Two challenging charts showing group distributions

Long-time reader Georgette A. found this chart from a Linkedin post by David Curran:

She found it hard to understand. Me too.

It's one of those charts that require some time to digest. And when you figured it out, you don't get the satisfaction of time well spent.

***

If I have to write a reading guide for this chart, I'd start from the right edge. The dataset consists of the top 2000 English words, ranked by popularity. The right edge of the chart says that roughly two-thirds of these 2000 words are of Germanic origin, followed by 20% French origin, 10% Latin origin, and 3% "others".

Now, look at the middle of the chart, where the 1000 gridline lies. The analyst did the same analysis but using just the top 1000 words, instead of the top 2000 words. Not surprisingly, Germanic words predominate. In fact, Germanic words account for an even higher percentage of the total, roughly three-quarters. French words are at 16% (relative to 20%), and Latin at 7% (compared to 10%).

The trend is this: as we restrict the word list to fewer and more popular words, the more Germanic words dominate. Of the top 50 words, all but 1 is of Germanic origin. (You can't tell that directly from the chart but you can figure it out if you measure it and do some calculations.)

Said differently, there are some non-Germanic words in the English language but they tend not to be used particularly often.

As we move our eyes from left to right on this chart, we are analyzing more words but the newly added words are less popular than those included prior. The distribution of words by origin is cumulative.

The problem with this data visualization is that it doesn't "locate" where these non-Germanic words exist. It's focused on a cumulative metric so the reader has to figure out where the area has increased and where it has flat-lined. This task is quite challenging in an area chart.

***

The following chart showing the same information is more canonical in the scientific literature.

This chart also requires a reading guide for those uninitiated. (Therefore, I'm not saying it's better than the original.)

The chart shows how words of a specific origin accumulates over the top X most popular English words. Each line starts at 0% on the left and ends at 100% on the right.

Note that the "other" line hugs to the zero level until X = 400, which means that there are no words of "other" origin in the top 400 list. We can see that words of "other" origin are mostly found between top 700-1000 and top 1700-2000, where the line is steepest. We can be even more precise: about 25% of these words are found in the top 700-1000 while 45% are found in the top 1700-2000.

In such a chart, the 45 degree line acts as a reference line. Any line that follows the 45 degree line indicates an even distribution: X% of the words of origin A are found in the top X% of the distribution. Origin A's words are not more or less popular than average anywhere in the distribution.

In this chart, nothing is on top of the 45 degree line. The Germanic line is everywhere above the 45 degree line. This means that on the left side, the line is steeper than 45 degrees while on the right side, its slope is less than 45 degrees. In other words, Germanic words are biased towards the left side, i.e. they are more likely to be popular words.

For example, amongst the top 400 (20%) of the word list, Germanic words accounted for 27%.

I can't imagine this chart is easy for anyone who hasn't seen it before; but if you are a scientist or economist, you might find this one easier to digest than the original.

 

 

Five-value summaries of distributions

BG commented on my previous post, describing her frustration with the “stacked range chart”:

A stacked graph visualizes cubes stacked one on top of the other. So you can't use it for negative numbers, because there's no such thing [as] "negative data". In graphs, a "minus" sign visualizes the opposite direction of one series from another. Doing average plus average plus average plus average doesn't seem logical at all.

***

I have already planned a second post to discuss the problems of using a stacked column chart to show markers of a numeric distribution.

I tried to replicate how the Youtuber generated his “stacked range chart” by appropriating Excel’s stacked column chart, but failed. I think there are some missing steps not mentioned in the video. At around 3:33 of the video, he shows a “hack” involving adding 100 degrees (any large enough value) to all values (already converted to ranges). Then, the next screen displays the resulting chart. Here is the dataset on the left and the chart on the right.

Afterwards, he replaces the axis labels with new labels, effectively shifting the axis. But something is missing from the narrative. Since he’s using a stacked column chart, the values in the table are encoded in the heights of the respective blocks. The total stacked heights of each column should be in the hundreds since he has added 100 to each cell. But that’s not what the chart shows.

