[Sane-analysis] A2 fit error band and d2 errors

[O. A. Rondon]

I have added the error band for the fit to A2, with and without
covariances, as for the A1 fits
https://userweb.jlab.org/~rondon/analysis/asym/world/fit_A2-invW.pdf

Using the error bands for the simpler 1/W fit form, I have calculated
the  fit errors on d2 which  represent the error on the matrix element,
since the fits include total errors (statistical and systematic).

I plotted the results for the conservative case of only including the
diagonal terms of the fits covariance matrices. The errors including
off-diagonal correlations are smaller, as expected, about 1/2 of the
diagonal only ones. See the plots on p. 4.
https://userweb.jlab.org/~rondon/analysis/asym/world/d2.pdf

The d2 values for the different fit forms (1/W vs W^c) differ by about
the size of the fit errors (diagonal terms only). Taking that difference
 as an estimate of model errors, combined fit + model errors are about
twice the size of the fit errors alone

d2(3GeV^2) =  0.0006+/-0.0005
d2(5GeV^2) =  0.0043+/-0.0003

In addition, I have done separate fits for the SLAC and SANE A1 and A2
data subsets. All the numbers, including parameters, their errors, etc.
are given on tabs A1_fits" and "A2 _fits" of the spreadsheet A1_fits.ods.
https://userweb.jlab.org/~rondon/analysis/asym/world/A1_fits.ods

I noticed that the fit parameters change considerably between SANE and
SLAC for the A1(W^c) fit, due to stronger correlations between some
parameters, and there is a similar, milder effect for the A2(1/W) fit,
too, so I applied the Kolmogorov-Smirnov test to the data sets, to check
whether they come from the same parent distribution.

While the K-S test is really valid only for quantities that depend on
only one variable, it should work for A1 and A2, since the W dependence
dominates over the Q^2 one. The results are posted as the files
kolm*.pdf (reports in files with *test* in name; and plots - SLAC is
solid curves/histos).

The conclusion is that SLAC and SANE A2 probably share the same parent
distribution, although there are outliers in the SLAC data which, may be
due to those outliers, does not have a normal distribution.

But the test seems to rule out the hypothesis that SLAC and SANE A1
share the same parent distribution. In fact SLAC's A1 is even less
normal than SLAC's A2, but SANE A1 and A2 are both consistent with the
normal distribution.

It's unclear whether the issue may lie with our SANE A1 or with SLAC's.
But this seems to point to having to use g1 computed from PDF's to get
d2, which involves finding a set of polarized PDF's that works correctly
at high x, low Q^2.

Cheers,

Oscar