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\end{equation}  This analytical procedure is used in Ref.~\cite{Grzadkowski_2000} to determine the sensitivity to top-quark electroweak couplings in $500\,{\rm fb}^{-1}$ of ${\rm e^+ e^-}$ collisions at $\sqrt{s} = 500$\,GeV, with or without incoming beam polarization. In this article, the authors evaluate the covariance matrix with Eq.~\ref{eq:rate}, but they let the total number of events float by adding a fictitious multiplicative form factor $\delta_0$ in front of $S^0$ in Eq.~\ref{eq:optimal}, hence increase the rank of the covariance matrix from 8 to 9. It was checked that this work-around is numerically equivalent to using Eq.~\ref{eq:norate}, {\it i.e.}, to not use the total event rate in the likelihood.   It can be seen from Fig.~\ref{fig:distributions}, however, that $f_A^\gamma(x,\cos\theta)$ (top-left corner) is almost degenerate with the standard model contributions $S^0(x,\cos\theta)$. $S^0(x,\cos\theta)$ (bottom-right corner).  Letting the normaization of the standard model contribution float is therefore bound to lead to very large statistical uncertainties on all form factors, as is observed in Ref.~\cite{Grzadkowski_2000}. For this reason, and as is done in Ref.~\cite{Baer_2013}, the present study includes the total event rate in the determination of the uncertainties, leading to an improvement by factors up to 50 with respect to not using it.