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

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

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

20160402_WOC883_icecream_PISA

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

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

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

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

Redo_econ_icecreamIQ_1A

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

***

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

Redo_econ_icecreamIQ_2

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

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

***

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

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

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

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

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

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

 

[PS. 11/3/2019: The comments below contain different theories that link the two variables, including theories that treat PISA score ("IQ") as the explanatory variable and ice cream consumption as the outcome. Also, I elaborated that the rule does not dictate which variable is the outcome - the designer effectively signals to the reader which variable is regarded as the outcome by placing it in the vertical axis.]


Form and function: when academia takes on weed

I have a longer article on the sister blog about the research design of a study claiming 420 "cannabis" Day caused more road accident fatalities (link). The blog also has a discussion of the graphics used to present the analysis, which I'm excerpting here for dataviz fans.

The original chart looks like this:

Harperpalayew-new-420-fig2

The question being asked is whether April 20 is a special day when viewed against the backdrop of every day of the year. The answer is pretty clear. From this chart, the reader can see:

  • that April 20 is part of the background "noise". It's not standing out from the pack;
  • that there are other days like July 4, Labor Day, Christmas, etc. that stand out more than April 20

It doesn't even matter what the vertical axis is measuring. The visual elements did their job. 

***

If you look closely, you can even assess the "magnitude" of the evidence, not just the "direction." While April 20 isn't special, it nonetheless is somewhat noteworthy. The vertical line associated with April 20 sits on the positive side of the range of possibilities, and appears to sit above most other days.

The chart form shown above is better at conveying the direction of the evidence than its strength. If the strength of the evidence is required, we use a different chart form.

I produced the following histogram, using the same data:

Redo_420day_2

The histogram is produced by first locating the midpoints# of the vertical lines into buckets, and then counting the number of days that fall into each bucket.  (# Strictly speaking, I use the point estimates.)

The midpoints# are estimates of the fatal crash ratio, which is defined as the excess crash fatalities reported on the "analysis day" relative to the "reference days," which are situated one week before and one week after the analysis day. So April 20 is compared to April 13 and 27. Therefore, a ratio of 1 indicates no excess fatalities on the analysis day. And the further the ratio is above 1, the more special is the analysis day. 

If we were to pick a random day from the histogram above, we will likely land somewhere in the middle, which is to say, a day of the year in which no excess car crashes fatalities could be confirmed in the data.

As shown above, the ratio for April 20 (about 1.12)  is located on the right tail, and at roughly the 94th percentile, meaning that there were 6 percent of analysis days in which the ratios would have been more extreme. 

This is in line with our reading above, that April 20 is noteworthy but not extraordinary.

 

P.S. [4/27/2019] Replaced the first chart with a newer version from Harper's site. The newer version contains the point estimates inside the vertical lines, which are used to generate the histogram.

 

 

 

 

 


A data graphic that solves a consumer problem

Saw this great little sign at Ippudo, the ramen shop, the other day:

Ippudo_board

It's a great example of highly effective data visualization. The names on the board are sake brands. 

The menu (a version of a data table) is the conventional way of displaying this information.

The Question

Customers are selecting a sake. They don't have a favorite, or don't recognize many of these brands. They know a bit about their preferences: I like full-bodied, or I want the dry one. 

The Data

On a menu, the key data are missing. So the first order of business is to find data on full- and light-bodied, and dry and sweet. The pricing data are omitted, possibly because it clutters up the design, or because the shop doesn't want customers to focus on price - or both.

The Visual

The design uses a scatter plot. The customer finds the right quartet, thus narrowing the choices to three or four brands. Then, the positions on the two axes allow the customer to drill down further. 

This user experience is leaps and bounds above scanning a list of names, and asking someone who may or may not be an expert.

Back to the Data

The success of the design depends crucially on selecting the right data. Baked into the scatter plot is the assumption that the designer knows the two factors most influential to the customer's decision. Technically, this is a "variable selection" problem: of all factors determining the brand choice, which two are the most important? 

Think about the downside of selecting the wrong factors. Then, the scatter plot makes it harder to choose the sake compared to the menu. 

 


Not following direction or order, the dieticians complain

At first glance, this graphic's message seems clear: what proportion of Americans are exceeding or lagging guidelines for consumption of different food groups. Blue for exceeding; orange for lagging. The stacked bars are lined up at the central divider - the point of meeting recommended volumes - to make it easy to compare relative proportions.