***

In the rest of the post, I’ll skip over how to make such a chart in Excel, and talk about the consequences of inserting “range” values into the heights of the blocks of a stacked column chart.

Let’s focus on London, Ontario; the five temperature values, corresponding to various average temperatures, are -3, 5, 9, 14, 24. Just throwing those numbers into a stacked column chart in Excel results in the following useless chart:

The temperature averages are cumulatively summed, which makes no sense, as noted by reader BG. [My daily temperature data differ somewhat from those in the Youtube. My source is here.]

We should ignore the interiors of the blocks, and instead interpret the edges of these blocks. There are five edges corresponding to the five data values. As in:

The average temperature in London, Ontario (during Spring 2023-Winter 2024) is 9 C. This overall average hides seasonal as well as diurnal variations in temperature.

If we want to acknowledge that night-time temperatures are lower than day-time temperatures, we draw attention to the two values bracketing 9 C, i.e. 5 C and 14 C. The average daytime (max) temperature is 14 C while the average night-time (min) temperature is 5 C. Furthermore, Ontario experiences seasons, so that the average daytime temperature of 14 C is subject to seasonal variability; in the summer, it goes up to 24 C. In the winter, the average night-time temperature goes down to -3 C, compared to 5 C across all seasons. [For those paying closer attention, daytime/max and night-time/min form congruous pairs because the max temperature occurs during daytime while the min temperature occurs during night-time. Thus, the average of maximum temperatures is the same as the average of daytime maximum temperatures.]

The above dotplot illustrates this dataset adequately. The Youtuber explained why he didn’t like it – I couldn’t quite make sense of what he said. It’s possible he thinks the gaps between those averages are more meaningful than the averages themselves, and therefore he prefers a chart form that draws our attention to the ranges, rather than the values.

***

Our basic model of temperature can be thought of as: temperature on a given day = overall average + adjustment for seasonality + adjustment for diurnality.

Take the top three values 9, 14, 24 from above list. Starting at the overall average of 9 C, the analyst gets to 14 if he hones in on max daily temperatures, and to 24 if he further restricts the analysis to summer months (which have the higher temperatures). The second gap is 10 C, twice as large as the first gap of 5 C. Thus, the seasonal fluctuations have larger magnitude than daily fluctuations. Said differently, the effect of seasons on temperature is bigger than that of hour of day.

In interpreting the “ranges” or gaps between averages, narrow ranges suggest low variability while wider ranges suggest higher variability.

Here's a set of boxplots for the same data:

The boxplot "edges" also demarcate five values; they are not the same five values as defined by the Youtuber but both sets of five values describe the underlying distribution of temperatures.

 

P.S. For a different example of something similar, see this old post.

What is this "stacked range chart"?

Long-time reader Aleksander B. sent me to this video (link), in which a Youtuber ranted that most spreadsheet programs do not make his favorite chart. This one:

Two questions immediately come to mind: a) what kind of chart is this? and b) is it useful?

Evidently, the point of the above chart is to tell readers there are (at least) three places called “London”, only one of which features red double-decker buses. He calls this a “stacked range chart”. This example has three stacked columns, one for each place called London.

What can we learn from this chart? The range of temperatures is narrowest in London, England while it is broadest in London, Ontario (Canada). The highest temperature is in London, Kentucky (USA) while the lowest is in London, Ontario.

But what kind of “range” are we talking about? Do the top and bottom of each stacked column indicate the maximum and minimum temperatures as we’ve interpreted them to be? In theory, yes, but in this example, not really.

Let’s take one step back, and think about the data. Elsewhere in the video, another version of this chart contains a legend giving us hints about the data. (It's the chart on the right of the screenshot.)

Each column contains four values: the average maximum and minimum temperatures in each place, the average maximum temperature in summer, and the average minimum temperature in winter. These metrics are mouthfuls of words, because the analyst has to describe what choices were made while aggregating the raw data.

The raw data comprise daily measurements of temperatures at each location. (To make things even more complex, there are likely multiple measurement stations in each town, and thus, the daily temperatures themselves may already be averages; or else, the analyst has picked a representative station for each town.) From this single sequence of daily data, we extract two subsequences: the maximum daily, and the minimum daily. This transformation acknowledges that temperatures fluctuate, sometimes massively, over the course of each day.

