Charts that ask questions about the German election

In the prior post about Canadian elections, I suggested that designers expand beyond plots of one variable at a time. Today, I look at a project by DataWrapper on the German elections which happened this week. Thanks to long-time blog supporter Antonio for submitting the chart.

The following is the centerpiece of Lisa's work:

Datawrapper_germanelections_cducsu

CDU/CSU is Angela Merkel's party, represented by the black color. The chart answers one question only: did polls correctly predict election results?

The time period from 1994 to 2021 covers eight consecutive elections (counting the one this week). There are eight vertical blocks on the chart representing each administration. The right vertical edge of each block coincides with an election. The chart is best understood as the superposition of two time series.

You can trace the first time series by following a step function - let your eyes follow the flat lines between elections. This dataset shows the popular vote won by the party at each election, with the value updated after each election. The last vertical block represents an election that has not yet happened when this chart was created. As explained in the footnote, Lisa took the average poll result for the last month leading up to the 2021 election - in the context of this chart, she made the assumption that this cycle of polls will be 100% accurate.

The second time series corresponds to the ragged edges of the gray and black areas. If you ignore the colors, and the flat lines, you'll discover that the ragged edges form a contiguous data series. This line encodes the average popularity of the CDU/CSU party according to election polls.

Thus, the area between the step function and the ragged line measures the gap between polls and election day results. When the polls underestimate the actual outcome, the area is colored gray; when the polls are over-optimistic, the area is colored black. In the last completed election of 2017, Merkel's party underperformed relative to the polls. In fact, the polls in the entire period between the 2013 and 2017 uniformly painted a rosier picture for CDU/CSU than actually happened.

The last vertical block is interpreted a little differently. Since the reference level is the last month of polls (rather than the actual popular vote), the abundance of black indicates that Merkel's party has been suffering from declining poll numbers on the approach of this week's election.

***

The picture shown above seems to indicate that these polls are not particularly good. It appears they have limited ability to self-correct within each election cycle. Aside from the 1998-2002 period, the area colors seldom changed within each cycle. That means if the first polling average overestimated the party's popularity, then all subsequent polling averages were also optimistic. (The original post focused on a single pollster, which exacerbates this issue. Compare the following chart with the above, and you'll find even fewer color changes within cycle here:

Datawrapper_germanelections_cdu_singlepoll

Each pollster may be systematically biased but the poll aggregate is less so.)

 

Here's the chart for SDP, which is CDU/CSU's biggest opponent, and likely winner of this week's election:

Datawrapper_germanelections_spd

Overall, this chart has similar features as the CDU/CSU chart. The most recent polls seem to favor the SPD - the pink area indicates that the older polls of this cycle underestimates the last month's poll result.

Both these parties are in long-term decline, with popularity dropping from the 40% range in the 1990s to the 20% range in the 2020s.

One smaller party that seems to have gained followers is the Green party:

Datawrapper_germanelections_green

The excess of dark green, however, does not augur well for this election.

 

 

 

 

 


Tongue in cheek but a master stroke

Andrew jumped on the Benford bandwagon to do a tongue-in-cheek analysis of numbers in Hollywood movies (link). The key graphic is this:

Gelman_hollywood_benford_2-1024x683

Benford's Law is frequently invoked to prove (or disprove) fraud with numbers by examining the distribution of first digits. Andrew extracted movies that contain numbers in their names - mostly but not always sequences of movies with sequels. The above histogram (gray columns) are the number of movies with specific first digits. The red line is the expected number if Benford's Law holds. As typical of such analysis, the histogram is closely aligned with the red line, and therefore, he did not find any fraud. 

I'll blog about my reservations about Benford-style analysis on the book blog later - one quick point is: as with any statistical analysis, we should say there is no statistical evidence of fraud (more precisely, of the kind of fraud that can be discovered using Benford's Law), which is different from saying there is no fraud.

***

Andrew also showed a small-multiples chart that breaks up the above chart by movie groups. I excerpted the top left section of the chart below:

Gelman_smallmultiples_benford

The genius in this graphic is easily missed.

Notice that the red lines (which are the expected values if Benford Law holds) appear identical on every single plot. And then notice that the lines don't represent the same values.

