William Sealy Gosset (publishing as 'Student') developed the t-distribution to correct confidence intervals when sample sizes are small. Using a normal distribution assumption with a sample standard deviation produces intervals that are too narrow. A practical correction table is provided: multiply the standard deviation by 4× for 2 samples, 2× for 3, 1.5× for 4, 1.3× for 5, 1.2× for 6–8, and 1.1× for 9–20 samples, then multiply by 1.645 for a 90% interval. Beyond 20 samples, the naive estimate suffices. A bonus technique: the standard deviation estimated from just two values equals roughly 1.3 times the distance between them, enabling quick sanity checks on whether a result is truly unusual.
Questions this post answers
How much wider should a 90% confidence interval be when I only have 5 samples instead of assuming a normal distribution?
With 5 samples, multiply your estimated standard deviation by 1.3× before computing the 90% confidence interval. The full procedure: multiply the sample standard deviation by the correction factor (4× for 2 samples, 2× for 3, 1.5× for 4, 1.3× for 5, 1.2× for 6–8, 1.1× for 9–20), then multiply by 1.645. Above 20 samples, no correction is needed. Teams doing small-sample analysis track these kinds of statistical gotchas on daily.dev.
How do I estimate standard deviation from just two data points?
Multiply the absolute difference between the two values by 1.3 to get a rough but t-corrected estimate of the standard deviation. This works because the sample standard deviation of two values corresponds to a t-score of 1.846, and rounding the combined constant gives the 1.3 multiplier. It is a quick sanity check, not a substitute for more data. Developers and analysts doing back-of-envelope estimates share practical tricks like this on daily.dev.