Here’s an example of sorts, from a quote at Ricochet:
We know that imprisonment hurts communities. Increased incarceration undermines local networks, increases crime and juvenile delinquency, and causes a decrease in everything from public health to housing values to political participation. And we know that dairy farms need help from consumers and policy-makers to succeed.
K, leaving aside that the solution is “give us money”… I think I can see how they got to what they “know.” High rates of imprisonment would be associated with poorly developed local networks, high crime, lots of juvenile delinquents, lower public health and not very high political participation. Doesn’t mean it causes it—here’s a shocking idea, high (reported) crime areas probably have more people sent to jail, and some criminal records mean you aren’t supposed to vote; I remember that juvenile delinquency is highly associated with both single parents (not lots of time for politics) and parents who don’t pay much attention to their kids (who, I’d guess, aren’t going to be major political fans). Still, I can see how they’d get there.
This may be a bit disjointed, but if y’all worried about that too much, you’d have left long ago….
First off: sleepless nights can be handy, if I manage to remember something more than “I had a great realization I really should share” when I get up the next day. I had a mental image of how to explain how every flip of the coin still had a one-in-two chance of being heads no matter what the prior result was, even though the chance of two heads in a row is one in four, and three in a row is one in eight: picture a maze. There’s one entry, and each time it splits there’s in two directions, which become their own path that can split. Each event has a pretty big chance of happening, it’s just that getting any specific result in small. We don’t look for it, but the chances of getting heads-heads-tails-heads-tails-tails-heads is the same as seven heads in a row is the same as heads-tails-heads-tails-etc.
Secondly: that example I just gave, about coins having a 50% chance of any result on every flip?
You do not have a 50% chance of getting heads with a coin-toss, because coins aren’t perfectly even—it’s the same way that toast famously always lands jelly-side-down. There’s even a small demand for gaming dice (d20 type) that are anti-weighted—calibrated so that they are much, much more likely to be random than traditionally made dice. (Yes, I have a set. Somewhere.) The map isn’t the place, as they say—but the coin toss is such a classic example that it’s not even thought about. It’s just assumed, and in practical applications it’s just fine. The classic use of “call it” has the person tossing the coin, and the caller not knowing if it’ll hit the ground or be caught and flipped over or what. (Well, in movies it’s always caught, but that just looks cool.)
Just to be a bit more complicated, there’s got to be some chance of the comic book solution of a coin landing on edge, or vaporizing in the air, or something.
Similarly to the right-answer-wrong-question setup of the coin, there’s those statistics about how X% of whatever do Y, or– applying that—“X women do Y in the US alone” type claims. Obviously, they didn’t ask all women in the US—they’re making an estimate. Depending on how accurate that estimate is, it may be no more good than the internet habit of saying “nobody actually does celibacy!” or “everyone masturbates!” (With the same habit of being tilted by folks not working in good faith—shop around enough and you’ll find a study that indicates pretty much anything, especially if you strip off the fine print and play telephone a bit.)
Surveys, statistics and “estimates” can all be abused. Obviously, this doesn’t mean they’re all bad, it’s just a good idea to keep in mind the limits and possible biases for official numbers.
Surveys can be tainted by too small of a number of people, asking a group that isn’t representative of the group you’re trying to model and the way you ask a question. The first two are called sampling problems and the last one is usually a bias problem. (Some things are a mix of both—if you send out letters asking for household population over age 18 who can’t read, your sample won’t include those who don’t want to fill it out, those whose households that can’t read, those who won’t pay 50c to send the survey back, and people outside of your area. As a bonus, there’s also the number of wise donkeys who will answer “one, yes” just because it strikes them as funny.)
Statistics are limited by requiring that things be reported, that they be reported in the same way, that the reported incidents actually happened, and that the numbers are passed on accurately.
Estimates are what you get when you apply surveys or statistics to a population—so they get all the problems of those, multiplied by however many different sources of information were used, plus the problem of figuring out what you’re going to guess the population is.
All of this because of the way people keep confusing or conflating stats with facts…well, that and because I couldn’t sleep.