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This study investigated the power of two-level hierarchical linear modeling (HLM) to explain variability in intervention effectiveness between participants in context of single-case experimental design (SCED) research. HLM is a flexible technique that allows the inclusion of participant characteristics (e.g., age, gender, and disability types) as moderators, and as such supplements visual analysis findings. First, this study empirically investigated the power to estimate intervention and moderator effects using Monte Carlo simulation techniques. The results indicate that larger values for the true effects and the number of participants resulted in a higher power. The more moderators added to the model, the more participants needed to detect the effects with sufficient power (i.e., power [greater than or equal to]0.80). When a model includes three moderators, at least 20 participants are required to capture the intervention effect and moderator effects with sufficient power. For that same condition, but only including one moderator, seven participants are sufficient. Specific recommendations for designing a SCED study with sufficient power to estimate intervention and moderator effects were provided. Second, this study introduced a newly developed user-friendly point and click Shiny tool, "PowerSCED." This tool assists applied SCED researchers in designing a SCED study that has sufficient power to detect intervention and moderator effects. To end, the use of HLM with the inclusion of moderators was demonstrated using two previously published SCED studies in the journal "School Psychology Quarterly."

This study investigated the power of two-level hierarchical linear modeling (HLM) to explain variability in intervention effectiveness between participants in context of single-case experimental design (SCED) research. HLM is a flexible technique that allows the inclusion of participant characteristics (e.g., age, gender, and disability types) as moderators, and as such supplements visual analysis findings. First, this study empirically investigated the power to estimate intervention and moderator effects using Monte Carlo simulation techniques. The results indicate that larger values for the true effects and the number of participants resulted in a higher power. The more moderators added to the model, the more participants needed to detect the effects with sufficient power (i.e., power [greater than or equal to]0.80). When a model includes three moderators, at least 20 participants are required to capture the intervention effect and moderator effects with sufficient power. For that same condition, but only including one moderator, seven participants are sufficient. Specific recommendations for designing a SCED study with sufficient power to estimate intervention and moderator effects were provided. Second, this study introduced a newly developed user-friendly point and click Shiny tool, "PowerSCED." This tool assists applied SCED researchers in designing a SCED study that has sufficient power to detect intervention and moderator effects. To end, the use of HLM with the inclusion of moderators was demonstrated using two previously published SCED studies in the journal "School Psychology Quarterly."