A set theoretic analysis of group interactions

Prior to the statistical treatment of experimentally derived data the experimenter must obtain the data. In many studies in psychology, the content of group interactions is obtained by a data coding scheme. Coding schemes are shown to possess hierarchical structures and can be characterized by a hierarchy of fields. Three examples of coding schemes as hierarchies of fields are given. Techniques for extracting numbers from the set are presented. Problems associated with the improper assignment of elements of a data coding scheme to a theoretical structure are examined. The main result is that there will be errors in assignment of data to theory unless the structure of the data coding scheme is identical with that structure which is relevant to the theory being tested. Whenever the structures are not equal, the results are hard to interpret. In fact, any size of assignment error can be obtained. Since these errors precede the usual statistical treatment of data, it would appear that reported empirical findings are only valid when there exists no assignment errors.This research was sponsored by N.S.F. Grant GS-1944.