Ridings, polls, elections, O Canada

Stephen Taylor reached out to me about his work to visualize Canadian elections data. I took a look. I appreciate the labor of love behind this project.

He led with a streamgraph, which presents a quick overview of relative party strengths over time.

I am no Canadian election expert, and I did a bare minimum of research in writing this blog. From this chart, I learn that:

• the Canadians have an irregular election schedule
• Canada has a two party plus breadcrumbs system
• The two dominant parties are Liberals and Conservatives. The Liberals currently hold just less than half of the seats. The Conservatives have more than half of the seats not held by Liberals
• The Conservative party (maybe) rebranded as "progressive conservative" for several decades. The Reform/Alliance party was (maybe) a splinter movement within the Conservatives as well.
• Since the "width" of the entire stream increased over time, I'm guessing the number of seats has expanded

That's quite a bit of information obtained at a glance. This shows the power of data visualization. Notice Stephen didn't even have to include a "how to read this" box.

The streamgraph form has its limitations.

The feature that makes it more attractive than an area chart is its middle anchoring, resulting in a form of symmetry. The same feature produces erroneous intuition - the red patch draws out a declining trend; the reader must fight the urge to interpret the lines and focus on the areas.

The breadcrumbs are well hidden. The legend below discloses that the Green Party holds 3 seats currently. The party has never held enough seats to appear on the streamgraph though.

The bars showing proportions in the legend is a very nice touch. (The numbers appear messed up - I have to ask Stephen whether the seats shown are current values, or some kind of historical average.) I am a big fan of informative legends.

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The next featured chart is a dot plot of polling results since 2020.

One can see a three-tier system: the two main parties, then the NDP (yellow) is the clear majority of the minority, and finally you have a host of parties that don't poll over 10%.

It looks like the polls are favoring the Conservatives over the Liberals in this election but it may be an election-day toss-up.

The purple dots represent "PPC" which is a party not found elsewhere on the page.

This chart is clear as crystal because of the structure of the underlying data. It just amazes me that the polls are so highly correlated. For example, across all these polls, the NDP has never once polled better than either the Liberals or the Conservatives, and in addition, it has never polled worse than any of the small parties.

What I'd like to see is a chart that merges the two datasets, addressing the question of how well these polls predicted the actual election outcomes.

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The project goes very deep as Stephen provides charts for individual "ridings" (perhaps similar to U.S. precincts).

Here we see population pyramids for Vancouver Center, versus British Columbia (Province), versus Canada.

This riding has a large surplus of younger people in their twenties and thirties. Be careful about the changing scales though. The relative difference in proportions are more drastic than visually displayed because the maximum values (5%) on the Province and Canada charts are half that on the Riding chart (10%). Imagine squashing the Province and Canada charts to half their widths.

Analyses of income and rent/own status are also provided.

This part of the dashboard exhibits a problem common in most dashboards - they present each dimension of the data separately and miss out on the more interesting stuff: the correlation between dimensions. Do people in their twenties and thirties favor specific parties? Do richer people vote for certain parties?

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The riding-level maps are the least polished part of the site. This is where I'm looking for a "how to read it" box.

It took me a while to realize that the colors represent the parties. If I haven't come in from the front page, I'd have been totally lost.

Next, I got confused by the use of the word "poll". Clicking on any of the subdivisions bring up details of an actual race, with party colors, candidates and a donut chart showing proportions. The title gives a "poll id" and the name of the riding in parentheses. Since the poll id changes as I mouse over different subdivisions, I'm wondering whether a "poll" is the term for a subdivision of a riding. A quick wiki search indicates otherwise.

My best guess is the subdivisions are indicated by the numbers.

Back to the donut charts, I prefer a different sorting of the candidates. For this chart, the two most logical orderings are (a) order by overall popularity of the parties, fixed for all ridings and (b) order by popularity of the candidate, variable for each riding.

The map shown above gives the winner in each subdivision. This type of visualization dumps a lot of information. Stephen tackles this issue by offering a small multiples view of each party. Here is the Liberals in Vancouver.

