You Draw It: Family Income vs. College Attendence
nytimes.com
nytimes.com
They said their guess and the data differ the same way as my guess. But then they think the data is correct and they just throw out their guess. That's actually wrong. This point is very important in statistics, but you actually already learn it in 4th or 5th grade math classes. Make a guess about the end result and if your calculated results is quite different be sceptical about your calculated result. Our ability to guess is not good at getting the exact numbers right, but it's really, really good at getting the big picture. Therefore when data and guess disagree there's a really good chance the data is wrong and we must question it and not just our guess (which we can also question, but questioning the data is more important).
PS: It's quite funny how often we consume lots of data and calculate a lot and still the right answer to the question is: "Dunno yet"
At least for me that's what I learned in the last few years on HN.
http://www.righto.com/2013/03/wealth-distribution-in-united-...
http://i.imgur.com/euPugla.png
Note that the data is from 2008, and only counts employed citizens.
I compiled the data from an official US government data/demographics/census website (I forget which one, sorry). I noticed I could query the average income for all counties split over many "occupation groups". This gave me relatively fine-grained buckets (it doesn't really matter what they were, just that they were small-ish), weighted by the number of people in it, allowing me to plot the histogram. The really proper way to build this histogram would be to bucket an actual list of income for each individual US citizen. But that list is not available, for obvious reasons.
But after a few rounds of scepticism, data analysis and model critique you should get to a point where you trust the data more than your own guess. Otherwise we could just as well stop doing science at all.
Or the start-up equivalent 'innovation theatre'.
The median guess probably suffers from a "connect the dots" bias, going from (0,0) to (100,100) through the suggested point.
Seeing how smooth the data is, it results from a large sample, and the measurements are objective, I fail to see how they could have gotten them wrong.
Sounds interesting, but I seemed to have both missed that and am not noticing anything like it. Got a link?
He's saying that, "Just because you can't guess the trend in the data (eg. the track of a soccer ball in yesterday's match) doesn't mean that something is wrong with the data; you often need to double-check both your hypothesis and your data. And in this case your hypothesis was probably at fault due to inherent bias rather than inaccuracies in the data."
After a few goes your data needs to take precedence and one's guess dumped.
If that data's real then I want to know why it's tied to income and not something like wealth.
One wild theory.. quotas are based to income somehow, and that impressively straight line is because admissions officers are really good at their jobs.
Yes, in science, say, you should make a guess about the end result, based on something, like first principles, direct observation, etc. Then, if the calculated result diverges, check both.
In this case though there is no reason for the general public to have had a good picture of appropriate curve; it's a lot of hearsay and ideology which biases what we think it should look like, and it is right to trust that less than the actual data.
But yes, the scientific method is: make a hypothesis, collect data, test your hypothesis, revise, do it again.
It just shows an S curved the other way to what I drew.
This is EDUCATION done right.... Quite fitting really as the article is about Uni and education in itself!
This post definitely gets my up-vote.
Incredible! If only text books worked like this.
Desmos is trying to do this for math lessons: https://teacher.desmos.com/
The scales in this particular example are problematic, though. By using a logarithmic scale for the x dimension, the non-linear relationship between income and college attendance is hidden to the majority of readers. Logarithmic scales are hard to grasp for most people not working with numbers all day. Having percentages on both axes but only one of them being linear further obfuscates the variable relationship.
The y axis uses percentages, too. But it displays an absolute number of people, so the number of people in the 10-20% bracket equals those in the 80-90% bracket and so on.
The actual number of children won't be the same for each income bracket, but the are evenly distributed on the y axis. I think :)
Something so linear just makes me question whether there is some trickery going on. You learn early on that data is never so easily fitted.
Here it is : http://www.nber.org/papers/w17633
The female advantage graphs are truly interesting.
> For the most recent cohorts, the four-year college graduation rate for women (32 percent) is ten points higher than the comparable rate for males (22 percent).
This means that women were completing college (I believe in the year 2006) at 1.5 times the rate that men did. That's a huge difference, and from the charts it appears that the difference has been increasing for decades without signs of leveling off.
