A simulation study on two analytical techniques for alternating treatments designs

Abstract

Alternating treatments designs (ATDs) are single-case experimental designs entailing the rapid alternation of conditions, and the specific sequence of conditions is usually determined at random. The visual analysis of ATD data entails comparing the data paths formed by connecting the measurements from the same condition. Apart from visual analyses, there are at least two quantitative analytical options also comparing data paths. On option is a visual structured criterion (VSC) regarding the number of comparisons for which one conditions has to be superior to the other to consider that the difference is not only due to random fluctuations. Another option, denoted as ALIV (a comparison involving Actual and Linearly Interpolated Values), computes the mean difference between the data paths and uses a randomization test to obtain a p value. In the current study, these two options are compared, along with a binomial test, in the context of simulated data, representing ATDs with a maximum of two consecutive administrations of the same condition and a randomized block design. Both VSC and ALIV control Type I error rates, although these are closer to the nominal 5% for ALIV. In contrast, the binomial test is excessively liberal. In terms of statistical power, ALIV plus a randomization test is superior to VSC. We recommend that applied researchers complement visual analysis with the quantification of the mean difference, as per ALIV, and with a p value whenever the alternation sequence was determined at random. We have extended an already existing website providing the graphical representation and the numerical results.