An old friend of mine from high school math team, Natalie Haynes, recently mentioned that she impressed her boss at work by identifying a Simpson’s paradox that helped the company she works for better understand some important data.  Simpson’s paradox is unfortunately very common.  As data begins to get the least bit complex (which happens very quickly with the inclusion of variables that aren’t perfectly correlated), Simpson’s paradox necessarily becomes inherent in some slicing of the data — so long as you look at the data from the “wrong angle”.  Even worse, that wrong angle very often masquerades as the right angle because it’s usually a “simple angle”.

The prevalence of Simpson’s paradox motivated the way I wrote the MIST Academy conditional probability lessons, which include one example of a Simpson’s paradox, then challenges the reader to unravel a storyline problem where the reader’s opinion of the data is typically anchored by the “wrong angle” and a lack of understanding of Bayesian statistics.

Natalie’s mention of her triumph spotting a Simpson’s paradox at work also helped me recognize something I’ve been doing for a while almost instinctively and without thought: I mentally correct for Simpson’s paradox or imagine potential corrections.

I recall vaguely the point at which I began to understand grammar rules well.  By “well” I specifically mean that I started spotting grammar mistakes everywhere: newspapers and magazines in particularly — not to mention advertisements and anywhere people might write in complete sentences.  As recognition of errors became more natural and automatic, it began to irritate me that I spotted quite so many errors by professional writers.  Then came acceptance, yadda yadda yadda.

The same evolution of understanding, recognition, and acceptance took place as I learned about conditional probability and analogous statistical concepts.  Now I see poor (or at least hastily accepted) interpretations of data everywhere.  It’s almost ubiquitous.  Several times while in college I spotted Simpson’s paradox in papers posted on doors in the Psychology building and offered to talk to researchers about the problem, which was the first time I really and truly got the first-hand feeling that not all scientists like to discover that they might be wrong. Though to be fair I should mention that I’ve had much better conversations with most scientists about these kinds of data problems.

Here’s an example from a professional economist:

Does that mean that college isn’t worth it? Not exactly. In fact, given the crappy economy, a college degree is more valuable than ever, a point that Levitt makes in a recent Freakonomics Radio podcast.  The most telling statistic as to the value of college: the unemployment rate among college graduates is less than half (4.5%) than people with only a high school diploma (9.7%). (See the BLS employment status table here.)

There may be arguments in favor of the high tuition costs at universities, but this one fails hard, and it’s disturbing to see a highly noted economist (and one whose works I enjoy) use it as the “most telling statistic”.  Other variables need to be considered.  On average, college graduates have higher IQs, more money, and better understanding of the structure of the society they live in to begin with than those with less education, so there is a clear selection bias.  If college involved involved nothing but football games and keg stands we would expect college graduates to achieve higher levels of employment.  Even the nature of the jobs considered matters.  Recently the increase in minimum wage knocked over a million jobs out of the economy.  Few if any of those jobs included college educated workers, but plenty included those with a high school diploma, setting up a clear conditional that must be resolved before the statistics above are particularly meaningful.  Really, these only begin to scratch the surface of my best arguments that important conditionals are missing in this case — they’re just the ones that are easiest to point out in one paragraph.  A whole book could be written on the conditionals that affect the above statistics and its damning to the economics community that few economists seem to recognize that. This point should at the very least be mentioned, and the moment it gets mentioned the economist would have to step back and reevaluate the story told by the statistics.

It may certainly be the case that college is economically worth the high costs, but any assertion that these statistics anchor the debate is absurd.

I see it everywhere.  Eventually I fell prey to acceptance.  I see it everywhere.  I sometimes complain about it to anyone who will listen (not that often).  I do nothing about it.

Well, I did eventually write some really cool classes about it for my students.  Now it’s a standard part of the curriculum I use with students as young as 10 years old.  These really are some of the more creative classes I’ve written, so I’m particularly proud of them.  But the reason I spent so much time thinking about them (and plan to spend even more in the near future) is because I’m shaking off the acceptance that the world needs to be this way.  It doesn’t.  And there is opportunity!

