As Justin Wolfers pointed out in his post on income inequality last week, the Census Bureau was talking statistical nonsense. I blame the whole idea of statistical significance. For its weasel adjective “statistical” concedes that the significance might not be the kind about which you care. Here, I’ll explain what statistical significance is, and how its use is harmful to society.
To evaluate the statistical significance of an effect, you calculate the so-called p value; if the p value is small enough, the effect is declared statistically significant. For an example to illustrate the calculations, imagine that your two children Alice and Bob play 30 rounds of the card game “War,” and that the results are 20-10 in favor of Bob. Was he cheating?
To calculate the p value, you need an assumption, called the null (or no-effect) hypothesis: here, that the game results are due to chance (i.e. no cheating). The p value is the probability of getting results at least as extreme as the actual results of 20-10. Here, the probability of Bob’s winning at least 20 games is 0.049. (Try it out at Daniel Sloper’s “Cumulative Binomial Probability Calculator.”) Read More »
Relatives from South Africa were visiting and we got to talking about which cities to visit in America. I shared my list: San Francisco, New York, Boston, Washington, DC, Seattle, and Philadelphia. Each city has a Chinatown. Coincidence? Or maybe the connection is just that I like Chinese food. Indeed, our family has been going to a favorite dim-sum restaurant most every week since moving to Boston seven years ago.
Then the larger connection came to me. Chinatowns were made by Chinese laborers building the railroads (when the laborers had finished this vast public-works program, the Chinese Exclusion Act barred most Chinese from emigration to or citizenship of the United States). Having a Chinatown marks a city as of the railroad era, built up before the wide deployment of the automobile. As Lewis Mumford said, “The right to have access to every building in the city by private motorcar in an age when everyone possesses such a vehicle is actually the right to destroy the city.” Cities with Chinatowns had enough roots to escape carmageddon. Read More »
Division is the most powerful arithmetic operation. It makes comparisons. When the numerator and denominator have the same units, the comparison makes a dimensionless number, the only kind that the universe cares about. Long division, however, is something else entirely. In my post “Dump algebra,” many commentators objected to my loathing of long division. But long division is not division! Long division is just one way to do the computation, and is far from the most useful way.
On America’s first subway, Boston’s Green line, the middle doors stopped opening. When I asked the driver to open the doors, he said that he couldn’t: now all boarding and deboarding at the above-ground stops is through the narrow front door by the fare box. Ah, the MBTA: making up for the 23 percent fare hikes on July 1 with improved service!
Me: “The new policy slows the ride for everyone. Now passengers cannot board and pay their fares until all the deboarding passengers have left.”
Driver, shrugging: “It’s the new policy. I just do what my boss tells me to do. I don’t question.”
Me: “We could use some questioning.”
Driver: “Questioning isn’t part of my job. I just wait for my pay day.” Read More »
Fellow blogger Daniel Hamermesh recently explained the virtues of exchange as a painter helped him break into his Berlin apartment. My exchange example is not as glamorous. Shopping at the local co-op in Cambridge, I heard over the public-address system, “If you are the owner of a gray Subaru Outback, you are being towed!” I leaped over a low chain and made a break for the parking lot, as a mother nearby offered to watch my daughters (ages 1 and 4). The Subaru was hooked up and about to be hoisted onto the tow truck. In view of my timely arrival, the tow-truck operator offered two options: Pick up the car later that day in Somerville for $200, or pay $50 (cash) and he’d unhook the car now. An offer I couldn’t refuse. Everybody gained, yet I am still furious!
Being a good teacher, I like to think, requires a curious and freethinking mind. A supporting example is Andrew Hacker, described by a former Cornell colleague as “the most gifted classroom lecturer in my entire experience of 50 years of teaching.” His book Higher Education?: How Colleges Are Wasting Our Money and Failing Our Kids—and What We Can Do About It, co-authored with Claudia Dreifus, convinced me that tenure is harmful. His latest broadside, “Is Algebra Necessary?”, in last Sunday’s New York Times, is as provocative.
He argues that we should stop requiring algebra in schools. Despite the vitriol in several hundred comments (“We read them so you don’t have to.”), he is right. Read More »
As a country, we are often at war. If it’s not against Germany, England, terrorism, or Grenada, it’s the war on poverty (that’s gone so well), the war on cancer (ditto), and, of particular interest to me, the Math Wars, which have been raging for decades. On one side, the traditionalists insist on drilling and back to basics, “on behalf of sanity and quality in math education.” On the other side, the reformers insist on conceptual understanding using computers and calculators, to “promot[e] the rational reform of mathematics education.”
Both are half-right and half-crazy. As the reformers say, students need to understand what the mathematics means. Students whose word problem for “6 x 3 = 18″ is of the form “There were 6 ducks, and 3 more showed up, so 6 times 3 is 18,” understand little. (See “Children Learning Multiplication, Part 1,” in the articles by Professor Thomas C. O’Brien.) As the traditionalists say, using computers for everything leads to needing a calculator to compute what 6.5 x 10 is.
However, there’s a tool to combine the merits of both sides: the Quick, Approximate, Mental Arithmetic (QAMA) calculator. Read More »
One midnight, fed up from revising our dissertations all day, a friend and I drove the 10 minutes from Caltech into Chinatown to dine at Full House Seafood, open until 2 AM. (My Ph.D. adviser once asked why graduate students all seem to live on Guam time.) The restaurant was lively and crowded but not packed, and we quickly got a table. While waiting to give our order, I noticed an African-American man sitting on the chairs near the front counter. Even though several tables were free, the waiters did not offer him a table. Other customers came in, and were seated. As our dumplings arrived and got eaten, and then the spicy tofu, the man still sat on the small chairs. Read More »