Each such subsequence is aggregated to four representative numbers. The first pair of max, min is just the averages of the respective subsequences. The remaining two numbers require even more explanation. The “summer average maximum temperature” should be the average of the max subsequence after filtering it down to the “summer” months. Thus, it’s a trimmed average of the max subsequence, or the average of the summer subsequence of the max subsequence. Since summer temperatures are the highest of the four seasons, this number suggests the maximum of the max subsequence, but it’s not the maximum daily maximum since it’s still an average. Similarly, the “winter average minimum temperature” is another trimmed average, computed over the winter months, which is related to but not exactly the minimum daily minimum.

Thus, the full range of each column is the difference between the trimmed summer average and the trimmed winter average. I assume weather scientists use this metric instead of the full range of max to min temperature because it’s less affected by outlier values.

***

Stepping out of the complexity, I’ll say this: what the “stacked range chart” depicts are selected values along the distribution of a single numeric data series. In this sense, this chart is a type of “boxplot”.

Here is a random one I grabbed from a search engine.

A boxplot, per its inventor Tukey, shows a five-number summary of a distribution: the median, the 25^th and 75^th percentile, and two “whisker values”. Effectively, the boxplot shows five percentile values. The two whisker values are also percentiles, but not fixed percentiles like 25^th, 50^th, and 75^th. The placement of the whiskers is determined automatically by a formula that determines the threshold for outliers, which in turn depends on the shape of the data distribution. Anything contained within the whiskers is regarded as a “normal” value of the distribution, not an outlier. Any value larger than the upper whisker value, or lower than the lower whisker value, is an outlier. (Outliers are shown individually as dots above or below the whiskers - I see this as an optional feature because it doesn't make sense to show them individually for large datasets with lots of outliers.)

The stacked range chart of temperatures picks off different waypoints along the distribution but in spirit, it is a boxplot.

***

This discussion leads me to the answer to our second question: is the "stacked range chart" useful?  The boxplot is indeed useful. It does a good job describing the basic shape of any distribution.

I make variations of the boxplot all the time, with different percentiles. One variation commonly seen out there replaces the whisker values with the maximum and minimum values. Thus all the data live within the whiskers. This wasn’t what Tukey originally intended but the max-min version can be appropriate in some situations.

Most statistical software makes the boxplot. Excel is the one big exception. It has always been a mystery to me why the Excel developers are so hostile to the boxplot.

 

P.S. Here is the official manual for making a box plot in Excel. I wonder if they are the leading promoter of the max-min boxplot that strays from Tukey's original. It is possible to make the original whiskers but I suppose they don't want to explain it, and it's much easier to have people compute the maximum and minimum values in the dataset.

The max-min boxplot is misleading if the dataset contains true outliers. If the maximum value is really far from the 75th percentile, then most of the data between the 75th and 100th percentile could be sitting just above the top of the box.

 

P.S. [1/9/2025] See the comments below. Steve made me realize that the color legend of the London chart actually has five labels, the last one is white which blends into the white background. Note that, in the next post in this series, I found that I could not replicate the guy's process to produce the stacked column chart in Excel so I went in a different direction.

Election coverage prompts good graphics

The election broadcasts in the U.S. are full-day affairs, and they make a great showcase for interactive graphics.

The election setting is optimal as it demands clear graphics that are instantly digestible. Anything else would have left viewers confused or frustrated.

The analytical concepts conveyed by the talking heads during these broadcasts are quite sophisticated, and they did a wonderful job at it.

***

One such concept is the value of comparing statistics against a benchmark (or, even multiple benchmarks). This analytics tactic comes in handy in the 2024 election especially, because both leading candidates are in some sense incumbents. Kamala was part of the Biden ticket in 2020, while Trump competed in both 2016 and 2020 elections.

In the above screenshot, taken around 11 pm on election night, the MSNBC host (that looks like Steve K.) was searching for Kamala votes because it appeared that she was losing the state of Georgia. The question of the moment: were there enough votes left for her to close the gap?

