Estimating Relative Change with Paired Data

Data from monitoring studies (e.g. on fish abundance) are often conveniently analyzed as paired data (before and after some intervention, for example). The usual statistical tool, a paired-t, does estimation and testing for incremental change (e.g. after minus before), with the increment measured separately within pairs and then summarized. Unfortunately, the question of interest is often one regarding relative change, which the paired-t cannot answer well (for testing or confidence intervals). There are two ways to assess relative change; one is the analogue to the paired-t, namely to form ratios (e.g. after divided by before) within pairs, then summarize; this leads to the Mean of Ratios (MoR). As it happens, the Ratio of Means (e.g. mean from after divided by mean from before; RoM) is inferentially quite different from the MoR, and, I think, often a quite apt summary statistic for answering questions of relative change. I will compare and contrast the properties of these three methods, and introduce an interactive Excel tool for estimation; it used a contemporary bootstrapping approach (the so-called BCa method) for constructing confidence intervals.