Again, we encounter ambiguity about the color scheme. Liberals have been associated with a red color but we are faced with abundant yellow. After clicking on the other parties, you get the idea that he has switched to a divergent continuous color scale (red - yellow - green). Is red or green the higher value? (The answer is red.)

I'd suggest using a gray scale for these charts. The hardest decision is going to be the encoding between values and shading. Should each gray scale be different for each riding and each party?

If I were to take a guess, Stephen must have spent weeks if not months creating these maps (depending on whether he's full-time or part-time). What he has published here is a great start. Fine-tuning the issues I've mentioned may take more weeks or months more.

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Stephen is brave and smart to send this project for review. For one thing, he's got some free consulting. More importantly, we should always send work around for feedback; other readers can tell us where our blind spots are.

To read more, start with this post by Stephen in which he introduces his project.

A little stitch here, a great graphic is knitted

The Wall Street Journal used the following graphic to compare hurricanes Ida and Katrina (link to paywalled article).

This graphic illustrates the power of visual communications. Readers can learn a lot from it.

The paths of the storms can be compared. The geographical locations of the landfalls are shown. The strengthening of wind speeds as the hurricanes moved toward Louisiana is also displayed. Ida is clearly a lesser storm than Katrina: its wind speed never reached Category 5, and is generally lower at comparable time points.

The greatest feature of the WSJ graphic is how the designer stitches the two plots into one graphic. The anchors are two time points: when each storm attained enough wind speed to be classified as a hurricane (indicated by open dots), and when each storm made landfall in Louisiana. It is this little-noticed feature that makes it so easy to place each plot in context of the other.

Bravo!

One of the most frequently produced maps is also one of the worst

Summer is here, many Americans are putting the pandemic in their rear-view mirrors, and gas prices are soaring. Business Insider told the story using this map:

What do we want to learn about gas prices this summer?

Which region has the highest / lowest prices?

How much higher / lower than the national average are the regional prices?

How much has prices risen, compared to last year, or compared to the last few weeks?

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How much work did you have to do to get answers to those questions from the above map?

Unfortunately, this type of map continues to dominate the popular press. It merely delivers a geography lesson and not much else. Its dominant feature tells readers how to classify the 50 states into regions. Its color encodes no data.

Not surprisingly, this map fails the self-sufficiency test (link). The entire dataset is printed on the map, and if those numbers were removed, we would be left with a map of the regions of the U.S. The graphical elements of the chart are not doing much work.

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In the following chart, I used the map as a color legend. Also, an additional plot shows each region's price level against the national average.

One can certainly ditch the map altogether, which makes having seven colors unnecessary. To address other questions, just stack on other charts, for example, showing the price increase versus last year.

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From a Trifecta Checkup perspective, we find that the trouble starts with the Q corner. There are several important questions not addressed by the graphic. In the D corner, no context is provided to interpret the data. Are these prices abnormal? How do they compare to the national average or to a year ago? In the V corner, the chart takes too much effort to comprehend a basic fact, such as which region has the highest average price.

For more on the Trifecta Checkup, see this guide.

 

Metaphors, maps, and communicating data

There are some data visualization that are obviously bad. But what makes them bad?

Here is an example of such an effort:

This visualization of carbon emissions is not successful. There is precious little that a reader can learn from this chart without expensing a lot of effort. It's relatively easy to identify the largest emitters of carbon but since the data are not expressed per-capita, the chart mainly informs us which countries have the largest populations. 

The color of the bubbles informs readers which countries belong to which parts of the world. However, it distorts the location of countries within regions, and regions relative to regions, as the primary constraint is fitting the bubbles inside the shape of a foot.

The visualization gives a very rough estimate of the relative sizes of total emissions. The circles not being perfect circles don't help. 

It's relatively easy to list the top emitters in each region but it's hard to list the top 10 emitters in the world (try!) 

The small emitters stole all of the attention as they account for most of the labels - and they engender a huge web of guiding lines - an unsightly nuisance.

