Abstract
A randomization test can be used to statistically test hypotheses in multiple baseline designs to complement the commonly used visual inspection analysis. A crossed factor simulation study was performed to investigate the power of a randomization test in an multiple baseline design. The results show that the degree of autocorrelation of the observations, the number of participants, the effect size, the overlap of possible start moments of the intervention between participants, the ratio of the number of measurements in the baseline- and intervention phase, a gradually emerging effect, and the number of measurements had strong main effects on the power. The two-way interactions between number of participants and effect size, and between the number of measurements and the number of start moments of the intervention also had a large effect. An online tool was developed to calculate the power of a multiple baseline design given several design characteristics.
Highlights
The single-case design has a long history in psychology as it was already used by famous founders like [1,2,3,4]
Despite the obvious advantages and the intuitive attractiveness of visual inspection in single case designs, it has been criticized for high error rates and subjectivity [22,23]. [24] compared visual inspection with statistical analysis and concluded that the conclusions from visual analysis and statistical analysis had low level of agreement. The results of these studies are informative in that they confirm that statistical inference cannot be replaced by conclusions formed purely on visual inspection, we argue that the comparison of the two kinds of analyses which are inherently different is questionable
In this study we provided information about the influence of several factors on the power of a randomization test in a single case multiple baseline across subjects design
Summary
The single-case design has a long history in psychology as it was already used by famous founders like [1,2,3,4]. The kind of research questions involved in single case designs often differ from multiple case designs, single case designs may be viable alternatives for ordinary randomized trial designs when the number of participants is small, normality and homogeneity of variance assumptions are not warranted, or the sample is not random [6] They are used in a clinical setting to evaluate the effect of a certain intervention on a small group of patients [7,8,9], and in an educational context to test whether a manipulation can help students [10,11,12]. The effect of the intervention is evaluated by comparing the pattern of observed outcomes under the different treatment conditions, in which each case serves as its own control [13]
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