In the graphic (first numeric column), we were seeing Kamala winning 65% of the votes, against Trump's 34%, in Douglas county in Georgia. At first sight, one would conclude that Kamala did spectacularly well here.

But, is 65% good enough? One can't answer this question without knowing past results. How did Biden-Harris do in the 2020 election when they won the presidency?

The host touched the interactive screen to reveal the second column of numbers, which allows viewers to directly compare the results. At the time of the screenshot, with 94% of the votes counted, Kamala was performing better in this county than they did in 2020 (65% vs 62%). This should help her narrow the gap.

If in 2020, they had also won 65% of the Douglas county votes, then, we should not expect the vote margin to shrink after counting the remaining 6% of votes. This is why the benchmark from 2020 is crucial. (Of course, there is still the possibility that the remaining votes were severely biased in Kamala's favor but that would not be enough, as I'll explain further below.)

All stations used this benchmark; some did not show the two columns side by side, making it harder to do the comparison.

Interesting side note: Douglas county has been rapidly shifting blue in the last two decades. The proportion of whites in the county dropped from 76% to 35% since 2000 (link).

***

Though Douglas county was encouraging for Kamala supporters, the vote gap in the state of Georgia at the time was over 130,000 in favor of Trump. The 6% in Douglas represented only about 4,500 votes (= 70,000*0.06/0.94). Even if she won all of them (extremely unlikely), it would be far from enough.

So, the host flipped to Fulton county, the most populous county in Georgia, and also a Democratic stronghold. This is where the battle should be decided.

Using the same format - an interactive version of a small-multiples arrangement, the host looked at the situation in Fulton. The encouraging sign was that 22% of the votes here had not yet been counted. Moreover, she captured 73% of those votes that had been tallied. This was 10 percentage points better than her performance in Douglas, Ga. So, we know that many more votes were coming in from Fulton, with the vast majority being Democratic.

But that wasn't the full story. We have to compare these statistics to our 2020 benchmark. This comparison revealed that she faced a tough road ahead. That's because Biden-Harris also won 73% of the Fulton votes in 2020. She might not earn additional votes here that could be used to close the state-wide gap.

If the 73% margin held to the end of the count, she would win 90,000 additional votes in Fulton but Trump would win 33,000, so that the state-wide gap should narrow by 57,000 votes. Let's round that up, and say Fulton halved Trump's lead in Georgia. But where else could she claw back the other half?

***

From this point, the analytics can follow one of two paths, which should lead to the same conclusion. The first path runs down the list of Georgia counties. The second path goes up a level to a state-wide analysis, similar to what was done in my post on the book blog (link).

Around this time, Georgia had counted 4.8 million votes, with another 12% outstanding. So, about 650,000 votes had not been assigned to any candidate. The margin was about 135,000 in Trump's favor, which amounted to 20% of the outstanding votes. But that was 20% on top of her base value of 48% share, meaning she had to claim 68% of all remaining votes. (If in the outstanding votes, she got the same share of 48% as in the already-counted, then she would lose the state with the same vote margin as currently seen, and would lose by even more absolute votes.)

The reason why the situation was more hopeless than it even sounded here is that the 48% base value came from the 2024 votes that had been counted; thus, for example, it included her better-than-benchmark performance in Douglas county. She would have to do even better to close the gap! In Fulton, which has the biggest potential, she was unable to push the vote share above the 2020 level.

That's why in my book blog (link), I suggested that the networks could have called Georgia (and several other swing states) earlier, if they used "numbersense" rather than mathematical impossibility as the criterion.

***

Before ending, let's praise the unsung heroes - the data analysts who worked behind the scenes to make these interactive graphics possible.

The graphics require data feeds, which cover a broad scope, from real-time vote tallies to total votes casted, both at the county level and the state level. While the focus is on the two leading candidates, any votes going to other candidates have to be tabulated, even if not displayed. The talking heads don't just want raw vote counts; in order to tell the story of the election, they need some understanding of how many votes are still to be counted, where they are coming from, what's the partisan lean on those votes, how likely is the result going to deviate from past elections, and so on.

