on several lattice correlators; we refer to this as a derived quantity and refer to the lattice correlators as primary observables. When calculating the errors in a derived quantity, we account for the correlations between primary observables by using the functional dependence of the derived quantity on the primary observables. As a cross-check of the statistical error estimate, we compared the results obtained with this approach with those obtained using a single-elimination jackknife procedure; we find that both the central values and statistical errors are consistent between the two error estimation methods. For example, Fig. 1 shows the determinations of m ∗ B$_{q}$ and Φ ren B$_{q}$ on the am$_{l}$ = 0 . 02 ensemble for the APE (upper plots) and HYP data sets (lower plots). The central value and statistical error of each data point in Fig. 1 are computed as functions of the primary observables C LW and C $^{WW}$. Then the value of the plateau and its error are computed using a function which averages the values of m ∗ B$_{q}$ (or Φ ren $_{B$_{q}$}$) on time-slices 12, 13, 14 and 15 because we do not observe excited-state contamination in this region. In order to reduce the size of the statistical errors, we average the correlators beginning at two time sources. We achieve the averaging of our two sources by replacing e.g. C $^{LW}$( t, 0) with [ C $^{LW}$( t, 0) + C $^{LW}$(20 a − t, 20 a ) ] / 2 in Eqs. (63)- (65). For the case of the HYP-smeared data, these are located at t/a = 0 and t/a = 20, whereas for the APE-smeared data the second source is located either at t/a = 20, 21, or 24. Finally, we compute the ratio Φ ren $_{B$_{s}$}$/ Φ ren B$_{l}$ on each ensemble as a function of Φ ren B$_{s}$ and Φ ren B$_{l}$ , which themselves depend on the corresponding primary observables C LW and C $^{WW}$; this is shown in Fig. 2. We obtain the plateau for the ratio from time-slices 12–15, where we do not observe excited-state contamination in the numerator Φ ren B$_{s}$ or the denominator Φ ren B$_{l}$ . Table V presents the values of Φ ren $_{B$_{s}$}$/ Φ ren B$_{l}$ on the three sea-quark ensembles. Despite the use of two time sources, the statistical errors in the ratio are as large as 7 . 5% in case of the data using APE smearing. The B$_{q}$ − B$_{q}$ mixing parameter in continuum QCD is defined in terms of the matrix element of the Δ B = 2 four-fermion operator via Eqs. (2) and (3). Because the matrix element M q behaves as m$_{B}$$_{q}$ in the limit of large B$_{q}$ -meson mass, we calculate the desired 19 B. Calculation of the ratio of B -meson mixing matrix elements