We discuss the constraints on the Standard Model Effective Field Theory inferred from global fits to electroweak data. Special attention is paid to two unconstrained combinations of Wilson coefficients that are present when the analysis is restricted to measurements of $\bar\psi\psi\to\bar\psi\psi$ scatterings. We illustrate how these unconstrained directions arise due to a reparameterization invariance that characterizes $\bar\psi\psi\to\bar\psi\psi$ processes but is not respected in $\bar\psi\psi\to\bar\psi\psi\bar\psi\psi$ scatterings. This invariance is independent of the operator basis adopted and of the choice of the input parameters. This is verified comparing the results obtained in the {$\hat\alpha_{em}, \hat m_Z, \hat G_F$} input scheme with those of a {$\hat m_W, \hat m_Z, \hat G_F$} scheme.