Analysis of single-case data: randomisation tests for measures of effect size.

Single-case experiments can be used to evaluate the effect of an intervention or treatment for a single entity. The internal validity and statistical conclusion validity of single-case experiments can be improved by incorporating randomisation in their design. In this article, we explain how to design randomised single-case phase and alternation studies as well as randomised simultaneous and sequential replication studies, and how to conduct randomisation tests for these designs. Advantages and limitations of randomisation tests are discussed. In order to not only determine the (non)randomness of an intervention effect, but also the magnitude of this effect, we propose to use an effect size index as a test statistic for the randomisation test. We illustrate this combination for the design and analysis of an ABAB phase study, using a free software package.