A convenient method and numerical tables for sample size determination in longitudinal-experimental research using multilevel models

Recent years have shown increased awareness of the importance of sample size determination in experimental research. Yet effective and convenient methods for sample size determination, especially in longitudinal experimental design, are still under development, and application of power analysis in a...

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Bibliographic Details
Published in:Behavior research methods 2014-12, Vol.46 (4), p.1207-1219
Main Author: Usami, Satoshi
Format: Article
Language:English
Subjects:
Analysis of Variance
Behavioral Research - methods
Behavioral Science and Psychology
Cognitive Psychology
Correlation analysis
Data Interpretation, Statistical
Experimental research
Longitudinal Studies
Models, Psychological
Models, Statistical
Multilevel Analysis
Psychology
Reproducibility of Results
Research Design
Research methodology
Sample Size
Statistical power
Variance analysis
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Summary:Recent years have shown increased awareness of the importance of sample size determination in experimental research. Yet effective and convenient methods for sample size determination, especially in longitudinal experimental design, are still under development, and application of power analysis in applied research remains limited. This article presents a convenient method for sample size determination in longitudinal experimental research using a multilevel model. A fundamental idea of this method is transformation of model parameters (level 1 error variance [ σ 2 ], level 2 error variances [ τ 00 , τ 11 ] and its covariance [ τ 01 ,  τ 10 ], and a parameter representing experimental effect [ δ ]) into indices (reliability of measurement at the first time point [ ρ 1 ], effect size at the last time point [ Δ T ], proportion of variance of outcomes between the first and the last time points [ k ], and level 2 error correlation [ r ]) that are intuitively understandable and easily specified. To foster more convenient use of power analysis, numerical tables are constructed that refer to ANOVA results to investigate the influence on statistical power by respective indices.
ISSN:1554-3528
1554-3528
DOI:10.3758/s13428-013-0432-0