It's interesting.
It's fun.
I started drawing from the left, with the approach given below, however by the time I was at the 50th percecntile mark I was nowhere near 50% so I moved those up a bit. Around 40th to 60th percentile is when I would have done the worst without the aid of the middle point. (Which brought my graph up.)
My graph: http://imgur.com/a/hjvdf
- You drew a more accurate picture of reality than about 98 percent of people who have tried so far.
- Your line was relatively straight, reflecting one of the more striking findings of this research: The relationship between college enrollment and parental-income rank is linear.
- Your guess was extremely accurate. Is that you, Raj Chetty?
This was my methodology for drawing "extremely accurately":
Starting at left (where I started drawing) I reasoned, primary and secondary education is free and mandatory in the united states, and there are huge scholarship and other support programs. So while the poorest of the poor have everything going against them in terms of family support and even culturally, plus likely the pressure of starting to work early, still, I reasoned at least one out of five can make use of the opportunities and begin attending college.
I then intended to proceed up steadily, but I intended to level off somewhat between the 40th and 70th percentile, because a lot of average-income people simply start working. As you can see, the free point moved my graph up (via adjustment by me when I saw that I was still short of it at that point) heavily.
I had then intended to proceed up linearly to a very high rate of college attendance, and after a certain income level (say, top 5%-3%) I intended to be around 100%. I thought basically 100% of the top of the top attended college, but for me being in the top 5% of income would have assured that. It's not like measuring "graduate degree" or something else. A college degree is quite standard for children of the top incomes. I also thought it would stop levelling up because some people from extremely rich families produce lazy children by spoiling them. If your child doesn't go to college when you're making $150,000, they're not going to go to college when you're making $200,000. If they're not going to go when you're pulling $1M per year, they certainly aren't when you're pulling $5M per year. (in fact might be slightly less likely to.)
As you can see from the rest of the album - http://imgur.com/a/hjvdf - I did quite well. But these effects aren't present at all.
Some of the poor attended exactly as I predicted, and this rose immediately with income. The effect I predicted that did NOT appear is that in the middle class, there is a firm distinction between being at the 40th or 60th percentile - it is still linear. I would have thought it didn't matter. If you look here - http://blogs.marketwatch.com/encore/2014/10/02/incomes-are-m... - sadly they only show a few select percentiles, but let's go around the $51,939 level at 50%. That is let's say $3,100 per month take-home pay, give or take. I wouldn't have expected there to be a huge decision on whether YOU will attend college, depending on whether YOUR FAMILY is earning $2,800 per month or $3,500 per month. Essentially, I think this wouldn't figure into your decision at all, period. Also, I think that being at the 40th to 60th percentile does NOT mark a shift in cultural status (what part of the middle class you're in), and also is incredibly fluid. A family's income could easily shift by this amount from one year to the next - what, would their child not attend college in 2003 but would attend in 2005, because they're taking home $3,500 per month instead of $2,800? Maybe to some small extend, but certainly not linearly.
So I expected a smooth or levelled-off part in the middle percentiles. This didn't happen, but the supplied point helped me avoid it - I actively adjusted my graph due to it.
I wonder what the reasoning was behind giving people a supplied point. I guess they wanted to know the shape people guessed, rather than the levels people guessed? Or set people's expectations, so that they don't have wild expectations about the percentage of the population that attends college?
Exactly. They essentially fix the "m" in the y = k*x + m equation, and let people guess only k. That is, you factor out a lot of the guesswork about how many actually attend higher education and let the question focus on how it varies with income. When you ask people for a guess it's much easier to average a scalar value than a tuple. Clever, if you ask me.
You drew a more accurate picture of reality than about 92 percent of people who have tried so far.
You correctly guessed that children from the very poorest families face tough odds in going to college – only about one in four do.
You underestimated the chances of college enrollment for the very richest children. In reality, about 94 percent of children from America’s richest families go to college. (You guessed around 77 percent.)This is almost the Comfortable Middle Class version of the Find-your-way-through-a-Maze puzzles that you find on paper placemats in roadside Burger Restaurants.