Adequate sample sizes for viable 2-level hierarchical linear modeling analysis : a study on sample size requirement in HLM in relation to different intraclass correlations

Through a simulation study with different design conditions (sample sizes at two levels ranging from 5 to 50, intraclass correlation ranging from 0.05 to 0.40), this study intends to provide some general guidelines about adequate sample sizes at two levels under different intraclass correlations (ICC) conditions for a viable two level HLM analysis (e.g., reasonably unbiased and accurate parameter estimates, reasonable power for detecting between-group variance). Because educational data typically have ICCs ranging from 0.1 to 0.2, we focus our discussions about adequate sample sizes under ICC = 0.15 as a representative condition. We discuss ranges o f sample sizes that are inadequate or adequate for statistical power, relative bias, and accuracy o f individual parameter estimates. To better choose adequate sample sizes under ICC = 0.1 and 0.2, we also examine effects o f ICCs smaller or larger than 0.15 on sample size requirements. Unlike previous studies that dogmatize "minimum" sample size requirement for various purposes, the current study, with more detailed simulation designs for small sample sizes and ICCs, provides numerous options o f "adequate" sample sizes under various ICC conditions. By providing these options and well-documented simulation results, this study emphasizes that "adequate" sample sizes at either level 1 or level 2 can be adjusted according to different interests in parameter estimates, different expectation o f statistical power, and different ranges o f tolerable bias and accuracy. Under different ICC conditions, we help readers identify level-1 sample size, level-2 sample size or both as the source o f variation in relative bias or accuracy for a certain parameter estimate. This will assist researchers in making better decisions for selecting adequate sample sizes in HLM analysis. A limitation o f this study is that we did not examine strength and weakness o f different estimation algorithms (e.g., ML, REML, and FML) to produce unbiased or accurate parameter estimates.

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Digitization of this thesis was made possible by a generous grant from the Jefferson Trust, 2015.

Thesis originally deposited on 2016-02-19 in version 1.28 of Libra. This thesis was migrated to Libra2 on 2017-03-23 16:36:45.