90% of the T Distribution
2 days ago
- #William Gosset
- #Confidence Intervals
- #Statistics
- William Sealy Gosset improved Guinness beer using statistics and invented new methods, publishing under the pseudonym 'Student'.
- Gosset corrected the naive method for 90% confidence intervals by accounting for uncertainty in standard deviation estimation.
- Correction factors depend on sample size: e.g., 2 samples = 4×, 3 = 2×, 4 = 1.5×, 5 = 1.3×, 6–8 = 1.2×, 9–20 = 1.1×.
- With more than 20 samples, the naive standard deviation estimation is sufficient for 90% intervals.
- Example: For 7 samples, mean 32, SD 8, corrected interval is 32 ± 8×1.2×1.645.
- For sloppy standard deviation estimation from just two samples, multiply the difference by 1.3.
- Practical example: Values 43 and 47, difference 4, estimated SD ≈ 5; 49 is within one SD from midpoint 45.