Funny Math in Wall Street Journal Pie Charts

This is a quickie to describe a mathematical disconnect I encountered last week.

While my wife and daughter were shopping in the mall, I hunkered down in the mall Starbucks with the Wall Street Journal. I never read the Wall Street Journal unless I’m hunkered down in a coffee shop.

Anyway, after doing the crossword puzzle, I started reading the articles. I came across an article entitled EU, Canada Near Free-Trade Pact After Farm Deal (the pact has since been approved). I wasn’t really reading the article, but there was an associated graphic, which featured pie charts. There were four of them, and Tufte likes multiple pies even less tahn he likes a single pie, so I looked a little closer to see if there was any fodder for a Chart Busters post.

Well, despite the multitude of pie charts, the pies were innocuous enough. The data they contained, however, caused me to scratch my head.

I’ll let you examine the graphic for a minute or two, so you have a chance to find what caught my eye.

EU, Canada Near Free-Trade Pact After Farm Deal - WSJ

Find it yet?

The charts show imports and exports in 2012 between Canada and the European Union, in billions of euros. But there are discrepancies. The imports from the EU (€43.3) don’t match the exports to Canada (€31.3), and the exports to the EU (€30.1) don’t match the imports from Canada (€30.5).

EU, Canada Near Free-Trade Pact After Farm Deal - WSJ

Shouldn’t these numbers match up? Or am I missing something?

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Comments

  1. Hi Jon,

    Nice spot. By your rationing, and something that I agree with, shouldn’t there only be two pies; total economy value for each area. Percentage contribution from other party would be within here, as imports and exports amount to the same thing, e.g. If I give £5 to you, you can’t have received £6.50 from me, right? Gift and receipt would e the same value.

    Looking forward to others opinions.

  2. César González says:

    Hello Jon.

    The data is taken from http://trade.ec.europa.eu/doclib/docs/2006/september/tradoc_113363.pdf, please see document notes for an explanation.

    Best regards.

  3. oops :)

  4. Scary stuff for October 31st. :)

  5. Hi César –

    Thanks for the citation. I read through the report quickly, shuddering at the charts. The only note I could see about any discrepancy was that sums of the individual categories of products might not equal the stated totals, because confidentiality regulations leave some individual items off the list. I didn’t see anything explaining why the numbers I questioned would vary.

  6. César González says:

    Hello Jon
    I send you the answer that the Europa Direct (http://europa.eu/europedirect/web_assistance/login/index_es.htm) give to me about this question:
    We invite you to consult the frequently asked questions document drawn up by Eurostat regarding international trade statistics, which explains why statistical discrepancies may appear:
    http://epp.eurostat.ec.europa.eu/portal/page/portal/international_trade/documents/FAQ_XT_WEB_EN_final_January2012.pdf

    Best Regards.

  7. I am no expert but I think I can guess what causes the difference. In order to do the calculation for Canada. They would have to take transaction done in the euro and convert them back to canadian dollars. If that is done at the dailey exchange rate it will not equal the euro at the end of the year. But that is just a guess.
    Jason

  8. @Jason G, that could possibly account for the small discrepancy in (EU imports from Canada) vs (Canada exports to EU), but not for the rather large discrepancy in (EU exports to Canada) vs (Canada imports from EU)

    :)

  9. Thanks again, César. I read through the follow-up link, and still did not see what may account for the discrepancies.

  10. Jason –

    I thought of this, but as Patrick said, I can’t see how this would account for the huge discrepancy regarding goods moving from the EU to Canada.

  11. I’ve been trying to figure out a better way they could have shown this, as I also fall in to the ‘pies are evil’ camp.

    what about venn diagrams? It seems like it would be relatively inexact, but would show the shared import/export value (assuming it should be the same number) and how it relates to the total exports imports of each country. Or is there a better way?

  12. Jayson –

    I think the Venn approach would be a lot of work, especially explaining it to people (and then to yourself, after you get confused). But simple bar charts might do the trick.

    These two charts show the total trade, with the trade between the EU and Canada highlighted. The top one is in the same order as the pies in the original. (And I don’t think the pies are as bad as four adjacent pies usually would be, since we’re only being asked to look at one piece from a much larger whole.) The bottom one is ordered to show the discrepancies more easily. You would need better labels, since the larger bar for each category is total, not just including the two entities in question.

    EU, Canada Near Free-Trade Pact After Farm Deal - WSJ

    We can see that EU’s trade is over 4 time that of Canada, and that each imports more overall than it exports. In both of these charts, the discrepancies aren’t hard to pick out, since we’re relying only on the length of the bars, not on the area of pie wedges which have different radii and angles.

    The next two charts show only the trade between EU and Canada. This clearly shows the discrepancy, especially the lower chart.

