Category Archives: Statistics

A Minor Correction to Richard Posner

I quoted the following passage from Richard Posner in my recent article on Scotland’s three-verdict system:

When . . . judges and juries are asked to translate the requisite confidence into percentage terms or betting odds, they sometimes come up with ridiculously low figures-in one survey, as low as 76 percent, see United States v. Fatico, 458 F. Supp. 388, 410 (E.D.N.Y. 1978); in another, as low as 50 percent, see McCauliff, Burdens of Proof: Degrees of Belief, Quanta of Evidence, or Constitutional Guarantees?, 35 Vand. L. Rev. 1293, 1325 (1982) (tab. 2). The higher of these two figures implies that, in the absence of screening by the prosecutor’s office, of every 100 defendants who were convicted 24 (on average) might well be innocent.

See if you can spot the error in this reasoning. Continue reading A Minor Correction to Richard Posner

Significance Tests as Leading Questions

Under the common law, lawyers are not allowed to ask witnesses “leading questions,” as witnesses can be influenced by the way questions are asked. A leading question is one that suggests a particular answer, for instance, “Were you at the country club on Saturday night?” is a leading question, while, “Where were you on Saturday night?” is not.

Econometricians should be as careful as lawyers when questioning the most unreliable of all witnesses: economic data. Most statistical software will automatically spit out t-tests for whether the coefficients in regression models equal zero. This is equivalent to asking the data, “Data, given these modelling assumptions, can you deny with 95% certainty that this coefficient equals zero?” That’s a leading question, and the econometrician shouldn’t ask it unless he has special reason to suspect that the coefficient is zero. Continue reading Significance Tests as Leading Questions

Mises, Probability, and the Two Envelopes Problem

In Human Action, Mises distinguishes between what he calls “class probability” and “case probability.” He defines class probability as such:

Class probability means: We know or assume to know, with regard to the problem concerned, everything about the behavior of a whole class of events or phenomena; but about the actual singular events or phenomena we know nothing but that they are elements of this class.

This is the ordinary sort of probability. We reach into an urn containing seven red balls and two white balls, so the probability of choosing a red ball is 7:2. We can say this because we have knowledge about the class of balls in the urn. Mises distinguishes this from case probability:

Case probability means: We know, with regard to a particular event, some of the factors which determine its outcome; but there are other determining factors about which we know nothing.

Continue reading Mises, Probability, and the Two Envelopes Problem

Erdmann, Empiricism, and the Minimum Wage

Erdmann's MW and teen unemployment graph
Pre-trend lines are for period from 27 to 3 months before MW hike. MW Trend lines are for period from 3 month before to 27 months after initial MW hike. [Y axis = Teen Employment To Population Ratio]
Kevin Erdmann, over at Idiosyncratic Whisk, posted a graph similar to the one shown above,* demonstrating that the trend in the US teen employment rate after a minimum wage hike was lower in all but one case than the trend before the hike.

There have been many responses, but I would like to focus on one over at Angry Bear that captures the worst of the criticism.** The writer goes way over the top in criticizing Erdmann, saying that people who oppose the minimum wage “apparently believe that the business cycle never impacts teen employment or unemployment.” To read this article, you’d think think that the only opposition to the minimum wage came in blog-post form. Frankly, no empirical analysis coming from a blog (including Angry Bear) can offer anything but a prima facie case for or against some proposition. I don’t read Erdmann as claiming that his little graph is the final word on the minimum wage.

The Angry Bear post goes on to use some very questionable econometrics to show that the minimum wage doesn’t have a big impact on teen unemployment. The author doesn’t use the inflation-adjusted minimum wage in his graphs (and presumably in his regression) for reasons unknown, making them pretty irrelevant. He then naively regresses the teen unemployment rate against adult unemployment, a recession dummy, the teen population, and the minimum wage to find that (surprise!) the minimum wage doesn’t have a big effect on teen unemployment. For someone who criticizes others about omitted variables, this regression should be pretty embarrassing. That’s time-series data! You don’t just apply OLS regression to time-series data. OLS regression assumes uncorrelated error terms, and the fact that adult (and teen) unemployment last month is highly correlated with adult (and teen) unemployment this month destroys that assumption. Continue reading Erdmann, Empiricism, and the Minimum Wage

Abstaining From Alcohol has Ambiguous Effect on Life Expectancy: Study

Alcohol! I only drink to make YOU more interesting!Can you imagine a news article with that title? Certainly not. How about  this one: Abstaining from alcohol significantly shortens life. There, that’s more sensational, isn’t it? (To be fair, that’s the title on the page, not the title of the article. I’m not sure why they aren’t the same.)

I’ve seen news articles circulating about a recent study from the University of Texas at Austin that followed 1,824 adults between the ages of 55 and 65, and compared how likely they were to die over a 20-year period depending on whether they abstained from drinking alcohol, drank moderately, or drank heavily. The results indicated that moderate drinkers had the  greatest longevity, followed by heavy drinkers, with abstainers being the most likely to die.

This is where the science reporters stopped paying attention, and started writing sensationalist “alcohol is good for you!” news articles.

I’m skeptical of this interpretation. The technique being used by the researchers is one that is very common in health and social science studies, whereby the researcher measures many real-world variables, and uses linear regression to tease out the effects of each variable on the variable under study. Continue reading Abstaining From Alcohol has Ambiguous Effect on Life Expectancy: Study