Robinson's Coefficient of Agreement – A Rejoinder

Extract

In a recent issue of this journal (Vol. 17, p. 151) Donald J. Lehmer protests against the coefficient of agreement used by W. S. Robinson in his paper on “A Method for Chronologically Ordering Archaeological Deposits” (American Antiquity, Vol. 16, pp. 293-301). Lehmer's objection to the coefficient

…lies in the fact that it takes no account of differences in the size of the collections. Every sherd collection must be regarded as a sample representing a universe which is made up of all of the sherds in that particular level, site, or whatever. The larger the sample, the more likely it is to give an accurate indication of the true proportions of the various sherd types in the universe from which it was drawn. The smaller the sample, the more likely it is to deviate from those true proportions. Any acceptable measure of the similarity between two such samples must inherently take this into account by allowing for a greater difference between samples from similar universes when those samples are small. Otherwise, the small sample and the large sample are accepted as being equally representative of the universes from which they are drawn.