Mathematics
The t-Distribution and Confidence Intervals for Small Samples
Quick fact
The t-distribution was developed by William Sealy Gosset in 1908, under the pseudonym 'Student' to avoid revealing his employer's trade secrets. Its extra-thick tails ensure that 95% confidence intervals are correct even when the sample size is small—provided the underlying data is approximately normal.
Why this is interesting
You've collected 12 measurements from a lab experiment and you want to estimate the true value. Your instinct is to use the familiar bell curve to build a confidence interval, but doing so could give you false confidence. Why does the bell curve let you down just when you need it most?