Entropic Thoughts
16 hours ago
- William Sealy Gosset improved beer brewing at Guinness by developing new statistical methods and published under the pseudonym 'Student'.
- Using the sample standard deviation in a normal distribution gives too narrow confidence intervals, as it ignores uncertainty in estimating the true standard deviation.
- Gosset introduced the t-distribution, which provides correction factors for confidence intervals based on sample size (e.g., 4× for 2 samples, 1.2× for 6–8 samples, 1.1× for 9–20 samples).
- For a 90% confidence interval, multiply the estimated standard deviation by both 1.645 and the correction factor from the table to get a wider, more accurate interval.
- With just two samples, the standard deviation can be roughly estimated as 1.3 times the range (high minus low), useful for quick practical judgments.
- An example shows that with two values (43 and 47 litres), the estimated standard deviation is about 5 litres, so 49 litres is within one standard deviation of the mean and not unusually high.