We consider the electron-positron annihilation process into hadrons ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ up to $\mathcal{O}({\ensuremath{\alpha}}_{s}^{3})$, and we adopt the smearing method suggest by Poggio, Quinn, and Weinberg to confront the experimental data with theory. As a theoretical model, we use a QCD coupling constant frozen in the low-energy regime, where this coupling can be parametrized in terms of an effective dynamical gluon mass (${m}_{g}$) which is determined through Schwinger-Dyson equations. In order to find the best fit between experimental data and theory, we perform a ${\ensuremath{\chi}}^{2}$ study, that, within the uncertainties of the approach, has a minimum value when ${m}_{g}/{\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}$ is in the range 1.2--1.4. These values are in agreement with other phenomenological determinations of this ratio and lead to an infrared effective charge ${\ensuremath{\alpha}}_{s}(0)\ensuremath{\approx}0.7$. We comment how this effective charge may affect the global duality mass scale that indicates the frontier between perturbative and nonperturbative physics.