    EU, Canada Near Free-Trade Pact After Farm Deal - WSJ

    I guess the one I’d pick would depend on exactly what point I wanted to make.

  13. My guess is that these are two different data sources. EU imports/exports come from Eurostat, while the Canadian numbers come from the IMF. Lots of lessons to be learned here…

  14. Sjoerd –

    I thought about different data sources, and even those different sources compile data from different second order sources. I also wondered if somehow the VAT was somehow included (or not excluded).

  15. I think that there are two sources of the import-export discrepancy. I agree with Sjoerd that the data probably come from two different sources perhaps with different conversions between Euros and Canadian dollars. I also guess that the big discrepancy between the 31.3 Euros exported from the EU to Canada and the 43.3 Euros imported from Canada to the EU is that someone forgot to convert 43.3 Canadian Dollars to Euros. Using the conversion factor of 1.35 given in the chart would reduce the “Imports from Canada to the EU” from 43.3 to 43.3/1.35 = 32.1 Euros, close enough to the “EU exports to Canada” figure of 31.3 euros to be in the range of error from using two different sources of data.
    Jayson says that he is in the “pies are evil camp.” I do not think that pies are evil, but they can be misused. A pie is designed to show the share of several items. When you have only two items a line bar chart as Jon suggested works better. Jon does not tell us what the blue and red colors on his bar charts represent. I replotted the data in a slightly different format, using the same color for all the Canada-EU data. (This required two separate charts; see http://www.csun.edu/~lcaretto/euCanadaTradeData.xlsx.)
    EU, Canada Near Free-Trade Pact After Farm Deal - WSJ

  16. Larry-

    Jon didn’t say what was what as he was doing a quick mock up. I’m sure that wouldn’t be the final product.

    Pie charts are supposed to allow us to see the share of several items, but they do it poorly. There is rarely a reliable sense of scale, and they are unable to show any amount of exactness in the data/details. Bar charts are often a more reliable choice.

  17. Jon-

    Thanks for the mock ups. Once again the bar chart to the rescue ;)

  18. Jayson — I realize that Jon was doing a quick mock-up, but the red color represents Canada-EU transactions in some bars and Canada-(World minus EU) in other parts, which I found confusing at first.

    I agree that Pie charts have the failing that they do not show the data as a bar chart does. The numbers for the various slices can be entered inside (or outside) the slices, but there is no scale as to read the numbers as there is with a bar chart. Pie charts only give a visual estimate of the relative shares, but sometimes this is all people want. (My experience with bar and pie charts is limited; I usually use scatter charts to get a scale on the horizontal axis.)

  19. For a throwaway blog post, this one has spawned a lot of good discussion.

    I’ve adjusted my charts. I think the top one below is what is needed to show the total trade and the fraction of trade with each other. It resembles Larry’s, but the categories are in my original order, and I’ve kept the red and green for the “with each other” trade values.

    The bottom chart shows me the discrepancy better, but the trade with each other may be secondary to the overall discussion.

    EU, Canada Near Free-Trade Pact After Farm Deal - WSJ

    For showing the proportions, this isn’t a bad use for pie charts. For trying to scale to the totals, different sized pie charts only work qualitatively, not quantitatively.

    I agree with Larry that applying the Euro-CDN conversion to the Imports from Canada makes the numbers line up pretty closely. I find it hard to believe that this error wasn’t caught, but maybe it’s like that feet-meters error that crashed one of the Mars rovers.

  20. In the grand scheme of things, a difference between 30.1 and 30.5 is just a Day in the Life in data usage (discrepancy of less-than 1.5%). On the other hand, 31.3 and 43.3? Somebody was asleep at the switch! Good catch!

  21. Jon,
    Your charts are great. The only thing I would like to see would be to color the Canda exports to the EU the same as EU imports from Canada (and EU exports to Canada the same as Canada imports from the EU) since they are, in reality, the exact same thing. I think if this were more common, people would have a better understanding of international trade (rather than the pervasive misunderstandings that terms like “trade deficit” tend to engender).

    BTW, although this is my first time commenting, I am a regular reader. Thank you so much for making this resource available…your bullet chart tutorial was particularly amazing.

  22. I made up a floating bar chart that I haven’t uploaded yet, that took only one view of the balance, the EU’s, and includes a third party, “rest of the world”. My goal was to show how the EU is in trade deficit with the world but in surplus with Canada, and Canada is in trade deficit with everyone. The result neatly matched all the flows like a double-entry account, but was visually uninteresting.

    A slightly more interesting but dodgy-on-principles approach might be a two-ring doughnut chart with the sectors given an arrow-like appearance, with one ring each for the flow each way between the three regions Canada, EU & RoW. I don’t know how to make the arrows, unless I load the graphic into Photoshop and fiddle with it.

