ThetaWin

Schrausser, D. G. (2025). ThetaWin: Graphical user interface for Theta applications within ConsoleApp_DistributionFunctions. ThetaWin DOI:10.5281/zenodo.7659263 Dietmar G. Schrausser orcid.org/0000-0002-4924-8280 Karl-Franzens University, Graz, Austria Graphical user interface for Theta applications (Schrausser, 2009) within ConsoleApp_Distribution Functions (Schrausser, 2024), generating distributions and estimators for several parameters 𝜃 via bootstrap method, with given number of resamples 𝐵, where bootstrap estimator 𝜃 𝐵=𝐵−1 ⋅∑𝜃𝑖∗ 𝐵 𝑖=1 , introduced by Efron (1979, 1981, 1982) as a further development of the Jackknife method (Quenouille, 1949). See also Monte-Carlo Methode (Metropolis & Ulam, 1949) and permutation or randomization tests, first mentioned by Fisher (1935), based on his own account of experiments in agriculture (Fisher, 1926) and the work by Neyman (1923). In this context see further Pitman (1937a, b, 1938), Fisher (1966, 1971), Efron et al. (1992), Good (2006), Edgington and Onghena (2007), Beasley and Rodgers (2009), Oneto (2020) or Kauermann et al. (2021). A fundamental comparative overview of the different methods and approaches is given by Schrausser (1996, 2025, res.). References Beasley, W. H., & Rodgers, J. L. (2009). Resampling Methods. In The Sage Handbook of Quantitative Methods in Psychology, edited by Millsap, R. E., & Maydeu-Olivares, A., 362–86. Thousand Oaks, California: Sage Publications Ltd. https://psycnet.apa.org/doi/10.4135/9780857 020994.n16 Edgington, E. S., & Onghena, P. (2007). Randomization Tests. 4th ed. New York: Chapman and Hall/ CRC. https://doi.org/10.1201/9781420011814 Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics, 7(1), 1–26. https://doi.org/10.1214/aos/1176344552 Efron, B. (1981). Nonparametric Estimates of Standard Error: The Jackknife, the Bootstrap and Other Methods. Biometrika, 68(3), 589–99. https:// doi.org/10.1093/biomet/68.3.589 Efron, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans. CBMS-NSF Regional Conference Series in Applied Mathematics, Monograph, 38. Philadelphia: SIAM, Society for Industrial and Applied Mathematics. https://doi. org/10.1137/1.9781611970319 Efron, B., & Kotz, S., & Johnson, N. L. (1992). Bootstrap Methods: Another Look at the Jackknife. In Breakthroughs in Statistics: Methodology and Distribution, 569–93. New York, NY: Springer New York. https://doi.org/10.1007/978-1-461 2-4380-9_41 Fisher, R. A. (1926). The Arrangement of Field Experiments. Journal of the Ministry of Agriculture, 33, 503–15. https://doi.org/10.23637/rotham sted.8v61q Fisher, R. A. (1935). The Design of Experiments. 1st ed. Edinburgh: Oliver & Boyd. https://psycnet. apa.org/record/1939-04964-000 Fisher, R. A. (1966). The Design of Experiments. 8th ed. Edinburgh: Hafner. https://scirp.org/reference /referencespapers.aspx?referenceid=895747 Fisher, R. A. (1971). The Design of Experiments. 9th ed. New York: Hafner Press. https://home.iitk.ac.in/ ~shalab/anova/DOE-RAF.pdf Good, P. (2006). Resampling Methods. 3rd ed. Basel: Birkhäuser. https://www.amazon.com/Resamplin g-Methods-Practical-Guide-Analysis/dp/08176 43869 Kauermann, G., Küchenhoff, H., & Heumann, C. (2021). Bootstrapping. In Statistical Foundations, Reasoning and Inference: For Science and Data Science, 197–229. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030 -69827-0_8 Metropolis, N., & Ulam, S. (1949). The Monte Carlo Method. Journal of the American Statistical Association, 44(247), 335–41. https://doi.org/ 10.1080/01621459.1949.10483310 Neyman, J. (1923). Sur les applications de la theorie des probabilites aux experience agricoles: Essay de principes. Roczniki Nank Polniczek, 10, 1–51. https://link.springer.com/chapter/10.1007/97 8-94-015-8816-4_10 Oneto, L. (2020). Resampling Methods. In Model Selection and Error Estimation in a Nutshell, 25–31. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-24359-3_4 Pitman, E. J. G. (1937a). Significance Tests Which May Be Applied to Samples from Any Populations. Supplement to the Journal of the Royal Statistical Society, 4(1), 119–30. http://www.jstor.org/ stable/2984124 Pitman, E. J. G. (1937b). Significance Tests Which May Be Applied to Samples from Any Populations. II. The Correlation Coefficient Test. Supplement to the Journal of the Royal Statistical Society, 4(2), 225–32. http://www.jstor.org/stable/298 3647 Pitman, E. J. G. (1938). Significance Tests Which May Be Applied to Samples from Any Populations: III. The Analysis of Variance Test. Biometrika, 29(3/4), 322–35. http://www.jstor.org/stable/ 2332008 Quenouille, M. H. (1949). Approximate Tests of Correlation in Time-Series. Journal of the Royal Statistical Society B, Methodological, 11(1), 68–84. https://doi.org/10.1111/j.2517-6161.1949.tb0 0023.x Schrausser, D. G. (1996). Permutationstests: Theoretische und praktische Arbeitsweise von Permutationsverfahren beim unverbundenen 2 Stichprobenproblem. Universität Graz: Naturwissenschaftliche Fakultät. https://zenodo.org/records/115 29663 Schrausser, D. G. (2009). ThetaWin Overview. Software. Academia. https://www.academia.edu/81800 920 Schrausser, D. G. (2024). Schrausser/ConsoleApp_Distribution_Functions: Console applicationes for distribution functions (version v1.5.0). https:// doi.org/10.5281/zenodo.7664141 Schrausser, D. G. (2025). Mathematical and Statistical Applications for HP Prime. SocArXiv Papers, August, 1–15. https://doi.org/10.31235/osf.io/ vs8a6_v1