Other pages in this series (7)
M2
Edition-to-edition exceedance
Share of moves between consecutive editions not covered by the two uncertainties
Takeaway
- Moves between consecutive editions exceeded twice the combined standard uncertainty of the two editions (|z| > 2) in 12.9% of pairs, about once in 8. The normal expectation is 4.55% (once in 22): what correct error bars would give.
- Moves beyond three times (|z| > 3) occurred in 9.1% (about once in 11), far more often than the normal 0.27% (once in 370).
- |z| > 1, by contrast, is rarer than the normal expectation: editions share data, so values mostly stay put and then move a long way at once when a new measurement or a corrected calculation arrives.
- Definition
- For each constant, the editions in which it is measured are put in order and each is paired with the next (an edition in which the constant is exact or absent is skipped). z is the change in value divided by the combined standard uncertainty √(u_old² + u_new²). z = 2 means a move of twice the combined width of the two error bars. The shares with |z| above 1, 2 and 3 are counted.
- Formula
- z = (x_new − x_old) / √(u_old² + u_new²). If the two editions were independent and normal, |z| > 1 would occur 31.7% of the time, >2 4.55%, >3 0.27%.
- Denominator
- 132 consecutive pairs over 17 core constants: 96 four-year pairs from 1998 on, 36 earlier pairs (4 to 13 years apart).
- How to read it
- |z| > 2 occurs in 12.9% of pairs (95% interval 9.4–16.3%), about once in 8. The normal expectation is 4.55% (once in 22), what correct, independent uncertainties would give. |z| > 3 occurs in 9.1% (5.1–13.3%), about once in 11, far above the normal 0.27% (once in 370). |z| > 1, by contrast, occurs in 26.5% (16.7–37.1%), below the normal 31.7%. Small moves are rare and large ones common.
- Caveats
- Consecutive editions share much of their experimental data, so they are not independent. Without new data a value barely moves (10 pairs did not change in any printed digit), pulling z toward zero. That is why the low share of |z| > 1 cannot be read as generous uncertainties (wide error bars). The share of large moves exceeds the normal expectation despite this. Intervals are a cluster bootstrap that resamples whole constants. With three candidates that meet the same selection rule added (helion and triton relative atomic masses, deuteron magnetic moment), the 20 constants give |z| > 2 in 12.1% and |z| > 3 in 8.1%.
ObservedNormalStudent-t (fitted to pairs with a change)
| Group | z | Threshold | Pairs | Constants | n | Rate % | 95% interval | Normal % |
|---|---|---|---|---|---|---|---|---|
| all pairs | z | |z| > 1 | 132 | 17 | 35 | 26.5 | 16.7–37.1% | 31.73 |
| all pairs | z | |z| > 2 | 132 | 17 | 17 | 12.9 | 9.4–16.3% | 4.55 |
| all pairs | z | |z| > 3 | 132 | 17 | 12 | 9.1 | 5.1–13.3% | 0.27 |
| 1998–2022 (4-year gaps) | z | |z| > 1 | 96 | 17 | 22 | 22.9 | 12.9–34.6% | 31.73 |
| 1998–2022 (4-year gaps) | z | |z| > 2 | 96 | 17 | 11 | 11.5 | 6.6–16.3% | 4.55 |
| 1998–2022 (4-year gaps) | z | |z| > 3 | 96 | 17 | 9 | 9.4 | 4.4–14.6% | 0.27 |
| 1969–1998 (4–13-year gaps) | z | |z| > 1 | 36 | 14 | 13 | 36.1 | 20.0–50.0% | 31.73 |
| 1969–1998 (4–13-year gaps) | z | |z| > 2 | 36 | 14 | 6 | 16.7 | 6.9–25.6% | 4.55 |
| 1969–1998 (4–13-year gaps) | z | |z| > 3 | 36 | 14 | 3 | 8.3 | 0.0–16.7% | 0.27 |
| all pairs | z_old | |z| > 1 | 132 | 17 | 37 | 28.0 | 17.2–40.0% | 31.73 |
| all pairs | z_old | |z| > 2 | 132 | 17 | 17 | 12.9 | 9.2–16.3% | 4.55 |
| all pairs | z_old | |z| > 3 | 132 | 17 | 12 | 9.1 | 5.1–13.3% | 0.27 |
Largest moves
| Name | Edition | z | z_old |
|---|---|---|---|
| fine-structure constant | 2006→2010 | 5.8058 | 6.4400 |
| proton rms charge radius | 2014→2018 | −5.2746 | −5.5246 |
| deuteron rms charge radius | 2014→2018 | −5.1051 | −5.3240 |
| Rydberg constant | 2014→2018 | −5.0946 | −5.3538 |
| deuteron relative atomic mass | 2018→2022 | −4.7051 | −5.0250 |
| alpha particle relative atomic mass | 1998→2002 | 4.4420 | 4.4490 |
| muon magnetic-moment anomaly | 1998→2002 | 4.2533 | 5.9219 |
| electron magnetic-moment anomaly | 1969→1973 | 3.8071 | 5.7419 |
| electron relative atomic mass | 1969→1973 | −3.7399 | −3.7471 |
| proton magnetic moment to nuclear magneton ratio | 1969→1973 | 3.7334 | 3.7412 |
| electron magnetic-moment anomaly | 2018→2022 | −3.2213 | −4.5556 |
| fine-structure constant | 2018→2022 | −3.2141 | −4.5455 |
Sensitivity: repeating the calculation over every 1998–2022 ASCII row whose name did not change (including rows that are conversions of one another) gives |z| > 1 38.8%, |z| > 2 11.4%, |z| > 3 9.2% (1640 pairs). The same move is counted in many rows, so the count is inflated.