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First of all, I want to make it abundantly clear that this post is not political in nature. It is not an attempt to endorse one candidate, or repudiate another candidate. It is, pure and simple, pointing out how easy it is to misuse mathematics and statistics to try to emphasize a point. Take a look at this image, which is floating around on facebook.
What is the intent of this picture? Well, looking at the caption under the photo, which read, "Who speaks for you? Bernie Sanders 2016," makes it clear that the intent was to show Sanders as a "man of the people" and the rest of them so insanely rich that they are out of touch with the American people.
But the reality is distorted by the image's choice of mathematical language. Specifically, the choice was made to use the text "¾ million" when referring to Cruz's home, instead of the text "750 Thousand." This, I am certain, was deliberate. Because "milllion" sounds massive compared to "thousand," and if they had written "750 Thousand" next to Cruz, people would be much more likely to realize that Cruz is in the same ballpark with Sanders, and not in the same ballpark as Trump, or even Clinton.
To those who are reading quickly, or who didn't do well in math, "¾ million" sounds much larger than "750 thousand," even though the two phrases are expressing exactly the same value.
In mathematical terms, instead of talking about "ballparks" we talk about "orders of magnitude." Two numbers have the same order of magnitude if the larger one divided by the small one is less than 10.
And guess what! Cruz and Sanders have the same order of magnitude. Would you like to see a graph of these values? Here it is:
Notice that compared to Trump, Clinton's homes seem inexpensive, but compared to both of them, Cruz and Sanders are downright indistinguishable*.
Do I care how rich these guys are? Not even a whit. I have no problem with a rich president. I have no problem with a middle class president. I have no problem with a poor president.
I have a problem with people using mathematics to deceive the people who do care about such things. A good piece of advice for you when looking at a set of statistics: take note of all the units given (in this case, "millions" was given as the units throughout, until the very end) and if the units are not consistent throughout, ask yourself why. It may be that there's a good reason, but it could very well be (as in this case) that someone is trying to fool you. To keep things consistent, the graphic creator should either have written the Cruz value as "750 Thousand" or the Sanders value as "3/10 Million."
The person responsible for the graphic probably was hoping for one of the following:
- You slept through the math lessons where your teacher taught you about place value and magnitude.
- You'll be in such a hurry to click "like" that you won't take a moment to remember the lessons you learned.
After all, it's an election year. What did you expect?
* You might be thinking to yourself, "You really think that the difference between a 300 thousand dollar home and a 750 thousand dollar home is not significant?" And if that's what you're thinking, you're sort of missing the point here. The point is that the person who made the graphic was afraid that if he represented the facts in an honest manner, you would think it was an insignificant difference, and so he chose a dishonest path, hoping that your gullibility would do the rest.
I'd like to begin this post by saying, our world is filled with complex issues - societal, religious, political, scientific, etc., and sometimes we do a lousy job discussing complex issues; we think that a complex issue can be summed up with a "facebook meme", and that once we've seen a tiny little sound bite about a subject, we know everything we need to know on that topic.
Sometimes, we need to have a conversation about the nature of our conversations, and that can be difficult, because we learn by example, and so talking about the nature of our conversations requires us to have specific conversations to analyze. Once I pick a particular conversation to examine, you'll be tempted to assume I'm writing about the topic of the conversation, rather than the nature of the conversation.
This problem has kept me from writing this post for a long time, because if I use something like race relations, gun control, religious freedom, government spending, gender equality, or any other hot topic as my example, people who have strong feelings (one way or the other) on the subject won't be able to see past the specific topic to the nature of the conversation.
But now, I have the perfect sound bite to talk about. It's about something that really isn't a hot topic (after all, I think we all agree that domestic violence is a bad thing no matter where it crops up in the world), so we can look at an example of irrational sound-bite conversation on this subject, and hopefully people won't get bogged down in the specific topic, and will be able to focus on the nature of the "conversation."
The image shown here has been cropping up on facebook since last October (click on the image to see it full size). I've left it entirely as-is. I thought about blocking out the author's name, because the letter is rather embarrassing for a "professor" to be writing, but then I realized - first, she posted it in a public place (newspaper), and second, more than ten thousand people have "liked" or "shared" this on facebook, so there's not much point in trying to protect her privacy, or keep her from embarrassment.
