This paper takes a critical look at theory-free, statistical methodologies for processing and interpreting data taken from respondents answering a set of dichotomous (yes-no) questions. The basic issue concerns to what extent theoretical conclusions based on such analyses are invariant under a class of "informationally equivalent" question transformations. First the notion of Boolean equivalence of two question sets is discussed. Then Lazarsfeld's latent structure analysis is considered in detail. It is discovered that the best fitting latent model depends on which (...) one of the many informationally equivalent question sets is used. This fact raises a number of methodological problems and pitfalls with latent structure analysis. Related problems with other methodologies are briefly discussed. (shrink)