  Two of the conditions that have been suggested to determine the lower
boundary of the conformal window in asymptotically free gauge theories are the
linear condition, $\gamma_{\bar\psi\psi,IR}=1$, and the quadratic condition,
$\gamma_{\bar\psi\psi,IR}(2-\gamma_{\bar\psi\psi,IR})=1$, where
$\gamma_{\bar\psi\psi,IR}$ is the anomalous dimension of the operator
$\bar\psi\psi$ at an infrared fixed point in a theory. We compare these
conditions as applied to an ${\cal N}=1$ supersymmetric gauge theory with gauge
group $G$ and $N_f$ pairs of massless chiral superfields $\Phi$ and $\tilde
\Phi$ transforming according to the respective representations ${\cal R}$ and
$\bar {\cal R}$ of $G$. We use the fact that $\gamma_{\bar\psi\psi,IR}$ and the
value $N_f = N_{f,cr}$ at the lower boundary of the conformal window are both
known exactly for this theory. In contrast to the case with a
non-supersymmetric gauge theory, here we find that in higher-order
calculations, the linear condition provides a more accurate determination of
$N_{f,cr}$ than the quadratic condition when both are calculated to the same
finite order of truncation in a scheme-independent expansion.