The diagram clings dearly to the "carbon footprint" metaphor. Does this metaphor help readers consume the emissions data? Conversely, does it slow them down?

A more conventional design uses a cartogram, a type of map in which the positioning of countries are roughly preserved while the geographical areas are coded to the data. Here's how it looks:

I can't seem to source this effort. If any reader can find the original source, please comment below.

This cartogram is a rearrangement of the footprint illustration. The map construct eliminates the need to include a color legend which just tells people which country is in which continent. The details of smaller countries are pushed to the bottom. 

In the footprint visualization, I'd even consider getting rid of the legend completely. This means trusting that readers know South Africa is part of Africa, and China is part of Asia.

Imagine: what if this chart comes without a color legend? Do we really need it?

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I'd like to try a word cloud visual for this dataset. Something that looks like this (obviously with the right data encoding):

(This map is by Michael Tompsett who sells it here.)

 

Reading an infographic about our climate crisis

Let's explore an infographic by SCMP, which draws attention to the alarming temperature recorded at Verkhoyansk in Russia on June 20, 2020. The original work was on the back page of the printed newspaper, referred to in this tweet.

This view of the globe brings out the two key pieces of evidence presented in the infographic: the rise in temperature in unexpected places, and the shrinkage of the Arctic ice.

A notable design decision is to omit the color scale. On inspection, the scale is present - it was sewn into the graphic.

I applaud this decision as it does not take the reader's eyes away from the graphic. Some information is lost as the scale isn't presented in full details but I doubt many readers need those details.

A key takeaway is that the temperature in Verkhoyansk, which is on the edge of the Arctic Circle, was the same as in New Delhi in India on that day. We can see how the red was encroaching upon the Arctic Circle.

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Next, the rapid shrinkage of the Arctic ice is presented in two ways. First, a series of maps.

The annotations are pared to the minimum. The presentation is simple enough such that we can visually judge that the amount of ice cover has roughly halved from 1980 to 2009.

A numerical measure of the drop is provided on the side.

Then, a line chart reinforces this message.

The line chart emphasizes change over time while the series of maps reveals change over space.

This chart suggests that the year 2020 may break the record for the smallest ice cover since 1980. The maps of Australia and India provide context to interpret the size of the Arctic ice cover.

I'd suggest reversing the pink and black colors so as to refer back to the blue and pink lines in the globe above.

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The final chart shows the average temperature worldwide and in the Arctic, relative to a reference period (1981-2000).

This one is tough. It looks like an area chart but it should be read as a line chart. The darker line is the anomaly of Arctic average temperature while the lighter line is the anomaly of the global average temperature. The two series are synced except for a brief period around 1940. Since 2000, the temperatures have been dramatically rising above that of the reference period.

If this is a stacked area chart, then we'd interpret the two data series as summable, with the sum of the data series signifying something interesting. For example, the market shares of different web browsers sum to the total size of the market.

But the chart above should not be read as a stacked area chart because the outside envelope isn't the sum of the two anomalies. The problem is revealed if we try to articulate what the color shades mean.

On the far right, it seems like the dark shade is paired with the lighter line and represents global positive anomalies while the lighter shade shows Arctic's anomalies in excess of global. This interpretation only works if the Arctic line always sits above the global line. This pattern is broken in the late 1990s.

Around 1999, the Arctic's anomaly is negative while the global anomaly is positive. Here, the global anomaly gets the lighter shade while the Arctic one is blue.

One possible fix is to encode the size of the anomaly into the color of the line. The further away from zero, the darker the red/blue color.

 

 

Dreamy Hawaii

I really enjoyed this visual story by ProPublica and Honolulu Star-Advertiser about the plight of beaches in Hawaii (link).

The story begins with a beautiful invitation:

This design reminds me of Vimeo's old home page. (It no longer looks like this today but this screenshot came from when I was the data guy there.) In both cases, the images are not static but moving.

