  A series of Higgs field quantum numbers in the anti-grand unification model,
based on the gauge group $SMG^3 \times U(1)_f$, is tested against the spectrum
of quark and lepton masses and mixing angles. A more precise formulation of the
statement that the couplings are assumed of order unity is given. It is found
that the corrections coming from this more precise assumption do not contain
factors of order of the number of colours, $N_c= 3$, as one could have feared.
We also include a combinatorial correction factor, taking account of the
distinct internal orderings within the chain Feynman diagrams in our
statistical estimates. Strictly speaking our model predicts that the
uncertainty in its predictions and thus the accuracy of our fits should be $\pm
60\%$. Many of the best fitting quantum numbers give a higher accuracy fit to
the masses and mixing angles, although within the expected fluctuations in a
$\chi^2$. This means that our fit is as good as it can possibly be.
