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Estimating statistical power for two-level models is complex. This tutorial provides practical guidance and rules of thumb for power analysis in multilevel studies using Monte Carlo simulation.

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Area of Science:

  • Multilevel modeling
  • Statistical power analysis
  • Psychological research methods

Background:

  • Two-level models are frequently used in psychology to analyze hierarchically structured data.
  • Estimating statistical power in these models is complex due to variance at multiple levels and predictors at multiple levels.
  • Existing power estimation methods rely on formulas or Monte Carlo simulation.

Purpose of the Study:

  • To provide a hands-on tutorial for conducting a priori and post hoc power analyses in two-level models.
  • To demonstrate specifying population models using standardized parameters for power analysis.
  • To offer practical guidelines for sample size and minimum detectable effect sizes in multilevel research.

Main Methods:

  • Utilizing Monte Carlo simulation via the SIMR package for flexible power estimation.
  • Specifying population models with standardized input parameters.
  • Developing case-sensitive rules of thumb for power analysis.

Main Results:

  • Medium and large fixed effects can be detected with lower-level sample sizes up to 30 and higher-level sample sizes up to 200.
  • Small higher-level direct or cross-level interaction effects are not detectable with up to 200 clusters.
  • Power analysis guidelines are provided for common effects and parameters in psychological research.

Conclusions:

  • The tutorial and guidelines assist researchers in planning multilevel studies.
  • Accurate power estimation is crucial for detecting effects in complex hierarchical data structures.
  • Researchers should consider the limitations for detecting small interaction effects in multilevel models.