Randomization Test for Single-Case Designs

The randomization test for single-case experimental designs is a permutation-based procedure that yields a valid statistical p-value for an intervention effect in a single participant, provided that some experimentally controllable feature of the design — typically the moment the intervention begins or the order in which conditions are presented — was randomly determined before data were collected. Eugene Edgington showed in 1980 that this design-embedded randomization is what licenses inference: because the random assignment is the source of the test's probability statements, the procedure draws valid conclusions without assuming that the data are normally distributed or serially independent, two assumptions that single-case time-series data routinely violate. Edgington and Onghena's monograph established the modern framework, in which the observed test statistic is referred to the distribution of statistics generated by every admissible re-assignment of the data. In disability research, where interventions are often delivered to one person at a time and group designs are impractical, the randomization test provides a defensible significance test that complements visual analysis.