When Numbers Lie
70% of families with 4 children have at least 3 of the same gender.
When I heard this tidbit over lunch a while ago I found it fascinating. You would think (or at least I initially did) that the larger percentage would belong to families with 2 boys and 2 girls. I was randomly thinking about it this morning when, like a lightening bolt to the brain I realized I had been a complete idiot. I shall explain.
If every child born has a 50/50 chance of being a boy or a girl (they don’t, but close enough), than you would think that half would be of each. But here’s the bitch. EACH child has a 50/50 shot, and, like dice, your chromosomes don’t remember what came before. So, putting aside the law of large numbers for a moment, two and two isn’t half the possible family variations.
Here are your options of family breakdowns with 4 children:
That’s it, that’s all of them.
Now, you’ll notice that only 1 of those 5 options (20%) does not conform to the statement at the top of the page. When laid out like this, that statistic is not remarkable at all. In fact, it seems remarkable to me that it’s not 80%, but hey, maybe I mis-remembered it (gasp!).
You may be asking yourself why this is important. I mean, who the fuck cares?If you aren’t one of those weirdos who loves statistics and numbers like I do you probably are no longer reading. But for those of you who hung on, there’s a point, I promise.
Statistics are like the news, you can’t believe them when you hear them, and you can’t have a valid informed opinion without them. Unfortunately they’ve been taken out of context and misunderstood so often that the maxim about statistics and making shit up is too often true. And because they are so often misconstrued, they are also easily dismissed. This is dangerous. Opinion without evidence is no better conscious ignorance.
This is really crucial. What ends up happening is people tend to believe statistics they agree with without question. But when they hear evidence supporting a position they don’t agree with, they insist it’s made up. This is not only a serious problem with the way we communicate and understand arguments, it’s just plain dumb. Your numbers are right, but their numbers are wrong? I can break down why this happens, but really: because, humans. Obviously statistics I agree with are true, it’s called confirmation bias, duh. And obviously statistics I disagree with are false, hellloooo…cognitive dissonance.
What’s most amazing to me is that the foundation of our understanding of evidence stands on such shaky ground. Numbers, those irrefutable objective facts, have become no more substantial than my mom’s opinion of my trombone playing.
How did we let this happen? Numbers and statistics are so easily misunderstood (like the example above), are oversimplified or are taken out of context. When encountering numbers, most people have found it easier to take them at face value or find their eyes have just plain glazed over.
Thirty-three thousand people die at gunpoint every year in the United States. That’s more than any other country. I’m sure you’ve heard that number touted around. It’s a significant number, and it is an objective fact. Many see it as their blazing evidence for gun control [sidebar — I am not arguing against gun control here, I am exemplifying good vs. bad evidence. As easy as it is to get off the rails with this one I need you to focus, people!]. But if you’re going to insist that we ban guns you might want to use a different number. Of those 33,000, a full two thirds (that’s 22,000) are suicides. I wouldn’t presume to know what is going on in the mind of someone bent on killing themselves, but I can’t imagine that it’s ‘oh, I don’t have a gun, guess I’ll just live’. The next largest affected demographics are gang related and then domestic violence. Mass shootings, including the one we just experienced in Las Vegas, and accidental gun deaths account for a tiny fraction of that 33,000 number.
Although this is a charged topic (not that that bothers me), I couldn’t think of a better example of oversimplification of the numbers. Another great oversimplification would be this gem that floated down my feed the other day:
We also often get stats wrong by taking them out of context, or as I like to call it, convenient data slicing.
So it’s been awhile since income mobility was on the front page, but this is still one of my favorites. Have you ever seen this graph?
What I absolutely love about it, is that despite its excessive use in the income mobility debate, it actually tells you ABSOLUTELY NOTHING about income mobility. To see income mobility, you would need to track individuals over time. 18 year olds may start out at the bottom and then move up over time — not may, they do — and tracking this kind of thing has shown that people at the top tend to fall off the line on a regular basis. (I had originally included a much longer explanation of this, but was told that my number nerd was showing.)
Now, the typical Bernie Sanders follower is doubting me right now. Not because they are Bernie Sanders followers, but because it’s human nature. The narrative that the rich get richer and the poor stay poor is so deeply believed that, to them, there is no other takeaway from this graph. We all do it when facing evidence that doesn’t conform to our beliefs (again, cognitive dissonance, that bitch).
I’ve always felt it a shame that high school students are encouraged to pick up calculus before statistics. If everyone had a basic understanding of how numbers and evidence worked, we wouldn’t so often be fooled by our own biases.
Its taken years of training my brain not to do this. Years of debate club, stats classes and even teaching quantitative research methods. And even I fall for it all the time. It’s a daily struggle, and I can only hope I’m not the only one fighting.
Note: I had originally included sources for many of the examples but removed them last minute in an effort to demonstrate that it doesn’t matter. For the sake of my argument the numbers have to be true. If you want to argue whether or not they are, it is an entirely different conversation.