Figure-2-1-eatingpatterns

The original chart is here, on the Health.gov website.

The little icons illustrating the food groups are cute and unintrusive.

It's when you read further that things start to get complicated. The last three rows display a flipping of the color scheme, with orange on the right, blue on the left. Up to this point, you may understand blue to mean over the recommended value, and orange is under. Suddenly, the orange is shown on the right side.

The designer was wrestling with a structural issue in the data. The last three food groups - sugars, fats and sodium - are things to eat less. So, having long bars on the right side is not good. The orange/blue colors should be interpreted as bad/good and not as under/over.

***
The problem with this design is that it draws attention to this color flip - that is to say, it draws attention to which food groups are favored and which ones are to be avoided. This insight is actually in the metadata, not what this dataset is about.

In the following chart, I enforce the bad/good color scheme while ignoring the direction of good. The text is adjusted to use words that do not suggest direction.

Redo_foodgroups1

Dieticians are probably distressed by this chart, given that most Americans are lagging on almost all of the recommendations.

In a final edit, I re-ordered the categories.

Redo_foodgroups2

 


Made in France stereotypes

France is on my mind lately, as I prepare to bring my dataviz seminar to Lyon in a couple of weeks.  (You can still register for the free seminar here.)

The following Made in France poster brings out all the stereotypes of the French.

Made_in_france_small

(You can download the original PDF here.)

It's a sankey diagram with so many flows that it screams "it's complicated!" This is an example of a graphic for want of a story. In a Trifecta Checkup, it's failing in the Q(uestion) corner.

It's also failing in the D(ata) corner. Take a look at the top of the chart.

Madeinfrance_totalexports

France exported $572 billion worth of goods. The diagram then plots eight categories of exports, ranging from wines to cheeses:

Madeinfrance_exportcategories

Wine exports totaled $9 billion which is about 1.6% of total exports. That's the largest category of the eight shown on the page. Clearly the vast majority of exports are excluded from the sankey diagram.

Are the 8 the largest categories of exports for France? According to this site, those are (1) machinery (2) aircraft (3) vehicles (4) electrical machinery (5) pharmaceuticals (6) plastics (7) beverages, spirits, vinegar (8) perfumes, cosmetics.

Compare: (1) wines (2) jewellery (3) perfume (4) clothing (5) cheese (6) baked goods (7) chocolate (8) paintings.

It's stereotype central. Name 8 things associated with the French brand and cherry-pick those.

Within each category, the diagram does not show all of the exports either. It discloses that the bars for wines show only $7 of the $9 billion worth of wines exported. This is because the data only capture the "Top 10 Importers." (See below for why the designer did this... France exports wine to more than 180 countries.)

Finally, look at the parade of key importers of French products, as shown at the bottom of the sankey:

Madeinfrance_topimporters

The problem with interpreting this list of countries is best felt by attempting to describe which countries ended up on this list! It's the list of countries that belong to the top 10 importers of one or more of the eight chosen products, ordered by the total value of imports in those 8 categories only but only including the value in any category if it rises to the top 10 of the respective category.

In short, with all those qualifications, the size or rank of the black bars does not convey any useful information.

***

One feature of the chart that surprised me was no flows in the Wine category from France to Italy or Spain. (Based on the above discussion, you should realize that no flows does not mean no exports.) So I went to the Comtrade database that is referenced in the poster, and pulled out all the wine export data.

How does one visualize where French wines are going? After fiddling around the numbers, I came up with the following diagram:

Redo_jc_frenchwineexports

I like this type of block diagram which brings out the structure of the dataset. The key features are:

  • The total wine exports to the rest of the world was $1.4 billion in 2016
  • Half of it went to five European neighbors, the other half to the rest of the world
  • On the left half, Germany took a third of those exports; the UK and Switzerland together is another third; and the final third went to Belgium and the Netherlands
  • On the right half, the countries in the blue zone accounted for three-fifths with the unspecified countries taking two-fifths.
  • As indicated, the two-fifths (in gray) represent 20% of total wine exports, and were spread out among over 180 countries.
  • The three-fifths of the blue zone were split in half, with the first half going to North America (about 2/3 to USA and 1/3 to Canada) and the second half going to Asia (2/3 to China and 1/3 to Japan)
  • As the title indicates, the top 9 importers of French wine covered 80% of the total volume (in litres) while the other 180+ countries took 20% of the volume

 The most time-consuming part of this exercise was finding the appropriate structure which can be easily explained in a visual manner.

