How Many Tiers Do We Need? Type I Errors and Power in Multiple Baseline Designs
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How Many Tiers Do We Need? Type I Errors and Power in Multiple Baseline Designs Marc J. Lanovaz 1,2
& Stéphanie
Turgeon 1
# The Author(s) 2020
Abstract Design quality guidelines typically recommend that multiple baseline designs include at least three demonstrations of effects. Despite its widespread adoption, this recommendation does not appear grounded in empirical evidence. The main purpose of our study was to address this issue by assessing Type I error rate and power in multiple baseline designs. First, we generated 10,000 multiple baseline graphs, applied the dualcriteria method to each tier, and computed Type I error rate and power for different number of tiers showing a clear change. Second, two raters categorized the tiers for 300 multiple baseline graphs to replicate our analyses using visual inspection. When multiple baseline designs had at least three tiers and two or more of these tiers showed a clear change, the Type I error rate remained adequate (< .05) while power also reached acceptable levels (> .80). In contrast, requiring all tiers to show a clear change resulted in overly stringent conclusions (i.e., unacceptably low power). Therefore, our results suggest that researchers and practitioners should carefully consider limitations in power when requiring all tiers of a multiple baseline design to show a clear change in their analyses. Keywords Error rate . Multiple baseline design . Power . Single-case design . Visual
analysis In behavior analysis, researchers and practitioners typically use single-case designs such as the reversal design, the alternating-treatment design, and the multiple baseline This study was supported in part by a salary award from the Fonds de recherche du Québec-Santé (#269462) to the second author. The authors acknowledge Antonia Giannakakos and Kieva Hranchuk for their support with visual analysis.
* Marc J. Lanovaz [email protected]
1
École de psychoéducation, Université de Montréal, C.P. 6128, succursale Centre-Ville, Montreal, QC H3C 3J7, Canada
2
Centre de recherche de l’Institut universitaire en santé mentale de Montréal, Montreal, QC, Canada
Perspectives on Behavior Science
design to demonstrate experimental control (Gast & Ledford, 2018; Horner et al., 2005; Kratochwill et al., 2010). Among these designs, researchers have found that multiple baseline designs were the most frequently used (Coon & Rapp, 2018; Shadish & Sullivan, 2011; Smith, 2012). In contrast with other single-case designs, the multiple baseline design does not require the withdrawal of the treatment or the establishment of a criterion to be gradually changed, which may explain its predominant use in singlecase research (Baer, Wolf, & Risley, 1968; Kratochwill & Levin, 2014). The multiple baseline design involves the sequential introduction of an independent variable across behaviors, contexts, or participants (see Fig. 1 for two examples of multiple baseline graphs). When analyzing multiple baseline graphs, experimenters depict each behavior, context, or participan
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