This is from a children’s book published in North Korea. It clearly shows a child running with an assault rifle, another child with a pistol who appears to be in charge, and another with an assault rifle with a bayonet fixed.
One might make excuses that this is page shows toys. And maybe the assault rifle in the foreground and the pistol are toys … but I have never, ever, anywhere, seen a toy bayonet.
This is drawn from the personal archives of a cultural anthropologist from Japan. He collects refuse from North Korea to learn about its culture. The photo is from a children’s book that was thrown away.
CAVEAT: I am not claiming that they’ve done this wrong: income is distributed along something like a power law, and there is some sense in having a middle that really isn’t in the middle at all. And, after all, you have to make some assumption about what constitutes the middle. What I am claiming is that most people would be surprised to find out what they’re doing won’t skew well with basic statistical understanding.
So, what’s the Pew’s middle? It’s everything between 2/3 of the median, an 2 times the median.
Recall that the median is the value which splits the data set in half: half of the observations are larger, and half are smaller.
For example, if your data set is all the numbers between 1 and 9, the median is 5.
Now, income isn’t distributed at all like the numbers 1 to 9. Even so, it would be in everyone’s interest if the Pew chose a method that worked well with unusual data sets.
Except that it doesn’t work here at all. The lower end, at 2/3 of the median, would mean that 3 is not included in the middle, but 4 is. That’s seems OK. But at the top end, twice the median takes us out to 10 … past the end of the data set.
So the Pew method is saying that the middle of the numbers 1 to 9 is 4 to 9. I don’t think most people would think that’s a good measure of the middle.
OK, so that’s a little weird. Is it a big deal? Or is it just a sort of arbitrariness that we need to be wary of?
What does that mean? It means that their data is binned. Binning is something that every student runs into in chapter 2 of their first statistics text. It means that you divvy up your range of data into some categories, and you put each piece of data in the appropriate spot — kind of like sorting mail into boxes. Thus, the name: binning.
Students also learn when they do binning that the choice of bin borders can effect the shape of the resulting histogram. You can make the data look quite different by choosing your bins carefully, so statisticians always tell people to be obvious and transparent about why they chose the bins they did.
One of the things that’s preached, although it’s not a hard and fast rule, is that binning is more transparent if the bins are the same size. For example, if you were going to bin this past week’s football teams by points scored, your bins might run 0 to 9, 10 to 19, 20 to 29, and so on; or maybe 0 to 7, 8 to 14, 15 to 21, and so on. Fans would look at that and see the sense of it.
But that’s not what the Census Bureau does. Now, admittedly, income follows something like a power law, so maybe the bins should increase in width as incomes go up. If that were the case, the widths might go 5, 10, 20, 40, or in some other multiples. But here’s the width of the Census Bureau’s bins in thousands of dollars: 15, 10, 10, 15, 25, 25, 50, 50, and everything else above that in one big bin. You can see this on page 31 of this report.
Funny thing about those numbers: they hit exactly all of the focal points our society is hung up on: $25K, $50K, $75K, $100K, $150K, $200K. So it’s not like they’re really chosen to match up with what the data tells us, so much as the arbitrary milestones we set for each other: rather like how we wonder if a baseball player is more likely to make the Hall of Fame with 300 rather 299 homers.
OK, so the Census Bureau bins unconventionally. What does this have to do with Pew’s odd definition of the middle? Well, again, the Census Bureau has 9 bins in their data, and they report the exact median in another column.
This is when things get interesting. Pew’s lower bound of 2/3 of the median is really close to the bottom border of the Census Bureau’s 4th bin. And Pew’s upper bound of 2 times the median is really close to the top border of the Census Bureau’s 6th bin.
Now, let me speculate: I suspect that Pew has chosen “round numbers” that get them close to picking out the 3 middle bins, from a set of fairly arbitrary definitions, chosen to match up with society’s easy to remember focal points.
And from this they claim that the middle class is shrinking?
Of course, that sounds a lot better than the proportion of the population in the 3 middle of 9 bins chosen somewhat arbitrarily with an eye towards matching up with focal points that society has (for better or worse) … just wouldn’t sound as convincing.
In the Illinois primary, voters vote for delegates who have their affiliation displayed. They do not vote directly for the candidates. And there can be more than one delegate for each candidate on the ballot.
Soltas then matched publicly available voting data to publicly available census data to estimate the “whiteness” of each delegate.
Trump delegates won significantly more votes when they had "whiter" last names relative to other delegates in their district. This effect does not appear for any of the other Republican candidates, and it is strongest in districts with high Trump vote shares.
Trump delegates who were likely to be perceived as nonwhite, in particular, won about 2 percentage points less of the vote …
My conclusion from all this is that Trump voters are significantly more racially motivated than Illinois Republicans who did not vote for Trump. Since Donald Trump won Illinois by 8 percentage points, the effect was politically important but not decisive.
I get the most mileage out of this when I think about what happened before Trump came along. I’m quite sure there were always racist voters. But these results are suggesting that they were spread evenly across Republicans. I don’t know of any data about Democrats, but I wouldn’t be surprised if they worked the same way.
So is Trump a magnet for existing racists, or did he help create new ones?
FWIW: I hate them both. My dislike for Trump runs deep, and goes back to him barging into a functioning USFL in 1983-4. My dislike for Clinton runs deep, and goes back to the revelations about the White House travel office that came out ten years later.
… I have a slight preference for a Trump victory [in November over H. Clinton]. The reason is that the same mainstream media that would fawn idiotically over a Clinton administration would be appropriately merciless on a Trump administration. President Trump would not receive, because he does not deserve, any benefit of the doubt. President Clinton would receive, even though she does not deserve, every benefit of the doubt.
I like this logic, but I’m not sure how true it holds. For me, right now, it doesn’t seem like the media is being tough on Trump in the slightest.
Personally, my experience of the last 25 years is that I found a constrained (Bill) Clinton of 1995-2000, and the constrained Obama of 2011-2016 … tolerable.
As to Bush II and the Republican controlled Congress of 2001-7 … well … I wish they’d been more constrained on nonsense like Medicare Part D.
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