Date of Award
Doctor of Philosophy (PhD)
Educational Policy Studies
Phill Gagné - Committee Chair
Frances A. McCarty - Committee Member
L. Juane Heflin - Committee Member
Paul A. Alberto - Committee Member
Hierarchical Linear Modeling (HLM) sample size recommendations are mostly made with traditional group-design research in mind, as HLM as been used almost exclusively in group-design studies. Single-case research can benefit from utilizing hierarchical linear growth modeling, but sample size recommendations for growth modeling with HLM are scarce and generally do not consider the sample size combinations typical in single-case research. The purpose of this Monte Carlo simulation study was to expand sample size research in hierarchical linear growth modeling to suit single-case designs by testing larger level-1 sample sizes (N1), ranging from 10 to 80, and smaller level-2 sample sizes (N2), from 5 to 35, under the presence of autocorrelation to investigate bias and power. Estimates for the fixed effects were good for all tested sample-size combinations, irrespective of the strengths of the predictor-outcome correlations or the level of autocorrelation. Such low sample sizes, however, especially in the presence of autocorrelation, produced neither good estimates of the variances nor adequate power rates. Power rates were at least adequate for conditions in which N2 = 20 and N1 = 80 or N2 = 25 and N1 = 50 when the squared autocorrelation was .25.Conditions with lower autocorrelation provided adequate or high power for conditions with N2 = 15 and N1 = 50. In addition, conditions with high autocorrelation produced less than perfect power rates to detect the level-1 variance.
Haardoerfer, Regine, "Power and Bias in Hierarchical Linear Growth Models: More Measurements for Fewer People." Dissertation, Georgia State University, 2010.