  We perform a fit of the real Compton scattering (RCS) data below
pion-production threshold to extract the electric ($\alpha_{E1}$) and magnetic
($\beta_{M1}$) static scalar dipole polarizabilities of the proton, using
fixed-$t$ subtracted dispersion relations and a bootstrap-based fitting
technique. The bootstrap method provides a convenient tool to include the
effects of the systematic errors on the best values of $\alpha_{E1}$ and
$\beta_{M1}$ and to propagate the statistical errors of the model parameters
fixed by other measurements. We also implement various statistical tests to
investigate the consistency of the available RCS data sets below
pion-production threshold and we conclude that there are not strong motivations
to exclude any data point from the global set. Our analysis yields $\alpha_{E1}
= (12.03^{+0.48}_{-0.54})\times 10^{-4} \text{fm}^3$ and $\beta_{M1} =
(1.77^{+0.52}_{-0.54})\times 10^{-4} \text{fm}^3$, with p-value $= 12\%$.