Declaration of Authority
The first thing I'd like to point out is that no one writes letters to the editor signing them "Joe Shmoe, Dental Hygenist at Canal Street Dentistry," or "Ferdie Jones, Truck Driver at Waste Management Services," because they know that doing so will not provide any weight to their opinion (unless it's on the subject of teeth, or the subject of garbage), but people in positions of academia are happy to post things like "Judy Haiven, Department of Management professor, Saint Mary's University, Halifax", because it provides an aura of academic wisdom and experience, and few people will stop to ask, "What does 'Department of Management' have to do with having special knowledge or insight about conditions in Pakistan?"
In addition, the "declaration of authority" implicit in the signature will cause people to be less cautious when it comes to trusting the content of the writing. Being a professor results in people expecting you to be able to reason and argue logically, but being a professor does not guarantee that you make use of those capabilities.
And of course, as you're reading this you should be thinking, "Wait a minute...who is this 'Professor Puzzler,' that's writing this post, anyway? What is he a professor of? Is he really a professor?" I'll leave you to track down the answer to that question; it's not hard to find the information on this site.
Removal of Context
The second thing I'd like to point out has nothing to do with the actual letter. It has to do with the fact that it has been shared thousands of times on facebook. When the letter was written, it had a context. You can't see the context, but you can tell what it context was; it was a letter to the editor in a newspaper. Which means the author had a reasonable expectation that people who read her letter would also have read the article it was about, and would therefore have a frame of reference in which to understand her response.
Through no fault of hers (probably), the letter has been removed from its context by people sharing it on social media. Do you know the newspaper in which the original article appeared? Probably not. Have you read the article which she was responding to? I expect you haven't. Furthermore, I would guess that of the thousands of people who have shared this, the vast majority have never read the original article.
And this has become the nature of our sound bite conversations: we learn about issues without the context of their larger complexities, and we learn about issues by reading only one side of the conversation.
This issue is painfully obvious in the world of politics, where both left and right grab opposing sound bites out of context and then respond to the sound bites as though they are actually a full conversation. And we all eat it up, because it helps to confirm our pre-existing biases.
Wouldn't it be great if - before posting/liking/sharing something on social media, we were required to read at least one article each from opposite sides of the issue, so we could gain a deeper understanding of the larger complexities of the issue?
Now let's talk about the actual letter, because there are a couple of glaring statistical and logical fallicies in it (hence the embarrassment to Professor Haiven!)
Misuse of Statistics
The letter purports to do a side by side comparison of what's happening in Pakistan to what is happening in the United States of America. Comparing the number of times something happens in Pakistan each year to the number of times it happens in the United States.
The author of this letter needs to learn a little thing we call "per capita" - per capita means "per head" or "per person." If we want to have a meaningful statistic, we need to take our total and divide it by the population, and then do our comparison. Let me show you how silly this can get if we don't do our statistics properly:
Alice lives in town A, which has a population of 2000, and Betty lives in town B, which has a population of 200,000. Listen to this conversation:
Alice: In our town we have 40 geniuses.
Betty: That's nothing! In our town we have 50 geniuses! Clearly the residents of B are smarter than the residents of A!
What is wrong with this? Obviously, 40 out of 2000 is a much higher rate than 50 out of 200,000! Divide the number of geniuses by the total population, and you have a per capita figure, and this is what Betty needs to be comparing.
40 / 200 = 0.2; 50/200,000 = 0.00025.
Now when we compare, we see that Alice's town has a much higher ratio of geniuses.
Professor Haiven should automatically know and understand that she can't compare what's happening in Pakistan to what's happening in the United States without doing some per capita calculations. And yet, that's what she's done. The fact that a college professor doesn't know this isn't just embarrassing - it's downright bizarre!
Am I going to do those calculations for you? No! You can look up the population of Pakistan in 2013, as well as the population of the United States, and I've shown you how to do the per capita calculation, so you can figure it out for yourself. The big question is: will you figure it out for yourself?
Herein lies one of the problems with our sound-bite conversation style: taking the time to actually research something is not really worth our time, so we don't bother. Instead we just accept whatever is spoon fed to us.
This issue of misusing statistics is a huge problem in our standard conversation style about any hot button topic; I see misuse of statistics in just about any discussion of race relations, gun control, etc. Statistics are great, because a little bit of math goes a long way toward making our point believable, and if people aren't paying attention, we can make numbers and statistics say anything we want them to.