It's great to have the red lines look the same everywhere because they represent the immutable Benford reference. Because the number of movies is so small, he's plotting counts instead of proportions. If you let the software decide on the best y-axis range for each plot, the red lines will look different on different charts!

You can find the trick in the R code from Gelman's blog.

First, the maximum value of each plot is set to the total number of observations. Then, the expected Benford proportions are converted into expected Benford counts. The first Benford count is then shown against an axis topping out at the total count, and thus, relatively, what we are seeing are the Benford proportions. Thus, every red line looks the same despite holding different values.

This is a master stroke.

 

 

 


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).

Wsj_ida_katrina_hurricanes

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!


Visually displaying multipliers

As I'm preparing a blog about another real-world study of Covid-19 vaccines, I came across the following chart (the chart title is mine).

React1_original

As background, this is the trend in Covid-19 cases in the U.K. in the last couple of months, courtesy of OurWorldinData.org.

Junkcharts_owid_uk_case_trend_july_august_2021

The React-1 Study sends swab kits to randomly selected people in England in order to assess the prevalence of Covid-19. Every month, there is a new round of returned swabs that are tested for Covid-19. This measurement method captures asymptomatic cases although it probably missed severe and hospitalized cases. Despite having some shortcomings, this is a far better way to measure cases than the hotch-potch assembling of variable-quality data submitted by different jurisdictions that has become the dominant source of our data.

Rounds 12 and 13 captured an inflection point in the pandemic in England. The period marked the beginning of the end of the belief that widespread vaccination will end the pandemic.

The chart I excerpted up top broke the data down by age groups. The column heights represent the estimated prevalence of Covid-19 during each round - also, described precisely in the paper as "swab positivity." Based on the study's design, one may generalize the prevalence to the population at large. About 1.5% of those aged 13-24 in England are estimated to have Covid-19 around the time of Round 13 (roughly early July).

The researchers came to the following conclusion:

We show that the third wave of infections in England was being driven primarily by the Delta variant in younger, unvaccinated people. This focus of infection offers considerable scope for interventions to reduce transmission among younger people, with knock-on benefits across the entire population... In our data, the highest prevalence of infection was among 12 to 24 year olds, raising the prospect that vaccinating more of this group by extending the UK programme to those aged 12 to 17 years could substantially reduce transmission potential in the autumn when levels of social mixing increase

***

Raise your hand if the graphics software you prefer dictates at least one default behavior you can't stand. I'm sure most hands are up in the air. No matter how much you love the software, there is always something the developer likes that you don't.

The first thing I did with today's chart is to get rid of all such default details.

Redo_react1_cleanup

For me, the bottom chart is cleaner and more inviting.

***

The researchers wanted readers to think in terms of Round 3 numbers as multiples of Round 2 numbers. In the text, they use statements such as:

weighted prevalence in round 13 was nine-fold higher in 13-17 year olds at 1.56% (1.25%, 1.95%) compared with 0.16% (0.08%, 0.31%) in round 12

It's not easy to perceive a nine-fold jump from the paired column chart, even though this chart form is better than several others. I added some subtle divisions inside each orange column in order to facilitate this task:

Redo_react1_multiples

I have recommended this before. I'm co-opting pictograms in constructing the column chart.

An alternative is to plot everything on an index scale although one would have to drop the prevalence numbers.

***

The chart requires an additional piece of context to interpret properly. I added each age group's share of the population below the chart - just to illustrate this point, not to recommend it as a best practice.

Redo_react1_multiples_popshare

The researchers concluded that their data supported vaccinating 13-17 year olds because that group experienced the highest multiplier from Round 12 to Round 13. Notice that the 13-17 year old age group represents only 6 percent of England's population, and is the least populous age group shown on the chart.

The neighboring 18-24 age group experienced a 4.5 times jump in prevalence in Round 13 so this age group is doing much better than 13-17 year olds, right? Not really.

While the same infection rate was found in both age groups during this period, the slightly older age group accounted for 50% more cases -- and that's due to the larger share of population.

A similar calculation shows that while the infection rate of people under 24 is about 3 times higher than that of those 25 and over, both age groups suffered over 175,000 infections during the Round 3 time period (the difference between groups was < 4,000).  So I don't agree that focusing on 13-17 year olds gives England the biggest bang for the buck: while they are the most likely to get infected, their cases account for only 14% of all infections. Almost half of the infections are in people 25 and over.

