Sample Size Determination for Categorical Responses

Abstract:  Procedures are reviewed and recommendations made for the choice of the size of a sample to estimate the characteristics (sometimes known as parameters) of a population consisting of discrete items which may belong to one and only one of a number of categories with examples drawn from forensic science. Four sampling procedures are described for binary responses, where the number of possible categories is only two, e.g., licit or illicit pills. One is based on priors informed from historical data. The other three are sequential. The first of these is a sequential probability ratio test with a stopping rule derived by controlling the probabilities of type 1 and type 2 errors. The second is a sequential variation of a procedure based on the predictive distribution of the data yet to be inspected and the distribution of the data that have been inspected, with a stopping rule determined by a prespecified threshold on the probability of a wrong decision. The third is a two-sided sequential criterion which stops sampling when one of two competitive hypotheses has a probability of being accepted which is larger than another prespecified threshold. The fifth procedure extends the ideas developed for binary responses to multinomial responses where the number of possible categories (e.g., types of drug or types of glass) may be more than two. The procedure is sequential and recommends stopping when the joint probability interval or ellipsoid for the estimates of the proportions is less than a given threshold in size. For trinomial data this last procedure is illustrated with a ternary diagram with an ellipse formed around the sample proportions. There is a straightforward generalization of this approach to multinomial populations with more than three categories. A conclusion provides recommendations for sampling procedures in various contexts.     

East German Intelligence and Ireland, 1949–90: Espionage,Terrorism and Diplomacy

This article analyses the writings of a prominent German social and political theorist ‐ Jürgen Habermas ‐ on the process of (reunification in Germany and examines responses to his interventions by right‐wing thinkers opposed to his views. (Re)unification is a setting of rapidly developing and changing events which present a challenge to Habermas’ thinking. Put simply, Habermas is highly critical of the ‘rush towards (re)unification’ and the process which has followed it. In particular, he objects to attempts by right‐wing thinkers, predominantly historians, to rewrite German history and which elude German responsibility in respect of the horrors of the Holocaust. Equally, he has explicitly shown the links between questions of German identity and the rewriting of German history and argues that the only viable identity for Germany post‐(re)Unification is that of ‘constitutional identity’ and not national identity. His writings have, however, been the subject of sometimes vehement and vitriolic critiques and this article seeks not only to engage with these but also to examine the interventions of Habermas in relation to his earlier more theoretical writings.