The tour de force of this visual story is an annotated walk along the Lanikai Beach. Here is a snapshot at one of the stops:

This shows a particular homeowner who, according to documents, was permitted to rebuild a destroyed seawall even though officials were supposed to disallow reconstruction in order to protect beaches from eroding. The property is marked on the map above. The image inside the box is a gif showing waves smashing the seawall.

As the reader scrolls down, the image window runs through a carousel of gifs of houses along the beach. The images are synchronized to the reader's progress along the shore. The narrative makes stops at specific houses at which point a text box pops up to provide color commentary.

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The erosion crisis is shown in this pair of maps.

There's some fancy work behind the scenes to patch together images, and estimate the boundaries of th beaches.

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The following map is notable for its simplicity. There are no unnecessary details and labels. We don't need to know the name of every street or a specific restaurant. Removing excess details makes readers focus on the informative parts. 

Clicking on the dots brings up more details.

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Enjoy the entire story here.

I made a streamgraph

The folks at FiveThirtyEight were excited about the following dataviz they published last week two weeks ago, illustrating the progression of vote-counting by state. (link) That was indeed the unique and confusing feature of the 2020 Presidential election in the States. For those outside the U.S., what happened (by and large) was that many Americans, skewing Biden supporters, voted by mail before Election Day but their votes were sometimes counted after the same-day votes were tallied.

 

A number of us kept staring at these charts, hoping for a how-to-read-it explanation. Here is a zoom-in for the state of Michigan:

To save you the trouble, here is how.

The key is to fight your urge to look at the brown area. I know, it's pretty hard to ignore the biggest areas of every chart. But try to make them disappear.

Focus on the top edge of the chart. This line gives the total number of votes counted so far. In Michigan, by hour 12, about 2.4 million votes were counted, and by hour 72, 2.8 million votes were on the book. This line gives the sum of the two major parties' vote totals [since third parties got negligible votes in this election, I'm ignoring them so as to simplify the discussion].

Next, look at the red and blue areas. These represent the gap in the number of votes between the two parties' current vote totals. If the area is red, Trump was leading; if blue, Biden was leading. Each color flip represents a lead change. Suppress the urge to interpret red as the number or share of Trump votes.

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What have we learned about the vote counting in Michigan?

Counting significantly slowed after the 12th hour. Trump raced to a lead on Election Day, and around hour 20, the race was dead even, and after that, Biden overtook Trump and never looked back. Throughout most of this period, the vote lead was small compared to the total votes cast although at the end, the Biden lead was noticeable.

If you insist on interpreting the brown area, it is equal to twice the vote total of the second-place candidate, so it really isn't something you want to look at.

Just for contrast, here is the chart for Iowa:

Trump led from beginning to end, with his lead widening slightly as more votes were counted.

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As I was stewing over this chart, a ominous thought overcame me. Would a streamgraph work for this data? You don't hear much about streamgraphs here because I rarely favor them (see this long-ago post) but let's just try one and see.

(These streamgraphs were made in R using the streamgraph package. Post-processing was applied to customize the labeling.)

This chart conveys all the key points listed before. You can see how the gap evolved over time, the lead flips, which candidate was in the lead, and the total mass of votes counted at different times. The gap is shown in the middle.

I can't say I'm completely happy with the streamgraph - I hope readers don't care about the numbers because it's hard to evaluate a difference when it's split two ways on either side of the middle axis!

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If you come up with a better idea, make sure to leave a comment.

 

 

 

 

Election visual 3: a strange, mash-up visualization

Continuing our review of FiveThirtyEight's election forecasting model visualization (link), I now look at their headline data visualization. (The previous posts in this series are here, and here.)

It's a set of 22 maps, each showing one election scenario, with one candidate winning. What chart form is this?

Small multiples may come to mind. A small-multiples chart is a grid in which every component graphic has the same form - same chart type, same color scheme, same scale, etc. The only variation from graphic to graphic is the data. The data are typically varied along a dimension of interest, for example, age groups, geographic regions, years. The following small-multiples chart, which I praised in the past (link), shows liquor consumption across the world.

