Even when you have a larger sample, however, the groups are not going to match the average of the whole population every time; by blind luck, sometimes the group will be exceptionally tall, sometimes exceptionally short. Statisticians understand this. But journal editors and journalists do not necessarily exercise appropriate caution. That’s not because journal editors are dumb and don’t get statistics, but because scientific journals are looking for novel and interesting results, not “We did a study and look, we found exactly what you’d have expected before you’d plowed through our four pages of analysis.” This “publication bias” means that journals are basically selecting for outliers. In other words, they are in the business of publishing papers that, for no failure of method but simply from sheer dumb luck, happened to get an unusual sample. They are going to select for those papers more than they should – especially in fields that study humans, who are expensive and reluctant to sit still for your experiment, rather than something like bacteria, which can be studied in numbers ending in lots of zeroes.
This is completely unsurprising. Why isn’t there a stronger culture of releasing full datasets and full code? Social scientists work primarily with software, rather than manual hand calculations – why not just release their R scripts and Excel sheets? (Answer: because when you do, like Reinhardt and Rogoff, people can call you out on your errors)
The standard explanation to the Monty Hall probability problem is not only imprecise but also wrong. It turns out the true explanation, based on conditional probabilities or Bayesian reasoning, has the double advantage of being not only correct but also not too hard to understand.
Europe’s monetary union has been based on bad economics from the start. As German economist Rudiger Dornbusch wrote in Foreign Affairs in 1996, “If there was ever a bad idea, EMU is it.” The eurozone does not have the features of what economists call an “optimal currency area.” According to the standard definition, an optimal currency area is characterized by perfect labor mobility, perfect wage flexibility, and a risk-sharing system, such as fiscal transfers when a region — or a member country — is affected by an economic or financial shock.
It’s unclear how the new Syriza government will be able to ditch austerity without also ditching the currency union. And European leaders aren’t softening their stance on their rejection of the idea of forgiving Greece’s debts — a prospect that would anger taxpayers in other European countries. Many analysts expect Tsipras will eventually have to find a face-saving compromise.
Yet while its competitors have been abandoning the business of making big bets with their own money, frequently citing the risks involved, Goldman has been quietly coming up with several new ways to put its own money to work in formats that appear to stay on the right side of Volcker.