 

 


Big Macs in Switzerland are amazing, according to my friend

Bigmac_chNote for those in or near Zurich: I'm giving a Keynote Speech tomorrow morning at the Swiss Statistics Meeting (link). Here is the abstract:

The best and the worst of data visualization share something in common: these graphics provoke emotions. In this talk, I connect the emotional response of readers of data graphics to the design choices made by their creators. Using a plethora of examples, collected over a dozen years of writing online dataviz criticism, I discuss how some design choices generate negative emotions such as confusion and disbelief while other choices elicit positive feelings including pleasure and eureka. Important design choices include how much data to show; which data to highlight, hide or smudge; what research question to address; whether to introduce imagery, or playfulness; and so on. Examples extend from graphics in print, to online interactive graphics, to visual experiences in society.

***

The Big Mac index seems to never want to go away. Here is the latest graphic from the Economist, saying what it says:

Econ_bigmacindex

The index never made much sense to me. I'm in Switzerland, and everything here is expensive. My friend, who is a U.S. transplant, seems to have adopted McDonald's as his main eating-out venue. Online reviews indicate that the quality of the burger served in Switzerland is much better than the same thing in the States. So, part of the price differential can be explained by quality. The index also confounds several other issues, such as local inflation and exchange rate

Now, on to the data visualization, which is primarily an exercise in rolling one's eyeballs. In order to understand the red and blue line segments, our eyes have to hop over the price bubbles to the top of the page. Then, in order to understand the vertical axis labels, unconventionally placed on the right side, our eyes have to zoom over to the left of the page, and search for the line below the header of the graph. Next, if we want to know about a particular country, our eyes must turn sideways and scan from bottom up.

Here is a different take on the same data:

Redo_jc_econbigmac2018

I transformed the data as I don't find it compelling to learn that Russian Big Macs are 60% less than American Big Macs. Instead, on my chart, the reader learns that the price paid for a U.S. Big Mac will buy him/her almost 2 and a half Big Macs in Russia.

The arrows pointing left indicate that in most countries, the values of their currencies are declining relative to the dollar from 2017 to 2018 (at least by the Big Mac Index point of view). The only exception is Turkey, where in 2018, one can buy more Big Macs equivalent to the price paid for one U.S. Big Mac. compared to 2017.

The decimal differences are immaterial so I have grouped the countries by half Big Macs.

This example demonstrates yet again, to make good data visualization, one has to describe an interesting question, make appropriate transformations of the data, and then choose the right visual form. I describe this framework as the Trifecta - a guide to it is here.

(P.S. I noticed that Bitly just decided unilaterally to deactivate my customized Bitly link that was configured years and years ago, when it switched design (?). So I had to re-create the custom link. I have never grasped  why "unreliability" is a feature of the offering by most Tech companies.)


Some Tufte basics brought to you by your favorite birds

Someone sent me this via Twitter, found on the Data is Beautiful reddit:

Reddit_whichbirdspreferwhichseeds_sm

The chart does not deliver on its promise: It's tough to know which birds like which seeds.

The original chart was also provided in the reddit:

Reddit_whichbirdswhichseeds_orig_sm

I can see why someone would want to remake this visualization.

Let's just apply some Tufte fixes to it, and see what happens.

Our starting point is this:

Slide1

First, consider the colors. Think for a second: order the colors of the cells by which ones stand out most. For me, the order is white > yellow > red > green.

That is a problem because for this data, you'd like green > yellow > red > white. (By the way, it's not explained what white means. I'm assuming it means the least preferred, so not preferred that one wouldn't consider that seed type relevant.)

Compare the above with this version that uses a one-dimensional sequential color scale:

Slide2

The white color still stands out more than necessary. Fix this using a gray color.

Slide3

What else is grabbing your attention when it shouldn't? It's those gridlines. Push them into the background using white-out.

Slide4

The gridlines are also too thick. Here's a slimmed-down look:

Slide5

The visual is much improved.

But one more thing. Let's re-order the columns (seeds). The most popular seeds are shown on the left, and the least on the right in this final revision.

Slide6

Look for your favorite bird. Then find out which are its most preferred seeds.

Here is an animated gif to see the transformation. (Depending on your browser, you may have to click on it to view it.)

