Contrasts are sketched between the kinds of populations archaeologists would like to sample, and the kinds we actually have to work with. Some problems which have often been overlooked in correlation studies are explained and illustrated. We must always worry about the precision of sample correlations as estimators of population correlations. If the correlations are based on unreliable measurements, as is bound to be true if the measurements are counts of specimens, there is also an attenuation effect, which makes sample correlations biassed as well as imprecise. It is suggested that probably we have to worry about this bias whenever average counts are below about 10. Retreat to simple presence-absence scoring does not avoid this problem.