Three men go hunting for bucks in the forest: an economist, a banker, and a statistician. The economist shoots his arrow first, and it lands 10 feet in front of the buck. The banker then fires his, and it lands 10 feet behind the buck. The statistician then leaps up and cries, joyfully, “We hit it!”

Despite the most elaborate precautions taken to ensure accuracy, when an object or physical phenomenon in the real world is measured repeatedly, the results are rarely, if ever, completely identical. As Menand recently pointed out, when a team of astronomers set out to chart the position of a star, the individual observations almost always vary. “The same problem arises,” he noted, “when a single astronomer makes multiple observations of the same star.” Because lack of agreement in repeated measurements is ever-present, how do we decide which one in a set of replications...

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