`ews_to_stellar_parameters`: `sigma_mean` is computed from `length` of a scalar, so no √N reduction is applied
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説明
Hi, I found an issue in `src/Fit/fit_via_EWs.jl:560-567`:
```julia
estimated_err = std(A[isfinite.(A)])
sigma_mean = estimated_err ./ sqrt(length(estimated_err))
teff_residual_sigma = estimated_err *
get_slope_uncertainty([line.E_lower for line in linelist[neutrals]])
vmic_residual_sigma = estimated_err * get_slope_uncertainty(REWs[neutrals])
[teff_residual_sigma, sigma_mean, vmic_residual_sigma, sigma_mean]
```
`estimated_err` is a scalar, so `length(estimated_err)` is 1 and `sigma_mean`
is just `estimated_err`. Looks like the standard error of a mean was intended.
Reproduction, no Korg call needed:
```julia
using Statistics
A = randn(150) .+ 7.5
estimated_err = std(A[isfinite.(A)])
sigma_mean = estimated_err ./ sqrt(length(estimated_err))
sigma_mean == estimated_err # true
estimated_err / sqrt(length(A)) # 0.0775 vs 0.9493 — factor 12.25
```
`sigma_mean` is returned for equations 2 and 4, both differences of means:
- eq. 2, `mean(A_I) - mean(A_II)`: should be `err * sqrt(1/n_I + 1/n_II)`,
inflated ~4.2x for 150 Fe I + 20 Fe II
- eq. 4, `mean(A) - ([m/H] + A_solar)`: should be `err / sqrt(n_total)`,
inflated ~12x for 150 lines
Both feed `param_uncertainties` at line 426, so reported σ(log g) and σ([m/H])
are too large by those factors. Conservative, not dangerous — but it also makes
them incomparable with σ(Teff) and σ(vmic), which are scaled correctly through
`get_slope_uncertainty`.
The two equations have different denominators, so one `sigma_mean` cannot cover
both:
```julia
n_neutral = count(neutrals .& isfinite.(A))
n_ionised = count((.!neutrals) .& isfinite.(A))
n_total = count(isfinite.(A))
sigma_ionisation = estimated_err * sqrt(1/n_neutral + 1/n_ionised)
sigma_metallicity = estimated_err / sqrt(n_total)
[teff_residual_sigma, sigma_ionisation, vmic_residual_sigma, sigma_metallicity]
```
I can PR this. It shrinks reported σ(log g) and σ([m/H]) by roughly an order of
magnitude, so it may warrant a release note despite being a bug fix.
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