Amid the flurry of scientific energy, the team faced a persistent problem: interpreting its data in the face of small sample sizes. One challenge the brewers confronted involves hop flowers, essential ingredients in Guinness that impart a bitter flavor and act as a natural preservative. To assess the quality of hops, brewers measured the soft resin content in the plants. Let’s say they deemed 8 percent a good and typical value. Testing every flower in the crop wasn’t economically viable, however. So they did what any good scientist would do and tested random samples of flowers.
The theory underlying these perennial questions in the domain of small sample sizes hadn’t been developed until Guinness came on the scene—specifically, not until William Sealy Gosset, head experimental brewer at Guinness in the early 20th century, invented the t-test. The concept of statistical significance predated Gosset, but prior statisticians worked in the regime of large sample sizes.
Gosset recognized that this approach only worked with large sample sizes, whereas small samples of hops wouldn’t guarantee that normal distribution. So he meticulously tabulated new distributions for smaller sample sizes. Now known as t-distributions, these plots resemble the normal distribution in that they’re bell-shaped, but the curves of the bell don’t drop off as sharply. That translates to needing an even larger signal-to-noise ratio to conclude significance. His t-test allows us to make inferences in settings where we couldn’t before.
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