 


Working hard at clarity

As I am preparing another blog post about the pandemic, I came across the following data graphic, recently produced by the CDC for a vaccine advisory board meeting:

CDC_positivevaccineintent

This is not an example of effective visual communications.

***

For one thing, readers are directed to scour the footnotes to figure out what's going on. If we ignore those for the moment, we see clusters of bubbles that have remained pretty stable from December 2020 to August 2021. The data concern some measure of Americans' intent to take the COVID-19 vaccine. That much we know.

There may have been a bit of an upward trend between January and May, although if you were shown the clusters for December, February and April, you'd think the trend's been pretty flat. 

***

But those colors? What could they represent? You'd surely have to fish this one out of the footnotes. Specifically, this obtuse sentence: "Surveys with multiple time points are shown with the same color bubble for each time point." I had to read it several times. I think it simply means "Color represents the pollster." 

Then it adds: "Surveys with only one time point are shown in gray." which simply means "All pollsters who have only one entry in the dataset are grouped together and shown in gray."

Another problem with this chart is over-plotting. Look at the July cluster. It's impossible to tell how many polls were conducted in July because the circles pile on top of one another. 

***

The appearance of the flat trend is a result of two unfortunate decisions made by the designer. If I retained the chart form, I'd have produced something that looks like this:

Junkcharts_redo_cdcvaccineintent_sameform

The first design choice is to expand the vertical axis to range from 0% to 100%. This effectively squeezes all the bubbles into a small range.

Junkcharts_redo_cdcvaccineintent_startatzero

The second design choice is to enlarge the bubbles causing copious amount of overlapping. 

Junkcharts_redo_cdcvaccineintent_startatzero_bigdots

In particular, this decision blows up the Pew poll (big pink bubble) that contained 10 times the sample size of most of the other polls. The Pew outcome actually came in at 70% but the top of the pink bubble extends to over 80%. Because of this, the outlier poll of December 2020 - which surprisingly printed the highest number of all polls in the entire time window - no longer looks special. 

***

Now, let's see what else we can do to enhance this chart. 

I don't like how bubble size is used to encode the sample size. It creates a weird sensation for anyone who's familiar with sampling errors, and confidence regions. The Pew poll with 10 times the sample size is the most reliable poll of them all. Reliability means the error bars around the Pew poll outcome is the smallest of them all. I tend to think of the area around a point estimate as showing the sampling error so the Pew poll would be a dot, showing the high precision of that estimate. 

But that won't work because larger bubbles catch more of the reader's attention. So, in the following version, all dots have the same size. I encode reliability in the opacity of the color. The darker dots are polls that are more reliable, that have larger sample sizes.

Junkcharts_redo_cdcvaccineintent_opacity

Two of the pollsters have more frequent polling than others. In this next version, I highlighted those two, which reveals the trend better.

Junkcharts_redo_cdcvaccineintent_opacitywithlines

 

 

 


Check your presumptions while you're reading this chart about Israel's vaccination campaign

On July 30, Israel began administering third doses of mRNA vaccines to targeted groups of people. This decision was controversial since there is no science to support it. The policymakers do have educated guesses by experts based on best-available information. By science, I mean actual evidence. Since no one has previously been given three shots, there can be no data on which anyone can root such a decision. Nevertheless, the pandemic does not always give us time to collect relevant data, and so speculative analysis has found its calling.

Dvir Aran, at Technion, has been diligently tracking the situation in Israel on his Twitter. Ten days after July 30, he posted the following chart, which immediately led many commentators to bounce out of their seats crowning the third shot as a magic bullet. Notably, Dvir himself did not endorse such a claim. (See here to learn how other hasty conclusions by experts have fared.)

When you look at Dvir's chart, what do we see?

Dvir_aran_chart

Possibly one of the following two things, depending on what concern you have in your head.

1) The red line sits far above the other two lines, showing that unvaccinated people are much more likely to get infected.

2) The blue line diverges from the green line almost immediately after the 3rd shots started getting into arms, showing that the 3rd shot is super effective.

If you take another moment to look, you might start asking questions, as many in Twitter world did. Dvir was startlingly efficient at answering these queries.