Each component graphic changes according to the data specific to a country. When we scan across the grid, we draw conclusions about country-to-country variations. As with convention, there are as many graphics as there are countries in the dataset. Sometimes, the designer includes only countries that are directly relevant to the chart's topic.

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What is the variable FiveThirtyEight chose to vary from map to map? It's the scenario used in the election forecasting model.

This choice is unconventional. The 22 scenarios is a subset of the 40,000 scenarios from the simulation - we are left wondering how those 22 are chosen.

Returning to our question: what chart form is this?

Perhaps you're reminded of the dot plot from the previous post. On that dot plot, the designer summarized the results of 40,000 scenarios using 100 dots. Since Biden is the winner in 75 percent of all scenarios, the dot plot shows 75 blue dots (and 25 red).

The map is the new dot. The 75 blue dots become 16 blue maps (rounded down) while the 25 red dots become 6 red maps.

Is it a pictogram of maps? If we ignore the details on the maps, and focus on the counts of colors, then yes. It's just a bit challenging because of the hole in the middle, and the atypical number of maps.

As with the dot plot, the map details are a nice touch. It connects readers with the simulation model which can feel very abstract.

Oddly, if you're someone familiar with probabilities, this presentation is quite confusing.

With 40,000 scenarios reduced to 22 maps, each map should represent 1818 scenarios. On the dot plot, each dot should represent 400 scenarios. This follows the rule for creating pictograms. Each object in a pictogram - dot, map, figurine, etc. - should encode an equal amount of the data. For the 538 visualization, is it true that each of the six red maps represents 1818 scenarios? This may be the case but not likely.

Recall the dot plot where the most extreme red dot shows a scenario in which Trump wins 376 out of 538 electoral votes (margin = 214). Each dot should represent 400 scenarios. The visualization implies that there are 400 scenarios similar to the one on display. For the grid of maps, the following red map from the top left corner should, in theory, represent 1,818 similar scenarios. Could be, but I'm not sure.

Mathematically, each of the depicted scenario, including the blowout win above, occurs with 1/40,000 chance in the simulation. However, one expects few scenarios that look like the extreme scenario, and ample scenarios that look like the median scenario.  

So, the right way to read the 538 chart is to ignore the map details when reading the embedded pictogram, and then look at the small multiples of detailed maps bearing in mind that extreme scenarios are unique while median scenarios have many lookalikes.

(Come to think about it, the analogous situation in the liquor consumption chart is the relative population size of different countries. When comparing country to country, we tend to forget that the data apply to large numbers of people in populous countries, and small numbers in tiny countries.)

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There's a small improvement that can be made to the detailed maps. As I compare one map to the next, I'm trying to pick out which states that have changed to change the vote margin. Conceptually, the number of states painted red should decrease as the winning margin decreases, and the states that shift colors should be the toss-up states.

So I'd draw the solid Republican (Democratic) states with a lighter shade, forming an easily identifiable bloc on all maps, while the toss-up states are shown with a heavier shade.

Here, I just added a darker shade to the states that disappear from the first red map to the second.

Election visuals 2: informative and playful

In yesterday's post, I reviewed one section of 538's visualization of its election forecasting model, specifically, the post focuses on the probability plot visualization.

The visualization, technically called  a pdf, is a mainstay of statistical graphics. While every one of 40,000 scenarios shows up on this chart, it doesn't offer a direct answer to our topline question. What is Nate's call at this point in time? Elsewhere in their post, we learn that the 538 model currently gives Biden a 75% chance of winning, thrice that of Trump's.

In graphical terms, the area to the right of the 270-line is three times the size of the left area (on the bottom chart). That's not apparent in the pdf representation. Addressing this, statisticians may convert the pdf into a cdf, which depicts the cumulative area as we sweep from the left to the right along the horizontal axis.  

The cdf visualization rarely leaves the pages of a scientific journal because it's not easy for a novice to understand. Not least because the relevant probability is 1 minus the cumulative probability. The cdf for the bottom chart will show 25% at the 270-line while the chance of Biden winning is 1 - 25% = 75%.