People will always misinterpret statistics, but motivated problem solvers can find ways to minimize the impact of the problem.  I once considered building a medical data consulting service that I figured would be based primarily on hunting down and extinguishing the damage caused by Simpson’s paradox and analogous Bayesian misunderstandings in health care/medicine — which is quite extensive and costly both in terms of dollars and lives!  I’ve decided to both blog about this idea and encourage others to take up this cause professionally so that I don’t have to change vocations to make a difference.

Health care is a slam dunk example.  You’d have a hard time convincing me that we can’t save billions of dollars annually in health care costs if we set some really smart people about the task of ferreting out all the problematic interpretations of data.  But there are examples of damaging data misinterpretations all over the world — including particularly valuable problems to solve in the business world.  In fact, an old friend of mine just found one…

A little while ago I checked Facebook.  Probably a bad habit, but there is certainly reward to having a Facebook page.  Here’s a great example from a status posted by a fellow mathophile a few minutes ago:

The car parked in front of me was about to get ticketed, and I offered to save them – the parking cop wouldn’t let me put money in the meter for someone else. So then I drove ahead of the cop and put coins in all the red meters for about a mile up the road.

I’m no expert at this, but I get better at it the more I work with children.  Here’s a post by Tyler Cowen (actually, mostly Gareth Cook) about bribing children.

I like the post, but I dislike the perspective of “bribery”.  What we’re talking about might be deemed “artificial positive reinforcement” with the goal of helping kids set goals and achieve rewards that dovetails with our immediate needs as adults to get children beyond the point of being dependent on us in particular capacities.  Here’s one quote I like:

Stay positive. In our house, we call them “challenges.’’ It is not about “fixing’’ a negative. Don’t nag. Let it be their choice. Pile on the praise.

Exactly.  The greater goal is not short term (unless you just don’t care about the future of the child/student).  The greater goal is the long term development of the child into someone capable of independently handling his/her own affairs.  This reminds me of one of my favorite quotes:

“Love is a better teacher than duty.” — Albert Einstein

I like Steven Levitt and in general the guys behind Freakonomics, so I read at least two or three of their blog posts most weeks.  They have informed me about some topics and given me plenty to think about over the past few years.  Today I came across one that I don’t particularly like so much.  The “Daughter Test” that Levitt applies seems very human, very “reasonable” in the sense of “just being human”.  But Levitt is an economist, and surely he recognizes that being swayed in this way creates a prisoner’s dilemma by which people desire to create laws that benefit their family construct to the possible detriment of others (and negative net benefit to society).

I give Levitt a bit of a pass because he seems to be applying the Daughter Test as a tie-breaker of sorts.  When he’s on the fence about an issue, he applies it.  Then again, not really, and he admits as much.  Do I give him a pass on close calls?

What about every person whose sense of family encroaches more and more on the liberties of others?  Were everyone as smart as Levitt, the failure of the Daughter test might pass under my radar.  But people are all kinds of irrational and I simply don’t like the idea of basing restrictive laws on what would ultimately lead to a plurality of cultural norms.  Levitt gives no consideration to the fact that driving “vice” activities underground might hurt another’s daughter much more, or that he’s likely not actually talking about his own daughter.

I propose the Prisoner’s Dilemma test: that every professional economist should consider whether any given decision calculus they propose erects a prisoner’s dilemma.  This is likely the best way to avoid unintended consequences in policy — at least insofar as policy is informed by economists.  Though to be fair, I think politicians usually prefer to inform economists of the views they must be prepared to justify.

