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Estimating Standardized Effect Sizes for Two- and Three-Level Partially Nested Data.

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A new maximum likelihood estimator improves effect size estimation for partially nested cluster randomized designs, offering greater efficiency and accuracy, especially with unequal cluster sizes and heterogeneous variances in primary research.

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Area of Science:

  • Statistics
  • Biostatistics
  • Psychometrics

Background:

  • Existing effect size estimators for partially nested cluster randomized designs have limitations.
  • These include inefficiency with primary data, potential bias under violated homogeneity of variance assumptions, and lack of empirical evaluation for finite sample properties.

Purpose of the Study:

  • To propose an alternative maximum likelihood estimator for standardized mean difference effect size and its sampling variance in partially nested designs.
  • To address limitations of existing methods, including variants that do not assume homogeneity of variance.

Main Methods:

  • Developed a new maximum likelihood estimator ([Formula: see text]) using parameter estimates from multilevel models.
  • Compared the new estimator with the typical estimator (d) using simulation studies.
  • Demonstrated methods with real-world data from preventive and intervention programs.

Main Results:

  • Both the typical estimator (d) and the new estimator ([Formula: see text]) yielded unbiased point and variance estimates for effect size.
  • The new estimator ([Formula: see text]) was generally more efficient than d, particularly with unequal cluster sizes, large average cluster sizes, and high intraclass correlations.
  • Under heterogeneous variances, [Formula: see text] showed greater relative efficiency with small sample sizes for unclustered control arms.

Conclusions:

  • The proposed maximum likelihood estimator offers an efficient and robust alternative for effect size estimation in partially nested cluster randomized designs.
  • This method is particularly beneficial for primary data analysis and situations with unequal cluster sizes or heterogeneous variances.
  • The study extends to three-level designs and provides practical guidance through real data examples.