Estimating significances of differences between slopes: A new methodology and software

Abstract

Determining the significance of slope differences is a common requirement in studies of self-thinning, ontogeny and sexual dimorphism, among others. This has long been carried out testing for the overlap of the bootstrapped 95% confidence intervals of the slopes. However, the numerical random re-sampling with repetition favours the occurrence of re-combinations yielding largely diverging slopes, widening the confidence intervals and thus increasing the chances of overlooking significant differences. To overcome this problem a permutation test simulating the null hypothesis of no differences between slopes is proposed. This new methodology, when applied both to artificial and factual data, showed an enhanced ability to differentiate slopes.

Keywords

• slope difference
• permutation
• bootstrap
• overlap
• randomization tests