Groups of too close radiocarbon dates

In the archaeological and palaeogeographical literature, it is relatively frequent to find groups of radiocarbon dates of too close values. Too close means here that the dates exhibit no other variability than that of random origin, quantified by the given measurement errors. The chi-squared statistic seems to be appropriate to test, if the given group of dates is of random variability, of larger variability (what is typical) or of too small variability. The last case is hard to explain.