Just because Professor Haiven can multiply 3 times 365 to obtain 1095 doesn't mean that she actually knows the significance of that number. But if you're going to read what she wrote, you need to be able to figure out the meaning of that statistic, before you swallow her reasoning.
Changing the Rules of the Discussion
Here's the other glaring issue here. Clearly, the writer of the original article was writing about something called "honor killings." The author must have had some sort of definition of what an "honor killing" is. You can do some research if you want to find out more about how that is typically defined (again, here is the problem with removing the letter from its context; we can only make educated guesses about the definition the original author was using!). What you will find is that the way in which "honor killing" is typically defined makes it a subset of domestic violence - in the same way that granny smith apples are a subset of apples.
Professor Haiven appears to have taken umbrage with whatever definition the original author was using, and she replies (in essence) "All domestic violence that results in death is a form of honor killing." What she's doing here is she's arguing about definitions.
She's welcome to have her own definition, of course, but if she's going to change the definition, she needs to understand that the statistic that went with the article's definition is not the statistic that goes with her definition. Is it like comparing apples with oranges? Yeah, it kind of is. Or, here's a more accurate comparison:
Clarence lives in town C, and Doris lives in town D (we'll assume they have the same population). Here's the conversation:
Clarence: Our town produces 100,000 Granny Smith apples every year.
Doris: Well, that's just ridiculous. Here in town D we actually have a "Granny Smith," and she loves all kinds of apples, so we don't hold with such silly designations; we just call all apples "Granny Smiths!" Furthermore, our town produces 1,000,000 granny smith apples every year, so clearly we have better apple production than you!
What's the issue with this conversation? I think it's fairly obvious; Doris has tried to change how we define granny smith apples, and yet she's still using Clarence's statistic which is based on his definition, not hers. In so doing, she has completely disregarded the fact that town C probably produces Cortland apples, red delicious apples, gala apples, etc.
Another way of putting it; Doris has started a new conversation, and is pretending that Clarence was participating in her discussion based on her rules.
If you change the definition, you have to recalculate any statistics based on the old definition, otherwise you're making no sense whatsoever. If you don't think that's what Professor Haiven is doing, you should probably go back and read her letter again.
And herein lies another problem with our sound-bite conversation style; we want to receive something without having to think carefully or deeply about it, and when we choose not to carefully evaluate the logic behind a statement, we are inviting people to mislead us.
When combined with the removal of context, this "changing the rules" issue becomes even more ugly, because now you've prevented the original writer/speaker from saying, "Hey! That's not how I defined my terms!"
Argument vs. Conclusion
You know what's really odd about this letter? If you remove all the stuff in Professor Haiven's letter that is illogical, you're left with one sentence - essentially - "We should be concerned about domestic violence in the west," and that's a statement I can get behind 100% - I completely agree with it!
In our world of sound bite conversations, whether or not you agree with the conclusion seems to be all that matters. This is a dangerous pattern of conversation, because it is actually a way of saying that rational thought doesn't matter. You actually can't have a real conversation if you don't care whether the things you say are true or not.
This has become so prevalent in social media. Someone shares a post that is irrational, illogical, misuses statistics, etc., but woe to the person who says, "But this is completely bogus reasoning because..."; the response typically is, "Yeah, but they make a good point, so shut up."
No, they really don't make a good point. The fact that you agree with their conclusion doesn't mean that they've made any point at all. And if we have become incapable of recognizing the difference between an argument and a conclusion, we have become incapable of discussion.
Even though I agree with Haiven's conclusion - domestic violence is something we should be concerned about here in the west - I would never share this image as a way of defending that conclusion, because she hasn't added anything useful or rational to the discussion on violence.
What can we learn from this letter that's been traveling around the internet?
- Content without context is next to useless.
- If you pass on information based on incorrect statistics, you're part of the problem.
- If you pass on information based on illogical reasoning, you're part of the problem.
- Taking the time to research something may be inconvenient, but without that step, there really isn't a conversation to be had.
- If you don't take the time to evaluate logic and reasoning, you open yourself up to deception.
- Having a title before or after your name doesn't automatically guarantee that you are a reliable source of information.
- Just because you agree with someone's conclusion doesn't mean you give them a pass on irrationality in their arguments.
We can also learn the following specific lessons in reasoning:
- Statistics about populations of people require per capita calculations.
- A change in definition requires a recalculation of statistics.
And hopefully, we can take these lessons into the hot topics that we reguarly discuss in this sound-bite world of ours!