PRM

Demo movie

Permutation Methods Calculator PRM (in development). Android application for the calculation of permutation tests, where

$$p(x)=p(\theta_{(x)} \ge \Theta_{(x)}|H_0), 0\le p\le1,$$

$$p=\frac{1}{M}⋅\sum_{i=1}^M\theta_{(i)}\ge\Theta_{(x)},$$

first mentioned by Fisher (1935), based on his own account of experiments in agriculture (Fisher, 1926) and the work by Neyman (1923).

See further Pitman (1937a, b, 1938), Fisher (1966, 1971), Cox & Hinkley (1974), Schrausser (1996, p. 4-22 ff., 1998a, b, 2022), Edgington & Onghena (2007) or Scambor & Schrausser (2023), also Schrausser (2024, p. 29).

Example 1 (c.f. Schrausser, 1998a).

Example 2 (c.f. Schrausser, 1998b).

References

Cox, D. R., & Hinkley, D. V. (1974). Theoretical Statistics (1st ed). New York: Chapman and Hall/CRC. eBook ISBN 9780429170218 DOI:10.1201/b14832

Edgington, E. S., & Onghena, P. (2007). Randomization tests (4th ed). New York: Chapman and Hall/CRC. ISBN 9780367577711, eBook ISBN 9780429142710 DOI:10.1201/9781420011814

Fisher, R. A. (1926). The Arrangement of Field Experiments. Journal of the Ministry of Agriculture 33: 503–15. DOI:10.23637/rothamsted.8v61q

———. (1935). The Design of Experiments. 1st ed. Edinburgh: Oliver & Boyd. https://psycnet.apa.org/record/1939-04964-000

———. (1966). The Design of Experiments. 8th ed. Edinburgh: Hafner. https://scirp.org/reference/referencespapers.aspx?referenceid=895747

———. (1971). The Design of Experiments. 9th ed. New York: Hafner Press. https://home.iitk.ac.in/~shalab/anova/DOE-RAF.pdf

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/10.1007/978-94-015-8816-4_10

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

———. (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/2983647

———. (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

Scambor, C., & Schrausser, D. G. (2023). Introduction (part II, permutation tests for repeated measurement designs). In: Permutation methods in single case studies:.... Thesis. Karl Franzens University, Institute of Psychology. Academia. www.academia.edu/94993376

Schrausser, D. G. (1996). Permutationstests: Theoretische und praktische Arbeitsweise von Permutationsverfahren beim unverbundenen 2 Stichprobenproblem. Diplom. Institut für Psychologie, Karl Franzens Universität, Graz. DOI:10.13140/RG.2.2.24500.32640/1

———. (1998a). Exakte Verfahren oder Asymptotische Approximation. In: Glück. J., Jirasco, M., & Rollett, B. (Hrsg.) Perspektiven psychologischer Forschung in Österreich, Teil 2. WUV-Univ.-Verl., Wien. ISBN 3851144414 DOI:10.5281/zenodo.11673333

———. (1998b). Die Permutationsmethode: Voraussetzungsfrei testen. 41. Kongreß der Deutschen Gesellschaft für Psychologie (DGPs). Dresden. DOI:10.13140/rg.2.2.19532.69768

———. (2022). Thesis chapter 1: Introduction. In: Permutation tests:.... Thesis. Karl Franzens University, Institute of Psychology. Academia. www.academia.edu/82224369

———. 2024. Handbook: Distribution Functions (Verteilungs Funktionen). PsyArXiv. DOI:10.31234/osf.io/rvzxa