All those computations must be automated, but manually checked. The graphics software has to be reliable; the hosts can touch any part of the map to reveal details, and it's not possible to predict all of the user interactions in advance.

Most importantly, things will go wrong unexpectedly during election night so many data analysts were on standby, scrambling to fix issues like breakage of some data feed from some county in some state.

Book review: Getting (more out of ) Graphics by Antony Unwin

Antony Unwin, a statistics professor at Augsburg, has published a new dataviz textbook called "Getting (more out of) Graphics", and he kindly sent me a review copy. (Amazon link)

I am - not surprisingly - in the prime audience for such a book. It covers some gaps in the market:
a) it emphasizes exploratory graphics rather than presentation graphics
b) it deals not just with designing graphics but also interpreting (i.e. reading) them
c) it covers data pre-processing and data visualization in a more balanced way
d) it develops full case studies involving multiple graphics from the same data sources

The book is divided into two parts: the first, which covers 75% of the materials, details case studies, while the final quarter of the book offers "advice". The book has a github page containing R code which, as I shall explain below, is indispensable to the serious reader.

Given the aforementioned design, the case studies in Unwin's book have a certain flavor: most of the data sets are relatively complex, with many variables, including a time component. The primary goal of Unwin's exploratory graphics can be stated as stimulating "entertaining discussions" about and "involvment" with the data. They are open-ended, and frequently inconclusive. This is a major departure from other data visualization textbooks on the market, and also many of my own blog posts, where we focus on selecting a good graphic for presenting insights visually to an intended audience, without assuming domain expertise.

I particularly enjoyed the following sections: a discussion of building graphs via "layering" (starting on p. 326), enumeration of iterative improvement to graphics (starting on p. 402), and several examples of data wrangling (e.g. p.52).

Unwin does not give "advice" in the typical style of do this, don't do that. His advice is fashioned in the style of an analyst. He frames and describes the issues, shows rather than tells. This paragraph from the section about grouping data is representative:

Sorting into groups gets complicated when there are several grouping variables. Variables may be nested in a hierarchy... or they may have no such structure... Groupings need to be found that reflect the aims of the study. (p. 371)

He writes down what he has done, may provide a reason for his choices, but is always understated. He sees no point in selling his reasoning.

The structure of the last part of the book, the "advice" chapters, is quite unusual. The chapter headers are: (data) provenance and quality; wrangling; colour; setting the scene (scaling, layout, etc.); ordering, sorting and arranging; what affects interpretation; and varieties of plots.

What you won't find are extended descriptions of chart forms, rules of visualization, or flowcharts tying data types to chart forms. Those are easily found online if you want them (you probably won't care if you're reading Unwin's book.)

***

For the serious reader, the book should be consumed together with the code on github. Find specific graphs from the case studies that interest you, open the code in your R editor, and follow how Unwin did it. The "advice" chapters highlight points of interest from the case studies presented earlier so you may start there, cross-reference the case studies, then jump to the code.

Unfortunately, the code is sparsely commented. So also open up your favorite chatbot, which helps to explain the code, and annotate it yourself. Unwin uses R, and in particular, lives in the "tidyverse".

To understand the data manipulation bits, reviewing the code is essential. It's hard to grasp what is being done to the data without actually seeing the datasets. There are no visuals of the datasets in the book, as the text is primarily focused on the workflow leading to a graphic. The data processing can get quite involved, such as Chapter 16.

I'm glad Unwin has taken the time to write this book and publish the code. It rewards the serious reader with skills that are not commonly covered in other textbooks. For example, I was rather amazed to find this sentence (p. 366):

To ensure that a return to a particular ordering is always possible, it is essential to have a variable with a unique value for every case, possibly an ID variable constructed for just this reason. Being able to return to the initial order of a dataset is useful if something goes wrong (and something will).

Anyone who has analyzed real-world datasets would immediately recognize this as good advice but who'd have thought to put it down in a book?

The most dangerous day

Our World in Data published this interesting chart about infant mortality in the U.S.

The article that sent me to this chart called the first day of life the "most dangerous day". This dot plot seems to support the notion, as the "per-day" death rate is the highest on the day of birth, and then drops quite fast (note log scale) over the the first year of life.

