  Whether a correlation exists between the radio and gamma-ray flux densities
of blazars is a long-standing question, and one that is difficult to answer
confidently because of various observational biases which may either dilute or
apparently enhance any intrinsic correlation between radio and gamma-ray
luminosities. We introduce a novel method of data randomization to evaluate
quantitatively the effect of these biases and to assess the intrinsic
significance of an apparent correlation between radio and gamma-ray flux
densities of blazars. The novelty of the method lies in a combination of data
randomization in luminosity space (to ensure that the randomized data are
intrinsically, and not just apparently, uncorrelated) and significance
assessment in flux space (to explicitly avoid Malmquist bias and automatically
account for the limited dynamical range in both frequencies). The method is
applicable even to small samples that are not selected with strict statistical
criteria. For larger samples we describe a variation of the method in which the
sample is split in redshift bins, and the randomization is applied in each bin
individually; this variation is designed to yield the equivalent to
luminosity-function sampling of the underlying population in the limit of very
large, statistically complete samples. We show that for a smaller number of
redshift bins, the method yields a worse significance, and in this way it is
conservative in that it does not assign a stronger, artificially enhanced
significance. We demonstrate how our test performs as a function of number of
sources, strength of correlation, and number of redshift bins used, and we show
that while our test is robust against common-distance biases and associated
false positives for uncorrelated data, it retains the power of other methods in
rejecting the null hypothesis of no correlation for correlated data.
