treating absolute and relative data simultaneously

A friend asked me to comment on the following chart:

Mobileprogrammatic_chart

Specifically, he points out the challenge of trying to convey both absolute and relative metrics for a given data series.

This chart presents projections of growth in the U.S. mobile display advertising market. It is specifically pointing out that the programmatic segment of this market is growing rapidly (visualized as the black columns).

The blue and red lines then make a mess of the situation. Even though both of these lines espress percentages, they report to different scales. The red line represents growth rates while the blue line represents share of market.

Both of these metrics are relative metrics useful for interpreting the trend. The growth rates (red) interpret the dollar values on the basis of past values while the market shares (blue) interpret the dollar values on the basis of the total market.

It is rarely a good idea to have many scales on the same canvas. Looking at the blue line for the moment, it is shocking to find that the values depicted almost doubled from one end to the other end. The blue line appears much too gentle.

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In the makeover, I expressed everything in the same scale (billions of dollars). I used side-by-side charts (small multiples) to isolate each trend that is found in the data. I allow readers to look at each individual segment of the market, and then examine how the individual trends affect the total market.

Redo_mobileprogrammatic_v2

One might argue that the stacked column chart by itself is sufficient. If there is a severe space limitation, I'd let go of the other two panels. However, having those panels makes the messages easier to obtain. This is particularly true of the steady growth assumption behind the programmatic spending trend (the orange columns).


Three short lessons on comparisons

I like this New York Times graphic illustrating the (over-the-top) reaction by the New York police to the Eric Garner-inspired civic protests during the holidays. This is a case where the data told a story that mere eyes and ears couldn't. The semi-strike was clear as day from the visualization.

There are three sections to the graphic, and each displays a different form of comparisons

The first chart is the most straightforward, comparing the number of summonses this year to that of the same time a year ago.

Nyt_nyc_summonses1


One could choose lines for both data series. The combination of one line and column also works. It creates a sensation that the columns should grow in height to meet last year's level. The traffic cops appear to have returned to work more quickly. That said, I don't care for the shades of brown/orange of the columns.

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The second chart accommodates a more complex scenario, one in which the simple year-on-year comparison is regarded as misleading because the overall crime rate materially dropped from 2013 to 2014. In this scenario, a before-after comparison may be more valid.

Nyt_nyc_summonses2

The chart has multiple sections and I am only showing the section concerning summonses (The horizontal axis shows time, the first black column being the first ten months, and the other orange columns being individual months since then. The vertical axis is the percent change from a year ago.).

The chart shows that in the first ten months of 2014, before the semi-strike, the number of summonses issued was already slightly below the same period the year before. Through the dotted line, the reader is invited to compare this level of change against those in the ensuing months. How starkly did the summonses rate fell!

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The final chart reveals yet another comparison. Geography is introduced here in the form of a proportional-symbol map.

Nyt_nyc_summonses3

Again, you can't miss the story: across every precinct, summonses have disappeared. This chart is very helpful to making the case that the observed drop is not natural.