Preface to Making Fair Comparisons

Making some progress on the Making Fair Comparisons textbook. The preface is below.

One thing I’ve learned from reading cheesy self-help books: If you believe a skill will change a person’s life, you should say it. At the end of the book, the reader will know if their life is changed or not. There’s time to be cynical later. At the beginning of the book, let your passion show.

So anyway, here’s the cheesy intro to the text. I love it.

Why we compare

Which intersection in town is the most dangerous?
How much more expensive will college be if I graduate a year late?
Which product line has given our business the best overall return in the past two years?
How much more campaign money was spent in the election of 2008 compared to previous elections?

Comparisons don’t happen in a vacuum. Usually when someone is comparing things, they are comparing them for a reason. In the case of the intersection question above, maybe there is an action pending – if we are going to upgrade one intersection, which one should it be? Businesses may want to know what products have been the most profitable so they can pursue profitable avenues at the expense of the less profitable ones. A political scientist may be investigating the influence of money on elections, and trying to determine if that influence has increased over time.

Ultimately, comparisons have real world consequences. If you rightly determine which intersection is the most dangerous as an urban planner, perhaps you can save a life. Knowing which product lines have given a company a good return could be the key to keeping a business afloat, saving your job and the jobs of others.  Determining whether money in elections is out of control or in line with historical trends can help us plot a course of action for our country that fixes what is wrong with our system while preserving what is right.

Depending on what profession you go into, you may use algebra or you may not. Some of you may use calculus or trigonometry. Some of you will be asked to use advanced statistical methods. Most won’t.

But every single one of you will be asked to compare things as an employee, consumer, and citizen. And whether you are able to compare things adequately will have dramatic effects on the success of your business, your family, and your community.

This is a book about how to use very simple statistical techniques to compare things. It is not so much about formulas as it is about critically thinking about numbers. We honestly believe this skill will be one of the most important skills you acquire in your college career.  Mastering it will change your life for the better, and get you closer to being the sort of person you want to be.

Comparing Election Spending

Everyone knows that campaign spending is out of control, right?

Except it’s not. In raw numbers, of course, the amount just keeps getting bigger, but controlled for inflation, it’s exactly what you would expect, and no more expensive than it was at the turn of the century, as the graph above from Mother Jones shows.

And if you control for eligible voters (remember that women did not get the right to vote until 1920, and 18-21 year olds did not get to vote until the 1970s), Jonathan Bernstein points out that we are spending far less on elections per voter than we did early in the century.

So what’s going on? Dana Houle notes at Rooted Cosmopolitan that the election reforms of 1973 capped contributions at $1,000. Because the cap was not indexed to inflation the cap very quickly moved from being relatively generous to exceedingly tight. You can see the result – as inflation skyrocketed, the real worth of $1,000 plummeted. In 2004, the cap was reset to $2,000 (which frankly only begins to adjust for post ’73 inflation), then in 2008 it was raised to $2,300, and what you see is the amount finally catching up to historical norms after its post-Watergate reform lows.

In the course we’re putting together on Making Fair Comparisons, one of the rules we give students is to control for inflation and population wherever you can, if only to see what happens. It’s hard to figure out how to control for something more complex, but you can get per capita numbers and inflation adjusted dollars pretty easily from WolframAlpha – it takes under 10 seconds to control a couple numbers and see what happens. Yet, no one does. We’d rather throw around “Most expensive campaign ever” nonsense, because it fits our intuitions or our politics.

I’ll make one more comment – it’s often mentioned by Lessig and others how much time politicians have had to spend raising money – a disciplined candidate will spend ten or more hours a week doing direct fundraising calls and as many hours doing fundraising events. Lessig claims that congressmen will spend 30% to 70% of their time raising money, implying this is a new phenomenon – looking at these charts I wonder if the increased fundraising time is a result of the non-indexed cap. In 1973, if you wanted to raise $1 million dollars for a general election race, you’d have to get maximum donations from 200 of those names on your call list. By 2004, you’d have to get more than four times that many maximum donations. No wonder congress members that served through the seventies forward have said that the amount of calls they had to make for money has increased – inflation was pushing them to it.

Incidentally, I favor publicly funded elections, for a variety of reasons. But we should be suspicious of claims that the current spending is exponentially larger than it was in the past. And as we tell our students, we should be ruthless with commentators and pundits who don’t at least attempt to control for relevant variables.

