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Sample Size Calculator (web)

Structural Equation Modeling - Root Mean Squared Error of Aproximation (RMSEA)

Expected RMSEA:
Degrees of freedom (df, may calculate here):
Significance level (α): Two-tailed
Power (1 - β): %
Expected dropout rate: %

Sample size, n =
Sample size (with 10% dropout), n_drop =

References:

Kim, K. H. (2005). The relation among fit indexes, power, and sample size in structural equation modeling. Structural Equation Modeling, 12(3), 368-390. [Sample size formula, Non-centrality parameter calculation]

References for algorithms (for calculating CDF of non-central chi-square):

Ding, C. G. (1992). Algorithm AS 275: computing the non-central χ² distribution function. Journal of the Royal Statistical Society. Series C (Applied Statistics), 41(2), 478-482.

Pearson, E. S. (1959). Note on an approximation to the distribution of non-central χ². Biometrika, 46(3/4), 364.

Wilson, E. B., & Hilferty, M. M. (1931). The distribution of chi-square. Proceedings of the National Academy of Sciences of the United States of America, 17(12), 684–688.

Ross, A. H. (1999). Algorithm for calculating the noncentral chi-square distribution. IEEE Transactions on Information Theory, 45(4), 1327-1333.

Suggested reference:

APA: Arifin, W. N. (2025). A web-based sample size calculator for structural equation modelling. Education in Medicine Journal, 17(1), 195–212. https://doi.org/10.21315/eimj2025.17.1.14

Vancouver: Arifin WN. A web-based sample size calculator for structural equation modelling. Education in Medicine Journal. 2025;17(1):195–212. https://doi.org/10.21315/eimj2025.17.1.14

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