A) Does the green line represent people with 2 or 3 doses, or is it strictly 2 doses? Aron asked this question and got the answer (the former):

AronBrand_israelcases_twoorthreedoses

It's time to check our presumptions. When you read that chart, did you presume it's exactly 2 doses or did you presume it's 2 or 3 doses? Or did you immediately spot the ambiguity? As I said in this article, graphs attain efficiency at communication because the designer leverages unspoken rules - the chart conveys certain information without explicitly placing it on the chart. But this can backfire. In this case, I presumed the three lines to display three non-overlapping groups of people, and thus the green line indicates those with 2 doses but not 3. That presumption led me to misinterpret what's on the chart.

B) What is the denominator of the case rates? Is it literal - by that I mean, all unvaccinated people for the red line, and all people with 3 doses for the blue line? Or is the denominator the population of Israel, the same number for all three lines? Lukas asked this question, and got the answer (the former).

Lukas_denominator

C) Since third shots are recommended for 60 year olds and over who were vaccinated at least 5 months ago, and most unvaccinated Israelis are below 60, this answer opens the possibility that the lines compare apples and oranges. Joe. S. asked about this, and received an answer (all lines display only 60 year olds and over.)

Joescholar_basepopulationquestion

Jason P. asked, and learned that the 5-month-out criterion is immaterial since 90% of the vaccinated have already reached that time point.

JasonPogue_5monthsout

D) We have even more presumptions. Like me, did you presume that the red line represents the "unvaccinated," meaning people who have not had any vaccine shots? If so, we may both be wrong about this. It has become the norm by vaccine researchers to lump "partially vaccinated" people with "unvaccinated", and call this combined group "unvaccinated". Here is an excerpt from a recent report from Public Health Ontario (link to PDF), which clearly states this unintuitive counting rule:

Ontario_case_definition

Notice that in this definition, someone who got infected within 14 days of the first shot is classified as an "unvaccinated" case and not a "partially vaccinated case".

In the following tweet, Dvir gave a hint of what he plotted:

Dvir_group_definition

In a previous analysis, he averaged the rates of people with 0 doses and 1 dose, which is equivalent to combining them and calling them unvaccinated. It's unclear to me what he did to the 1-dose subgroup in our featured chart - did it just vanish from the chart? (How people and cases are classified into these groups is a major factor in all vaccine effectiveness calculations - a topic I covered here. Unfortunately, most published reports do a poor job explaining what the analysts did).

E) Did you presume that all three lines are equally important? That's far from true. Since Israel is the world champion in vaccination, the bulk of the 60+ population form the green line. I asked Dvir and he responded that only 7.5%, or roughly 100K are unvaccinated.

DvirAran_proportionofunvaccinated

That means 1.2 million people are part of the green line, 12 times higher. There are roughly 50 cases per day among unvaccinated, and 370 daily cases among those with 2 or 3 doses. In other words, vaccinated people account for almost 90% of all cases.

Yes, this is inevitable when over 90% of the age group have been vaccinated (but it is predictable on the first day someone blasted everywhere that real-world VE is proved by the fact that almost all new cases were in the unvaccinated.)

If your job is to minimize infections, you should be spending most of your time thinking about the 370 cases among vaccinated than the 50 cases among unvaccinated. If you halve the case rate, that would be a difference of 185 cases vs 25. In Israel, the vaccination campaign has already succeeded; it's time to look forward, which is exactly why they are re-focusing on the already vaccinated.

***

If what you worry about most is the effectiveness of the original two-dose regimen, Dvir's chart raises a puzzle. Ignore the blue line, and remember that the green line already includes everybody represented by the blue line.

In the following chart, I removed the blue line, and added reference lines in dashed purple that correspond to 25%, 50% and 75% vaccine effectiveness. The data plotted on this chart are unadjusted case rates. A 75% effective vaccine cuts case rate by three quarters.

Junkcharts_dviraran_israel_threeshotschart

This chart shows the 2-dose mRNA vaccine was nowhere near 90% effective. (As regular readers know, I don't endorse this simplistic calculation and have outlined the problems here, but this style of calculation keeps getting published and passed around. Those who use it to claim real-world studies confirm prior clinical trial outcomes can either (a) insist on using it and retract their earlier conclusions, or (b) admit that such a calculation was, and is, a bad take.)

