The Power to Explain Variability in Intervention Effectiveness in Single-Case Research Using Hierarchical Linear...

Area of Science:

• Psychology
• Statistics
• Research Methodology

Background:

• Single-case experimental designs (SCED) are crucial for evaluating interventions.
• Visual analysis in SCED has limitations in explaining variability.
• Hierarchical linear modeling (HLM) offers advanced analytical capabilities for SCED data.

Purpose of the Study:

• To investigate the statistical power of HLM for explaining intervention effectiveness variability in SCED research.
• To provide empirical evidence on the relationship between sample size, effect size, number of moderators, and statistical power.
• To introduce a user-friendly tool, PowerSCED, to aid researchers in designing powerful SCED studies.

Main Methods:

• Monte Carlo simulation techniques were employed to empirically assess power for estimating intervention and moderator effects.
• The study examined the impact of varying true effects, participant numbers, and the quantity of moderators on statistical power (≥.80).
• HLM was applied to two published SCED studies to demonstrate its utility with moderator inclusion.

Main Results:

• Higher true effects and increased participant numbers significantly enhance statistical power in HLM for SCED.
• Adding more moderators to the HLM model necessitates a larger number of participants to achieve sufficient power.
• With three moderators, a minimum of 20 participants is recommended for adequate power; seven participants suffice with one moderator.

Conclusions:

• HLM is a powerful supplement to visual analysis in SCED, particularly for exploring intervention effect variability.
• Researchers must carefully consider the number of participants and moderators when designing SCED studies to ensure adequate statistical power.
• The PowerSCED tool provides practical support for applied researchers in optimizing SCED study design for robust effect estimation.