Analysing indicators of performance, satisfaction or safety using the empirical logit transformation
Stevens S., Valderas J., Doran T., Perera R., Kontopantelis E.
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% may be more difficult and require more effort than improving from 55% to 65%. As such, analysis of these indicators is not always straightforward and standard linear analysis may 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, algebraically describe the relevant steps in the transformation process, provide guidance on interpretation and provide a tool for analysis.