Analysing indicators of performance, satisfaction, or safety using empirical logit transformation

Abstract

Performance, satisfaction, and safety indicators are commonly measured on a percentage scale. Such indicators are often subject to ceiling or floor effects and performance may be inherently non-linear. For example, improving from 85% to 95% might be more difficult and need more effort than improving from 55% to 65%. As such, analysis of these indicators is not always straightforward and standard linear analysis could be problematic. We present the most common approach to dealing with this problem: a logit transformation of the score, following which standard linear analysis can be conducted on the transformed score. We also demonstrate how estimates can be back-transformed to percentages for easier communication of findings. In this paper, we discuss the benefits of this method, use algebra to describe the relevant steps in the transformation process, provide guidance on interpretation, and provide a tool for analysis.