Also observe how the vaccinated (green) line is moving away from the unvaccinated (red) line. The vaccine apparently is becoming more effective, which runs counter to the trend used by the Israeli government to justify third doses. This improvement also precedes the start of the third-shot campaign. When the analytical method is bad, it generates all sorts of spurious findings.

***

As Dvir said, it is premature to comment on the third doses based on 10 days of data. For one thing, the vaccine developers insist that their vaccines must be given 14 days to work. In a typical calculation, all of the cases in the blue line fall outside the case-counting window. The effective number of cases that would be attributed to the 3-dose group right now is zero, and the vaccine effectiveness using the standard methodology is 100%, even better than shown in the chart.

There is an alternative interpretation of this graph. Statisticians call this the selection effect. On July 30, the blue line split out of the green: some people were selected to receive the 3rd dose - this includes an official selection (the government makes certain subgroups eligible) as well as a self-selection (within the eligible subgroup, certain people decide to get the 3rd shot earlier.) If those who are less exposed to the virus, or more risk averse, get the shots first, then all that is happening may be that we have split off a high VE subgroup from the green line. Even if the third shot were useless, the selection effect itself could explain the gap.

Statistics is about grays. It's not either-or. It's usually some of each. If you feel like Groundhog Day, you're getting the picture. When they rolled out two doses, we lived through an optimistic period in which most experts rejoiced about 90-100% real-world effectiveness, and then as more people get vaccinated, the effect washed away. The selection effect gradually disappears when vaccination becomes widespread. Are we starting a new cycle of hope and despair? We'll find out soon enough.


Tip of the day: transform data before plotting

The Financial Times called out a twitter user for some graphical mischief. Here are the two charts illustrating the plunge in Bitcoin's price last week : (Hat tip to Mark P.)

Ft_tradingview_btcprices

There are some big differences between the two charts. The left chart depicts this month's price actions, drawing attention to the last week while the right chart shows a longer period of time, starting from 2012. The author of the tweet apparently wanted to say that the recent drop is nothing to worry about. 

The Financial Times reporter noted another subtle difference - the right chart uses a log scale while the left chart is linear. Specifically, it's a log 2 scale, which means that each step up is double the previous number (1, 2, 4, 8, etc.). The effect is to make large changes look smaller. Presumably most readers fail to notice the scale. Even if they do, it's not natural to assign different differences to the same physical distances.

***

Junkcharts_redo_fttradingviewbitcoinpricechart

These price charts always miss the mark. That's because the current price is insufficient to capture whether a Bitcoin investor made money or lost money. If you purchased Bitcoins this month, you lost money. If your purchase was a year ago, you still made quite a bit of money despite the recent price plunge.

The following chart should not be read as a time series, even though the horizontal axis is time. Think date of Bitcoin purchase. This chart tells you how much $1 of Bitcoin is worth last week, based on what day the purchase was made.

Junkcharts_redo_fttradingviewbitcoinpricechart_2

People who bought this year have mostly been in the red. Those who purchased before October 2020 and held on are still very pleased with their decision.

This example illustrates that simple transformations of the raw data yield graphics that are much more informative.

 


Losses trickle down while gains trickle up

In a rich dataset, it's hard to convey all the interesting insights on a single chart. Following up on the previous post, I looked further at the wealth distribution dataset. In the previous post, I showed this chart, which indicated that the relative wealth of the super-rich (top 1%) rose dramatically around 2011.

Redo_bihouseholdwealth_legend

As a couple of commenters noticed, that's relative wealth. I indiced everything to the Bottom 50%.

In this next chart, I apply a different index. Each income segment is set to 100 at the start of the time period under study (2000), and I track how each segment evolved in the last two decades.

Junkcharts_redo_bihouseholdwealth_2

This chart offers many insights.

The Bottom 50% have been left far, far behind in the last 20 years. In fact, from 2000-2018, this segment's wealth never once reached the 2000 level. At its worst, around 2010, the Bottom 50% found themselves 80% poorer than they were 10 years ago!

