We have measured the asymmetry parameter ${\alpha }_{-}$ for the nonleptonic decay ${\Sigma }^{-}\to n+{\pi }^{-}$ as well as the asymmetry parameter ${\alpha }_{\mathrm{lept}}$ for the leptonic decays ${\Sigma }^{-}\to n+e^{-}+{\overline{\nu }}_e$ and ${\Sigma }^{-}\to n+{\mu }^{-}+{\overline{\nu }}_{\mu }$, using polarized ${\Sigma }^{-}$ produced in the reaction $K^{-}+p\to {\Sigma }^{-}+{\pi }^{+}$ in the vicinity of the $\Lambda \mathrm{}\left(1520\right)\mathrm{}$ resonance. Measurements were carried out on the Yale Precision Encoding and Pattern Recognition (PEPR) system, and leptonic decays were subjected to gap-length analysis. Using the ${\Sigma }^{-}$ polarization function of Thompson, we find ${\alpha }_{-}=-0.067\mathrm{}\pm 0.011$ based on 60 000 two-body decays; ${\alpha }_{\mathrm{lept}}=+0.23\mathrm{}\pm 0.44$ based on 44 electron decays; ${\alpha }_{\mathrm{lept}}=+0.36\mathrm{}\pm 0.39$ based on 44 electron decays and 19 muon decays. Our value of ${\alpha }_{\mathrm{lept}}$ yields a ratio of axial-vector to vector matrix elements given by $\frac{g_A}{g_V}=-0.33_{-0.85\mathrm{}}^{}{}_{}{}^{+0.39\mathrm{}}$, using a sign convention in which this ratio is negative for the neutron. While our data favor a negative sign for this ratio (in disagreement with the Cabibbo theory), a positive sign cannot be excluded.

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