Liberal Arts and Transfer

In a Moneybox post I mostly agree with, Matt Yglesias says this:

In order to do well in courses on 19th Century British Literature or Social Anthropology or Philosophy or American History in a properly running American college, what you need to do is get pretty good at reading and writing documents in the English language…. [And] If you can compose an email that’s 10 percent clearer in 90 percent of the time as the other guy, you’re going to get ahead in a wide range of fields. Outside of office work, a big part of the difference between a hard-working individual who’s pretty good at his job and a person who’s able to leverage his skills and hardwork into an entrepreneurial or managerial role is precisely the ability to research things and write up plans. Everyone knows that a kid growing up in rural India is obtaining valuable skills if he gets better at English, but this is equally true for a kid growing up in Indiana.

To which I would say, yes – but there is not as much transfer in that area as you might think. In many ways, academic writing trains one in habits that have to be unlearned in a business environment (as a former language and linguistics grad student I can attest to this). The quality of business writing among faculty, who have practiced writing more intensely than most, is not any better than that in the general population.

Liberal Arts *can* be very useful to business, but it has to be taught for transfer, in an integrative way.  It requires getting beyond the term paper conception of writing and into something less formal but more regular. And maybe more varied — again, transfer (for many students) requires practice across multiple domains with explicit explanation of how the domains relate. The kid at the top of your class is going to move from Milton to competitive analysis reports just fine, but the kids in the middle need guidance.


Another day, another misguided graph on happiness research. This time Fast Company (tech populations are ground zero for happiness research for some reason) puts up the graph above. Which seems interesting, right?

Except that in the article we find this:

Some countries are significantly happier than others (happiness is, of course, subjective). Indonesia, India Mexico, and Brazil lead the pack in happiness, while Russia, South Korea, and Hungary are all pretty miserable (see the chart). There are other factors as well: People who are under 25 are most likely to say they’re “very happy”; Latin American countries as a whole have the most “very happy” people; and people with high income and extensive education are also most likely to report being “very happy.”

I got interested in how much the age question figures in, because just glancing at the big graphic I could see it looked almost identical to what these nations would look like if ranked by median age.

Turns out it probably figures in a lot. Here are the top five “happy” nations and their median age (from WolframAlpha):

Indonesia: 27.6 yr
India: 25.3 yr
Mexico: 26.3 yr
Brazil: 28.6 yr
Turkey: 27.7 yr

Here are the bottom five:

Italy: 43.3 yr
Spain: 41.1 yr
Russia: 38.4 yr
South Korea: 37.3 yr
Hungary: 39.4 yr

So, in other words, most of what we are seeing in the above graph may be attributable to age — not country at all. Young people say they are happier, countries with a lot of young people will therefore have higher reported happiness, which tell us… well, nothing except those countries are young demographically.

Is it the whole story? Well, probably not. But I have no idea why you wouldn’t control for median age in a graph like the one above.

I’ll also add that I think the sociolinguistics of “happy” are pretty difficult. Young people value happiness (and respond to polls accordingly). Older people, especially those with children, often see happiness as too thin a word for what governs their life — life is partially about sacrifice, a parent hitting a 5-point bubble on a Likert scale may see that as an indication of selfishness (rightly or wrongly). So even with the age difference, I’m not sure what happiness research is really getting at.


Students really don’t get randomness. This is the classic Trick Coin Flip question — I have a trick coin that either comes up heads a bit more than tails, or tails a bit more than heads [They sell trick coins both ways, apparently]. I don’t know whether this particular trick coin tends towards heads or tails, and I don’t know by how much.

We call the tendency of the trick coin to “tilt” results in one direction it’s bias. I have the trick coin in my hand. Which of the following would give me the best idea of the coin’s bias?

  • 10 flips?
  • 100 flips?
  • 1000 flips?
  • or, it doesn’t matter, all of these give you the same idea of the coin’s bias.

The results from class you can see above. More later on this.

I want to do this in a class….

What a neat way of combining two textbooks to get a novel course design (which meshes with current theories of interleaving):

In an effort to maximize spacing and encoding variability, Robert Bjork once taught an honors introductory psychology course twice in one term. Up to the point of the midterm, the basic concepts of introductory psychology were covered using a textbook that adopted a history of psychology approach and emphasized the contributions of key individuals in the history of psychology, such as Pavlov, Freud, and Skinner. After the midterm exam, the basic concepts were covered again, this time using a textbook that adopted a brain mechanisms approach. The goal was to have key concepts come up in each half of the course (spacing) and from a different standpoint (variation).

From here.