In the meantime, the other half of the population has seen their wealth climb continuously through the 20 years. This is particularly odd because the major crisis of these two decades was the Too Big to Fail implosion of financial instruments, which the Bottom 50% almost surely did not play a part in. During that crisis, the top 50% were 30-60% better off than they were in 2000. Is this the "trickle-down" economy in which losses are passed down (but gains are passed up)?

The chart also shows how the recession hit the bottom 50% much deeper, and how the recovery took more than a decade. For the top half, the recovery came between 2-4 years.

It also appears that top 10% are further peeling off from the rest of the population. Since 2009, the top 11-49% have been steadily losing ground relative to the top 10%, while the gap between them and the Bottom 50% has narrowed.

***

This second chart is not nearly as dramatic as the first one but it reveals much more about the data.

 


Finding the hidden information behind nice-looking charts

This chart from Business Insider caught my attention recently. (link)

Bi_householdwealthchart

There are various things they did which I like. The use of color to draw a distinction between the top 3 lines and the line at the bottom - which tells the story that the bottom 50% has been left far behind. Lines being labelled directly is another nice touch. I usually like legends that sit atop the chart; in this case, I'd have just written the income groups into the line labels.

Take a closer look at the legend text, and you'd notice they struggled with describing the income percentiles.

Bi_householdwealth_legend

This is a common problem with this type of data. The top and bottom categories are easy, as it's most natural to say "top x%" and "bottom y%". By doing so, we establish two scales, one running from the top, and the other counting from the bottom - and it's a head scratcher which scale to use for the middle categories.

The designer decided to lose the "top" and "bottom" descriptors, and went with "50-90%" and "90-99%". Effectively, these follow the "bottom" scale. "50-90%" is the bottom 50 to 90 percent, which corresponds to the top 10 to 50 percent. "90-99%" is the bottom 90-99%, which corresponds to the top 1 to 10%. On this chart, since we're lumping the top three income groups, I'd go with "top 1-10%" and "top 10-50%".

***

The Business Insider chart is easy to mis-read. It appears that the second group from the top is the most well-off, and the wealth of the top group is almost 20 times that of the bottom group. Both of those statements are false. What's confusing us is that each line represents very different numbers of people. The yellow line is 50% of the population while the "top 1%" line is 1% of the population. To see what's really going on, I look at a chart showing per-capita wealth. (Just divide the data of the yellow line by 50, etc.)

Redo_bihouseholdwealth_legend

For this chart, I switched to a relative scale, using the per-capita wealth of the Bottom 50% as the reference level (100). Also, I applied a 4-period moving average to smooth the line. The data actually show that the top 1% holds much more wealth per capita than all other income segments. Around 2011, the gap between the top 1% and the rest was at its widest - the average person in the top 1% is about 3,000 times wealthier than someone in the bottom 50%.

This chart raises another question. What caused the sharp rise in the late 2000s and the subsequent decline? By 2020, the gap between the top and bottom groups is still double the size of the gap from 20 years ago. We'd need additional analyses and charts to answer this question.

***

If you are familiar with our Trifecta Checkup, the Business Insider chart is a Type D chart. The problem with it is in how the data was analyzed.


The time has arrived for cumulative charts

Long-time reader Scott S. asked me about this Washington Post chart that shows the disappearance of pediatric flu deaths in the U.S. this season:

Washingtonpost_pediatricfludeaths

The dataset behind this chart is highly favorable to the designer, because the signal in the data is so strong. This is a good chart. The key point is shown clearly right at the top, with an informative title. Gridlines are very restrained. I'd draw attention to the horizontal axis. The master stroke here is omitting the week labels, which are likely confusing to all but the people familiar with this dataset.

Scott suggested using a line chart. I agree. And especially if we plot cumulative counts, rather than weekly deaths. Here's a quick sketch of such a chart:

Junkcharts_redo_wppedflu_panel

(On second thought, I'd remove the week numbers from the horizontal axis, and just go with the month labels. The Washington Post designer is right in realizing that those week numbers are meaningless to most readers.)

The vaccine trials have brought this cumulative count chart form to the mainstream. For anyone who have seen the vaccine efficacy charts, the interpretation of the panel of line charts should come naturally.

Instead of four plots, I prefer one plot with four superimposed lines. Like this:

Junkcharts_redo_wppeddeaths_superpose2