Statistical Analysis of a Questionnaire: Voluntary Health Insurance Implementation Among Patients Suffering From Allergy and Asthma

We consider statistical analysis of multiple answers in a questionna- ire. We propose a new method of calculating simultaneous confidence regions. In a communication presented at the European Academy of Allergy and Clinical Immunology the authors (Borowicz et al. (2009)) reported the proportions of respondents which gave one of three po- ssible exclusive answers in a questionnaire concerning the role of vo- luntary health insurance. There were three possible answers. Apart from percentages of answers confidence intervals of every single an- swer have been reported. Unfortunately inference about the popula- tion based on such intervals may lead to imprecise conclusions. The inference about the respective population suffering from allergy and asthma proportions requires the construction of two-dimensional confidence region. We propose the use of a simultaneous confidence intervals to inference about true population proportions. Most of our attention is given to the case of three possible answers but the results may be generalized to any questionnaire with more than two excluding answers.