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M3
Miss rate against the 2022 edition
Share of earlier error bars that do not contain the 2022 value
Takeaway
- The ±2σ ranges of earlier editions (twice the standard uncertainty: generous error bars) miss the 2022 value in 29% of cases, about 3 in 10. The normal expectation is 4.55% (once in 22).
- The 1969–1986 editions (25%) and the 1998–2018 editions (31%) miss about equally often: uncertainties shrank more than ten-thousand-fold, but the miss rate did not.
- Definition
- Using each earlier edition's value and standard uncertainty, count whether the 2022 value falls inside ±1σ (that edition's error bar) and inside ±2σ (the bar doubled). Henrion & Fischhoff's (1986) two indices are given too: the interquartile index, the share within ±0.674σ (about two-thirds of the bar; exactly the normal 75% quantile, 0.67449; normal expectation 50%), and the surprise index, the share outside ±2.326σ, the 98% interval (the bar stretched about 2.3 times; exactly the 99% quantile, 2.32635; normal expectation 2%).
- Formula
- z = (x_2022 − x_old) / u_old. Miss at kσ: |z| > k. Normal expectation: 31.7% outside 1σ, 4.55% outside 2σ, interquartile index 50%, surprise index 2%.
- Denominator
- By edition, the core constants measured in that edition and present in 2022 (10 to 17; the 2018 edition has 15, h and k being exact). Overall 134 (edition, constant) combinations over 17 constants.
- How to read it
- The 2022 value lies outside the earlier edition's ±1σ in 46% of cases (95% interval 30–62%) and outside ±2σ in 29% (19–40%); the normal expectations are 31.7% and 4.55%. The surprise index (outside ±2.326σ) is 25% (15–36%; normal 2%). Older editions do not clearly miss more often: at ±2σ, 25% for 1969–1986 and 31% for 1998–2018.
- Caveats
- With the three candidates meeting the same rule added (20 constants), 28% fall outside ±2σ. The 2022 edition is the current recommendation, not a set of true values, and may change. For constants exact from 2018 (fixed by definition rather than measured), such as the Planck and Boltzmann constants, the defined value is the reference (it was set from the 2017 special adjustment). Editions of the same constant are not independent, so pooled rates rest on fewer effective observations than their count suggests.
±1σ missed±2σ missedNormal expectation (if the uncertainties were right)
| Edition | n | Constants | 1σ % | 95% interval | 2σ % | 95% interval | IQ % | SI % | Median |z| |
|---|---|---|---|---|---|---|---|---|---|
| 1969 | 10 | 10 | 60 | 30–90% | 50 | 20–80% | 40 | 50 | 2.15 |
| 1973 | 12 | 12 | 42 | 17–67% | 17 | 0–42% | 42 | 17 | 0.78 |
| 1986 | 14 | 14 | 36 | 14–64% | 14 | 0–36% | 43 | 7 | 0.72 |
| 1998 | 15 | 15 | 60 | 33–87% | 40 | 13–67% | 40 | 33 | 1.57 |
| 2002 | 17 | 17 | 41 | 18–65% | 24 | 6–47% | 47 | 18 | 0.77 |
| 2006 | 17 | 17 | 47 | 24–71% | 35 | 12–59% | 47 | 29 | 0.88 |
| 2010 | 17 | 17 | 53 | 29–76% | 35 | 12–59% | 47 | 24 | 1.11 |
| 2014 | 17 | 17 | 53 | 29–76% | 29 | 12–53% | 35 | 29 | 1.24 |
| 2018 | 15 | 15 | 27 | 7–53% | 20 | 0–40% | 67 | 20 | 0.28 |
| 1969–1986 pooled | 36 | 14 | 44 | 26–62% | 25 | 12–38% | 42 | 22 | 0.78 |
| 1998–2018 pooled | 98 | 17 | 47 | 29–65% | 31 | 16–46% | 47 | 26 | 0.78 |
| all | 134 | 17 | 46 | 30–62% | 29 | 19–40% | 46 | 25 | 0.78 |