  23. Yes, good catch. And a good question.
    I’m an economist and work regularly with trade data, and I’m a long-time reader of your articles. Take a look at page 15 of the PDF that César posted, titled “Why are there extra EU statistical discrepancies.” That has most of the answers you’re looking for.
    About the issue of different data sources: while the WSJ cites just once source, yes, in effect there are different data sources at work here since some data is originating from different customs agencies and can be self reported by the exporters/imports themselves. There are multiple and various ways for goods (and services too) to cross national borders, so it’s difficult to correctly “capture” the true volume of trade. Since most countries (especially wealthy countries) have restrictions and tariffs (a.k.a duties) on imports rather than exports, customs agencies have a greater interest in finding imports, so imports generally are identified to a greater extent than exports.
    Then there’s the method of valuation. Besides the difference owing to the exclusion or inclusion of freight and insurance costs, a country may ignore shipments by certain types of exporters (think processing plants in border towns).
    Also, there’s always going to be a lag in identifying all trade since some some countries take longer, and some self-reporters take longer (either inadvertently or purposefully). Trade is identified and therefore reported to statistical agencies on a rolling basis, and usually with a lag of a couple months. It takes time (sometimes years) to reach the “true” value of trade. Some data sources reported “annual 2012″ data only starting around May this year, but that number, due to the rolling inflow of trade data, surely got revised when a new bit of data came in the next month, and then again the month after that, and so it goes. Trade data is therefore continually revised. Given time, the numbers will approach each other. For example, at this time, the IMF reports Canada’s imports from the EU as $55 billion (the image you put up doesn’t indicate when the WSJ pulled their data).
    Lastly, some countries are overall just better reporters of trade data than others. Statistics Canada is well run and has to deal with just a single country, whereas the EU statistics agency is dealing with many countries. With each bilateral pair of trade partners (the EU and Canada in this case), you can actually be looking at data from different reporters in the same data set.
    ——
    ——
    Keep going with the visualization ideas! I’m always looking for better ways to present trade data.

  24. Wondering if you happened upon this gem of a chart.

    Article: http://www.forbes.com/sites/parmyolson/2013/11/12/heres-where-teens-are-going-instead-of-facebook/
    Just chart: http://b-i.forbesimg.com/parmyolson/files/2013/11/Facebook-Teens-Top-20-growing-social-platforms-and-apps-GlobalWebIndex-copy.png

    Is the percentage listed:
    A) the % of teens between Q1 2013 and Q3 2013 Global excluding China
    OR
    B) % change in Millions?

    (choices as presented by the chart!)

  25. Jayson –

    What's in a percentage?

    Well, when it tops out at over 1000%, I guess it’s not percent of any group. It’s probably % Change, although of course % Change in Millions doesn’t make any sense.

  26. I was wondering… in the red circles on the right (with the numbers “2” and “3” below them), the red portions of the circles occupy ~80-90% of the circle area, yet represent only the 2nd & 3rd sources, respectively. I would think that that means the larger sources, when added in, must bring the total trade to well over 100%… if I’m understanding that right.

  27. Craig –
    The color scheme is confusing. It’s the gray regions that are the 2nd and 3rd sources.

  28. Nice catch. I’d venture to guess most people who read the WSJ and look at the charts, never bother to do what you just did. Even if they did, the percentage would be small. As a final loophole, the copy editor would need to catch that as well and probably didn’t or didn’t even know how. They just trusted the author. Who knows, maybe the whole thing was outsourced? Regardless, really nice. I’m trying to get up to speed on Excel and it seems I’ve found an “advanced” but highly technical and useful site. Thanks. These are interesting puzzles. I hope you catch a few more and can share with us.

  29. Typically the import/exports of countries don’t match up. Its either due to each other’s calculation (taxes, method, what goods are direct imports/exports to that country) and sometimes its due to the countries under/over stating imports/exports for their own benefit (see China/USA which channels goods through HK)

    -Economics expert and aspiring excel pro

  30. I didn’t have time to read through all comments to see if anyone else has already brought this up, but there are some EU import/export rules that help create these discrepancies, especially in Export to Canada category. I’m going to explain with a hypothetical example. Let’s imagine Company A in European country EU1 receives an order from Canada for Good X. Since A sources Good X from across the EU they put in orders to intra-EU companies to send Good X. This is counted as intra-EU trade and doesn’t show up on export databases. Since Good X is to be exported to Canada, company A doesn’t remove it from containers at international ports of EU. These containers are then labelled as export from this specific port (as witnessed by Canadian authorities and recorded) but some fail to register on EU database as being finally exported to outside the EU. This explains the great difference between what EU believes to have exported to Canada and what Canada sees as imports from the EU.

    There are also other factors, as I have seen already explained.

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