The cdf presentation is also wasteful for the election scenario. No one cares about any threshold other than the 270 votes needed to win, but the standard cdf shows every possible threshold.

The second graphical concept in the 538 post (link) is an attempt to solve this problem.

If you drop all the dots to an imaginary horizontal baseline, the above dotplot looks like this:

There is a recent trend toward centering dots to produce symmetry. It's actually harder to perceive the differences in heights of the band.

The secret sauce is to put down 100 dots, with a 75-25 blue-red split that conveys the 75% chance of a Biden win. Imposing the pdf line from the other visualization, I find that the density of dots roughly mimics the probability of outcomes.

It's easier to estimate the blue vs red areas using those dots than the lines.

The dots are stuffed toys. Clicking on each dot reveals a map showing one of the 40,000 scenarios. It displays which candidate wins which state. For example, the most extreme example of a Trump win is:

Here is a scenario of a razor-tight election won by Trump:

This presentation has a weakness as well. It gives the impression that each of the dots is equally important because they are the same size. In reality, the importance of each dot is proportional to the height of the band. Since the band is generally wider near the middle, the dots near the middle are more likely scenarios than the dots shown on the two edges.

On balance, I like this visualization that is both informative and playful.

As before, what strikes me about the simulation result is the flatness of the probability surface. This feature is obscured when we summarize the result as 75% chance of a Biden victory.

Designs of two variables: map, dot plot, line chart, table

The New York Times found evidence that the richest segments of New Yorkers, presumably those with second or multiple homes, have exited the Big Apple during the early months of the pandemic. The article (link) is amply assisted by a variety of data graphics.

The first few charts represent different attempts to express the headline message. Their appearance in the same article allows us to assess the relative merits of different chart forms.

First up is the always-popular map.

The advantage of a map is its ease of comprehension. We can immediately see which neighborhoods experienced the greater exoduses. Clearly, Manhattan has cleared out a lot more than outer boroughs.

The limitation of the map is also in view. With the color gradient dedicated to the proportions of residents gone on May 1st, there isn't room to express which neighborhoods are richer. We have to rely on outside knowledge to make the correlation ourselves.

The second attempt is a dot plot.

We may have to take a moment to digest the horizontal axis. It's not time moving left to right but income percentiles. The poorest neighborhoods are to the left and the richest to the right. I'm assuming that these percentiles describe the distribution of median incomes in neighborhoods. Typically, when we see income percentiles, they are based on households, regardless of neighborhoods. (The former are equal-sized segments, unlike the latter.)

This data graphic has the reverse features of the map. It does a great job correlating the drop in proportion of residents at home with the income distribution but it does not convey any spatial information. The message is clear: The residents in the top 10% of New York neighborhoods are much more likely to have left town.

In the following chart, I attempted a different labeling of both axes. It cuts out the need for readers to reverse being home to not being home, and 90th percentile to top 10%.

The third attempt to convey the income--exit relationship is the most successful in my mind. This is a line chart, with time on the horizontal axis.

The addition of lines relegates the dots to the background. The lines show the trend more clearly. If directly translated from the dot plot, this line chart should have 100 lines, one for each percentile. However, the closeness of the top two lines suggests that no meaningful difference in behavior exists between the 20th and 80th percentiles. This can be conveyed to readers through a short note. Instead of displaying all 100 percentiles, the line chart selectively includes only the 99th , 95th, 90th, 80th and 20th percentiles. This is a design choice that adds by subtraction.

Along the time axis, the line chart provides more granularity than either the map or the dot plot. The exit occurred roughly over the last two weeks of March and the first week of April. The start coincided with New York's stay-at-home advisory.

This third chart is a statistical graphic. It does not bring out the raw data but features aggregated and smoothed data designed to reveal a key message.

I encourage you to also study the annotated table later in the article. It shows the power of a well-designed table.

[P.S. 6/4/2020. On the book blog, I have just published a post about the underlying surveillance data for this type of analysis.]