Statistical Analysis of Electron-Proton Scattering

We have made a statistical analysis of Stanford measurements of electron-proton scattering. We find that the Rosenbluth formula is valid within the experimental errors in the range $7\le q^2\le 25$ ${\mathrm{F}}^{-2\mathrm{}}$, and in the range of angles covered. We evaluate the form factors $G_E$, $G_M$ and $F_1$, $F_2$, their errors, and correlated errors. Our values for the form factors are in reasonable agreement with the analyses of Hofstadter et al., and of Richard Wilson et al. The errors in $G_M$ are particularly small; the errors in $F_1$, $F_2$, and $G_E$ are of similar magnitude. The coefficient of correlation between the errors of the form factors $F_1$ and $F_2$ is large and negative (-84% to -99%); the coefficient of correlation between the errors of $G_E$ and $G_M$ is almost as large and negative (-74% to -99%). $G_E$ is about 40% larger than $\frac{G_M}{2.79}$ for $16.5\le q^2\le 25$ ${\mathrm{F}}^{-2\mathrm{}}$; the ratio of $G_E$ to $\frac{G_M}{2.79}$ is about two standard deviations from unity in this range of $q^2$.