Redojc_birdsseeds_all_2

 

PS. [7/23/18] Fixed the 5th and 6th images and also in the animated gif. The row labels were scrambled in the original version.

 


Foodies say, add dataviz spice please

This Buzzfeed article proves that foodies love their food served with dataviz (tip: Chris P.). Menus are an undertapped resource when it comes to data visualization.

There are several examples worth discussing.

Buzzfeed-venn-menu

Venn diagrams are not easy to read, people.

Plus they are hard to construct well... note the asymmetric areas.

Here is one without circles:

Jc_redo_vennmenu_1

Then, I pared it down to its essence:

Jc_redo_vennmenu_2

***

This beer map is pretty great:

Buzzfeed-beer-menu

Some of its virtues:

  • The spacious layout utilizing two dimensions, instead of a one-dimensional list of dense text
  • Ordering using two dimensions relevant to the decision problem (assuming those two dimensions are the most important for their clients)
  • Unconventional, attention-grabbing
  • More equitable: different readers will read the chart in different orders. I'll hypothesize that they will end up with a more even distribution of drink orders than with a list in which everyone reads top to bottom

Potential problems:

  • Not enough space to explain the drinks. Don't the clients want to know what's in them?
  • I wonder how they measured the degree of "classic"-ness.

***

This next menu contains an error:

Buzzfeed-coffee-menu

When the drink comes in one size, only one price is listed. If it comes in two sizes, two prices should be listed.

Is the cafe owner shading Americans as not good at math?


Fantastic visual, but the Google data need some pre-processing

Another entry in the Google Newslab data visualization project that caught my eye is the "How to Fix It" project, illustrating search queries across the world that asks "how." The project web page is here.

The centerpiece of the project is an interactive graphic showing queries related to how to fix home appliances. Here is what it looks like in France (It's always instructive to think about how they would count "France" queries. Is it queries from google.fr? queries written in French? queries from an IP address in France? A combination of the above?)

Howtofixit_france_appliances

I particularly appreciate the lack of labels. When we see the pictures, we don't need to be told this is a window and that is a door. The search data concern the relative sizes of the appliances. The red dotted lines show the relative popularity of searches for the respective appliances in aggregate.

By comparison, the Russian picture looks very different:

Howtofixit_russia_appliances

Are the Russians more sensible? Their searches are far and away about the washing machine, which is the most complicated piece of equipment on the graphic.

At the bottom of the page, the project looks at other queries, such as those related to cooking. I find it fascinating to learn what people need help making:

Howtofixit_world_cooking

I have to confess that I searched for "how to make soft boiled eggs". That led me to a lot of different webpages, mostly created for people who search for how to make a soft boiled egg. All of them contain lots of advertising, and the answer boils down to cook it for 6 minutes.

***

The Russia versus France comparison brings out a perplexing problem with the "Data" in this visualization. For competitive reasons, Google does not provide data on search volume. The so-called Search Index is what is being depicted. The Search Index uses the top-ranked item as the reference point (100). In the Russian diagram, the washing machine has Search Index of 100 and everything else pales in comparison.

In the France example, the window is the search item with the greatest number of searches, so it has Search Index of 100; the door has Index 96, which means it has 96% of the search volume of the window; the washing machine with Index 49 has about half the searches of the window.

The numbers cannot be interpreted as proportions. The Index of 49 does not mean that washing machines account for 49% of all France queries about fixing home appliances. That is really the meaning of popularity we want to have but we don't have. We can obtain true popularity measures by "normalizing" the Search Index: just sum up the Index Values of all the appliances and divide the Search Index by the sum of the Indices. After normalizing, the numbers can be interpreted as proportions and they add up to 100% for each country. When not normalized, the indices do not add to 100%.

Take the case in which we have five appliances, and let's say all five appliances are equally popular, comprising 20% of searches each. The five Search Indices will all be 100 because the top-ranked item is given the value of 100. Those indices add to 500!

By contrast, in the case of Russia (or a more extreme case), the top-ranked query is almost 100% of all the searches, so the sum of the indices will be only slightly larger than 100.

If you realize this, then you'd understand that it is risky to compare Search Indices across countries. The interpretation is clouded by how much of the total queries accounted for by the top query.

In our Trifecta Checkup, this is a chart that does well in the Question and Visual corners, but there is a problem with the Data.