The goodness-of-fit problem is addressed and two among the more efficient tests presently available are revisited and discussed: the autocorrelation method and the sign test recently proposed by Paolo Minguzzi [J. Mol. Spectrosc. 209, (2001) 169], both based on residual analysis. A mathematical proof of the empirical relations needed in the sign test is proposed; it allows more insight in the comparison of both methods and shows that more information may be available from the sign test. Some differences of efficiency are pointed out in special cases, but finally these methods prove to be closely related. A general procedure is deduced that takes advantage of the practical usefulness of both approaches, of their efficiency and of the statistical information each of them can provide.
