Table of Content:

• R function to compute the worst-case scenario variance under a sub-optimal design: https://github.com/FInnocenti-Stat/SampNorm/tree/main/MaxPredVar_R_function

• Shiny app to compute the required sample size under the optimal design for univariate test norming: https://github.com/FInnocenti-Stat/SampNorm/tree/main/ShinyApp_OD_Univariate_Norming

• Shiny app to compute the required sample size under the optimal design for multivariate test norming: https://github.com/FInnocenti-Stat/SampNorm/tree/main/ShinyApp_SampSize_MahalaDist

• Shiny app to compute the relative efficiency and the required sample size increase for a sub-optimal design: https://github.com/FInnocenti-Stat/SampNorm/tree/main/ShinyApp_RE_SubOD

If you use any of these R Shiny apps in your work, please use the following recommended citation:

Innocenti, F., & Cassese, A. (19 Nov 2025). Sample Size Determination for Optimal and Sub-Optimal Designs in Simplified Parametric Test Norming. Multivariate Behavioral Research. https://doi.org/10.1080/00273171.2025.2580712

When using these R Shiny apps, you may also consult the following references:

• Innocenti, F., Tan, F. E., Candel, M. J., & van Breukelen, G. J. (2023). Sample size calculation and optimal design for regression-based norming of tests and questionnaires. Psychological Methods, 28(1), 89–106. https://doi.org/10.1037/met0000394

• Innocenti, F., Candel, M. J., Tan, F. E., & van Breukelen, G. J. (2024). Sample size calculation and optimal design for multivariate regression-based norming. Journal of Educational and Behavioral Statistics, 49(5), 817–847. https://doi.org/10.3102/10769986231210807