Confidence intervals for a product of proportions: application to importance values

Importance values (proportional use × proportional availability of a resource) add a useful component to studies of resource selection. The merit of the metric is that it identifies commonly available resources that are nonetheless critical components in the ecology of an organism. Such resources would not be identified as being selected in comparisons of use relative to availability (e.g., use/availability). Importance values have received limited use in the ecological literature because they have been descriptive in nature and lack a framework for hypothesis testing. In this paper we present a simple asymptotic one‐ and two‐tailed method for calculating confidence intervals for the product of proportions. The approach is easily extended to importance values. Results from simulations indicate that our method is effective across a wide range of sample sizes, but performs poorly when designs are unbalanced. As a result, we recommend rarifying availability data in matched‐case designs for determining resource selection, before calculating confidence intervals for importance values. Applications of our method extend beyond the calculation of confidence intervals for importance values. Indeed, the approach is applicable for any situation in which confidence intervals are needed for the product of proportions, including product of more than two proportions.