***

Based on the same dataset, I created the following different view of the data, using the same dot plot form:

By this measure, a baby has 99.63% chance of surviving the first 30 days while the survival rate drops to 99.5% by day 180.

There is an important distinction between these two metrics.

The "per day" death rate is the chance of dying on a given day, conditional on having survived up to that day. The chance of dying on day 2 is lower partly because some of the more vulnerable ones have died on day 1 or day 0,  etc.

The survival rate metric is cumulative: it measures how many babies are still alive given they were born on day 0. The survival rate can never go up, so long as we can't bring back the dead.

***

If we are assessing a 5-day-old baby's chance of surviving day 6, the "per-day" death rate is relevant since that baby has not died in the first 5 days.

If the baby has just been born, and we want to know the chance it might die in the first five days (or survive beyond day 5), then the cumulative survival rate curve is the answer. If we use the per-day death rate, we can't add the first five "per-day" death rates It's a more complicated calculation of dying on day 0, then having not died on day 0, dying on day 1, then having not died on day 0 or day 1, dying on day 2, etc.

 

The radial is still broken

It's puzzling to me why people like radial charts. Here is a recent set of radial charts that appear in an article in Significance magazine (link to paywall, currently), analyzing NBA basketball data.

This example is not as bad as usual (the color scheme notwithstanding) because the story is quite simple.

The analysts divided the data into three time periods: 1980-94, 1995-15, 2016-23. The NBA seasons were summarized using a battery of 15 metrics arranged in a circle. In the first period, all but 3 of the metrics sat much above the average level (indicated by the inner circle). In the second period, all 15 metrics reduced below the average, and the third period is somewhat of a mirror image of the first, which is the main message.

***

The puzzle: why prefer this circular arrangement to a rectangular arrangement?

Here is what the same graph looks like in a rectangular arrangement:

One plausible justification for the circular arrangement is if the metrics can be clustered so that nearby metrics are semantically related.

Nevertheless, the same semantics appear in a rectangular arrangement. For example, P3-P3A are three point scores and attempts while P2-P2A are two-pointers. That is a key trend. They are neighborhoods in this arrangement just as they are in the circular arrangement.

So the real advantage is when the metrics have some kind of periodicity, and the wraparound point matters. Or, that the data are indexed to directions so north, east, south, west are meaningful concepts.

If you've found other use cases, feel free to comment below.

***

I can't end this post without returning to the colors. If one can take a negative image of the original chart, one should. Notice that the colors that dominate our attention - the yellow background, and the black lines - have no data in them: yellow being the canvass, and black being the gridlines. The data are found in the white polygons.

The other informative element, as one learns from the caption, is the "blue dashed line" that represents the value zero (i.e. average) in the standardized scale. Because the size of the image was small in the print magazine that I was reading, and they selected a dark blue encroaching on black, I had to squint hard to find the blue line.

 

 

Adjust, and adjust some more

This Financial Times report illustrates the reason why we should adjust data.

The story explores the trend in economic statistics during 14 years of governing by conservatives. One of those metrics is so-called council funding (local governments). The graphic is interactive: as the reader scrolls the page, the chart transforms.

The first chart shows the "raw" data.

The vertical axis shows year-on-year change in funding. It is an index relative to the level in 2010. From this line chart, one concludes that council funding decreased from 2010 to around 2016, then grew; by 2020, funding has recovered to the level of 2010 and then funding expanded rapidly in recent years.

When the reader scrolls down, this chart is replaced by another one:

This chart contains a completely different picture. The line dropped from 2010 to 2016 as before. Then, it went flat, and after 2021, it started raising, even though by 2024, the value is still 10 percent below the level in 2010.

What happened? The data journalist has taken the data from the first chart, and adjusted the values for inflation. Inflation was rampant in recent years, thus, some of the raw growth have been dampened. In economics, adjusting for inflation is also called expressing in "real terms". The adjustment is necessary because the same dollar (hmm, pound) is worth less when there is inflation. Therefore, even though on paper, council funding in 2024 is more than 25 percent higher than in 2010, inflation has gobbled up all of that and more, to the point in which, in real terms, council funding has fallen by 20 percent.

