The concepts underlying numerical taxonomy and factor analysis are examined in relation to the goals and requirements of archaeological classification. Numerical taxonomy, represented in the archaeological literature most commonly by cluster analysis on raw data, is found to be inappropriate for these goals. In contrast, the technique of re-mode factor analysis fits very well with the nature of achaeological data and the general aims of archaeological classification. The results of three experiments are presented which illustrate the drastically different interpretations that can be engendered by the two procedures from the same data.