Statistical Analyses of Extreme Proportions
Abstract:
A number of product categories are highly fragmented, with dozens of brands or market entries. The proportion of consumers who use many of these brands can be quite small. Yet, total industry sales may be sufficiently large that even a small proportion of users translates to millions of dollars in sales. A study of category users may yield brand usage proportions and confidence bounds around such proportions are desirable to obtain upper and lower bounds on possible sales. However, with small proportions, the usual confidence interval calculations may yield uninterpretable results. This paper discusses the use of arcsin transformation of extreme, very small or large, proportions as a way of estimating these confidence bounds correctly.