This is one material adjustment!

Wait, they have a third chart:

It's unfortunate they didn't stabilize the vertical scale. Relative to the middle chart, the lowest point in this third chart is about 5 percent lower, while the value in 2024 is about 10 percent lower.

This means, they performed a second adjustment - for population change. It is a simple adjustment of dividing by the population. The numbers look worse probably because population has grown during these years. Thus, even if the amount of funding stayed the same, the money would have to be split amongst more people. The per-capita adjustment makes this point clear.

***

The final story is much different from the initial one. Not only was the magnitude of change different but the direction of change reversed.

Whenever it comes to adjustments, remember that all adjustments are subjective. In fact, choosing not to adjust is also subjective. Not adjusting is usually much worse.

 

 

 

 

Excess delay

The hot topic in New York at the moment is congestion pricing for vehicles entering Manhattan, which is set to debut during the month of June. I found this chart (link) that purports to prove the effectiveness of London's similar scheme introduced a while back.

This is a case of the visual fighting against the data. The visual feels very busy and yet the story lying beneath the data isn't that complex.

This chart was probably designed to accompany some text which isn't available free from that link so I haven't seen it. The reader's expectation is to compare the periods before and after the introduction of congestion charges. But even the task of figuring out the pre- and post-period is taking more time than necessary. In particular, "WEZ" is not defined. (I looked this up, it's "Western Extension Zone" so presumably they expanded the area in which charges were applied when the travel rates went back to pre-charging levels.)

The one element of the graphic that raises eyebrows is the legend which screams to be read.

Why are there four colors for two items? The legend is not self-sufficient. The reader has to look at the chart itself and realize that purple is the pre-charging period while green (and blue) is the post-charging period (ignoring the distinction between CCZ and WEZ).

While we are solving this puzzle, we also notice that the bottom two colors are used to represent an unchanging quantity - which is the definition of "no congestion". This no-congestion travel rate is a constant throughout the chart and yet a lot of ink of two colors have been spilled on it. The real story is in the excess delay, which the congestion charging scheme was supposed to reduce.

The excess on the chart isn't harmless. The excess delay on the roads has been transferred to the chart reader. It actually distracts from the story the analyst is wanting to tell. Presumably, the story is that the excess delays dropped quite a bit after congestion charging was introduced. About four years later, the travel rates had creeped back to pre-charging levels, whereupon the authorities responded by extending the charging zone to WEZ (which as of the time of the chart, wasn't apparently bringing the travel rate down.)

Instead of that story, the excess of the chart makes me wonder... the roads are still highly congested with travel rates far above the level required to achieve no congestion, even after the charging scheme was introduced.

***

I started removing some of the excess from the chart. Here's the first cut:

This is better but it is still very busy. One problem is the choice of columns, even though the data are found strictly on the top of each column. (Besides, when I chop off the unchanging sections of the columns, I created a start-not-from-zero problem.) Also, the labeling of the months leaves much to be desired, there are too many grid lines, etc.

***

Here is the version I landed on. Instead of columns, I use lines. When lines are used, there is no need for month labels since we can assume a reader knows the structure of months within a year.

A priniciple I hold dear is not to have legends unless it is absolutely required. In this case, there is no need to have a legend. I also brought back the notion of a uncongested travel speed, with a single line (and annotation).

***

The chart raises several questions about the underlying analysis. I'd interested in learning more about "moving car observer surveys". What are those? Are they reliable?

Further, for evidence of efficacy, I think the pre-charging period must be expanded to multiple years. Was 2002 a particularly bad year?

Thirdly, assuming WEZ indicates the expansion of the program to a new geographical area, I'm not sure whether the data prior to its introduction represents the travel rate that includes the WEZ (despite no charging) or excludes it. Arguments can be made for each case so the key from a dataviz perspective is to clarify what was actually done.

 

P.S. [6-6-24] On the day I posted this, NY State Governer decided to cancel the congestion pricing scheme that was set to start at the end of June.

What's a histogram?

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.

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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?

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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.

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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.