Truth seeking is the motivation behind the scientific method, hence behind all of science.  So it stands to reason that any system through which we put future scientists should encourage honest behavior.  Unfortunately our current system of compulsory education does the opposite (hat tip Eli Ross).  Unfortunately this discussion isn’t likely to find footing in today’s political environment where those in charge of the system routinely castigate anyone with criticisms inherent to the system — because creative destruction is not a political option [or so the people in charge believe].  And so we’ll see even the reformers fail (hat tip James Johnson) time and again.

The solutions are surprisingly simple, but I suspect that it will take the further development of disruptive technologies to lead people to those solutions, because we’ll need to excuse people for their “involuntary” behavior.

Strictly Ballroom is one of my favorite movies.  It’s the tale of a dancing family whose son breaks away from the establishment and dances “his own steps”.  In the meantime he falls in love with the artificially awkward and socially abused girl who began the film as a blur in the background of the dance school.  It’s a serious social critique moved along by a sometimes wacky series of sad and comedic events.

One of the themes Strictly Ballroom explores is how established institutions quickly fall prey to the desires of their clergy to maintain their status.  This point is personified by the dance federation director, Barry Fife: “If you can’t dance a step, you can’t teach it, and if you can’t teach it — we might as well all pack up and go home. With young Liz available again, you’ve got a chance to get your status quo vadis back… so to speak.”

Somewhere in all this is one of the most important lessons in education, but I’ll leave that part to the reader.

Everybody knows that the number of homeschoolers has increased dramatically over the past decade.  The reasons for more homeschooling have been split between primarily academic and primarily religious, though I’d throw in “primarily philosophical” as a category that seems to be expanding, though this probably gets lumped into “primarily academic”.

Homeschooling is a substantial commitment and means giving up around $12,000 per student per year in taxpayer funded support of the public school systems.  So I expected a few homeschooled students to join MIST Academy when I moved here.  A few have, but surprisingly the larger number of homeschoolers joining MIST seem to be from the Huntsville/Madison area which makes me ponder whether more families there are rejecting the public schools for academic reasons.  Having spent two years teaching there, I can understand.  Nobody seems satisfied.

This makes me wonder: will there be some city in which the academic homeschool community grows so large that they simply become a sort of mega-school community?  I bet so!  It will be interesting to see where this happens first.  It will also be interesting to see how the tax politics change when that happens.

This is an interesting post about the relationship between the two.  I think this is another case in point about how resistant the current system is to change.

I wish the post had mentioned whether or not the threats to fire cheating teachers had teeth.  That matters a lot in this case (and in general).

Hat tip: James Edward Johnson

The Freakonomics guys say it’s about 30%, and that number is due to a clever study based on the Vietnam draft that incentivized college education for those young men with “bad draft numbers” (in terms of lottery position).  But we live in a different world.  It’s not clear how much of that 30% increase is due to signaling and networking, and how much is due to the subject matter of the classes.  I suspect the subject matter itself is of lower importance for most fields, and higher importance for highly technical fields.  But how can I know?

And in the end, do we now live in a world of higher signal rates and constant network connectivity that pushes us into dense networks with or without college?

Hopefully it won’t take us another draft to find out, but I’m not willing to stand on the assumption that our world is enough like the 60′s to say 30% is “correct”.

That said, I think the value of learning to educate yourself is higher than ever — whether you do it inside of school, at home, or wherever you might be.

Many of my friends in the U.S. complain about wealth inequality in the U.S.  There is a distinct class of wealthy workers that is really several groups: inheriters, highly educated top producers, and stealers.  They point toward larger middle classes in some European nations.

I have nuanced opinions about the matter that I’m not really interested in writing about at the moment.

Many of  my friends in Europe complain about labor inequality in Europe.  They say that yes the wealth is spread out, but the work is not.  As one of my friends put it on Facebook today: “People here work eight hour days that include two three hour naps,” while others work all day. And “Everybody who aspires to be anything aspires to be American.”

Sometimes it all just seems like greener grass and a fence in between that allows us to rationalize all of our misunderstandings of our own problems.