Significances of differences between slopes: An upgrade for replicated time series

Abstract

In some ecology subjects the slope of the line fit between x and y variables is the focus of concern. Such is the case of self-thinning theory, developed for plant demography and later verified also occurring in algae and animals. Different slopes identify statistical populations subject to different conditions. Therefore, it is fundamental that a test is able to identify honestly significant differences between slopes. The most used tested for the overlap of the 95% confidence intervals of the bootstrapped slopes. However, Vieira and Creed (2013) demonstrated it to possess weak theoretical grounds having proposed a permutation methods alternative. Unfortunately, both were fallible upon small sample sizes and/or large data scatter. Data about self-thinning, as well as other subjects, often comes in replicated time series enabling upgrading the test algorithm to randomize sampling units only within the respective time frame. This was added to the previous software, increasing outstandingly the capacity of the permutation test in identifying both true and false differences between slopes.

Keywords

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