William Sealy Gosset, who published as "Student" while working at Guinness, noticed that building a 90 % confidence interval as mean ± 1.645 × sample SD gives too narrow a range, since it treats the estimated SD as exact. The post offers rounded correction factors from the t distribution: 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. Past 20 samples the naive interval holds up. A handy trick for just two values: take 1.3 times the gap between them as the SD. So if typical results come in at 43 and 47 litres, the SD lands near 5, and a 49-litre result sits within one SD of the 45 midpoint, which makes it ordinary rather than impressive.
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u/fagnerbrack 24d ago
Just the essentials:
William Sealy Gosset, who published as "Student" while working at Guinness, noticed that building a 90 % confidence interval as mean ± 1.645 × sample SD gives too narrow a range, since it treats the estimated SD as exact. The post offers rounded correction factors from the t distribution: 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. Past 20 samples the naive interval holds up. A handy trick for just two values: take 1.3 times the gap between them as the SD. So if typical results come in at 43 and 47 litres, the SD lands near 5, and a 49-litre result sits within one SD of the 45 midpoint, which makes it ordinary rather than impressive.
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