Quality control in small groups
Faculty of Sciences. Physics
New York, N.Y. :AIP, 2008
Engineering sciences. Technology
Bayesian Inference and Maximum Entropy Methods in Science and Engineering, 28th International Workshop / Souza Lauretto, de, M. [edit.]; et al. [edit.]
University of Antwerp
The smallness of some groups in a set up to control the quality of a service using questionnaires limits the size of the samples, this limitation has several consequences. Indeed the common approach used for relatively large groups, based on the central limit theorem and the law of large numbers, cannot be used anymore to construct estimators for the parameters of the model. Using an inverse probability will lift these restrictions. A questionnaire is a collection of items. In an item the respondent indicates on a Likert scale his or her agreement with a statement. Dimensions are a set of items dealing with one aspect of the service. In a questionnaire several dimensions are addressed but usually the items are presented in a random sequence. The model for an item is hierarchical with following components: a multivariate hypergeometric model takes the sampling in a finite population into account, the multinomial serves as a prior for the sampling and the Dirichlet-distribution serves as a prior for the multinomials. The composition of dimensions allows to use the posterior for one of the items as a prior for another item of that dimension and so on. After analysis of several questionnaires using this model, the reliability of the responses from some respondents turned out to be a key-problem, in the sense the responses can be classified into at least two classes and a decision rule had to be developed to neglect some of them. The influence of rejecting some answers, on the confidence for the most plausible statement can be estimated. This leads often to the result that there is only minimal evidence for the most probable statement.