Graphical user interface for Theta applications (Schrausser, 2009) within ConsoleApp_DistributionFunctions (Schrausser, 2024),
generating distributions and estimators for several parameters
introduced by Efron (1979, 1981, 1982) as a further development of the Jackknife method (Quenouille, 1949). See also Monte-Carlo Methode (Metropolis and 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).
Usage: Theta [sd] [min] [max] [qq] [q] [v] [s] [[x]] [[g]]
[sd] ........... Seed: |0| Zeitwert
[min] ........... R Minimalwert
[max] ........... R Maximalwert
[qq] ........... Theta-Theta/
[q] ........... Theta:
|0| Harmonisches Mittel (HM)
|1| Arithmetisches Mittel (AM)
|2| Summe (SUM)
|3| Standardabweichung (SD)
|4| Populationsvarianzschaetzung (VAR)
|5| Produktsumme(PSM)
|6| Geometrisches Mittel(GM)
|7| Schrausser's d (D)
|8| DvarO (DV)
[v] ........... n zu Theta (v)
[s] ........... n Subpopulationen (s)
[x] ........... Vergleichswert x
[g] ........... |1| Wertebereich ganzzahlig
Usage: Theta_Q [sd][min][max][qq][qp][qs1][qs2][qQ][v][m][n][s] [[x]] [[g]]
[sd] ........................... Seed: |0| Zeitwert
[min] ........................... R Minimalwert
[max] ........................... R Maximalwert
[qq] ........................... Theta-Theta/
[qp] ........................... Theta P/
[qs1] [qs2] ..................... Theta S1, S2:
|0| Harmonisches Mittel (HM)
|1| Arithmetisches Mittel (AM)
|2| Summe (SUM)
|3| Standardabweichung (SD)
|4| Populationsvarianzschaetzung (VAR)
|5| Produktsumme(PSM)
|6| Geometrisches Mittel(GM)
|7| Schrausser's d (D)
|8| DvarO (DV)
[qQ] ........................... Theta Q:
|1| Differenz
|2| Quotient
|3| Summe
|4| Produkt
[v] ........................... n zu Theta P (v)
[m] ........................... n zu Theta S1 (m)
[n] ........................... n zu Theta S2 (n)
[s] ........................... n Subpopulationen (s)
[x] ........................... Vergleichswert x
[g] ........................... |1| Wertebereich ganzzahlig
Usage: Theta_Qv [sd][min][max][qq][qp][qs1][qs2][qQ][QQ][v][n][s] [[x]] [[g]]
[sd] ........................... Seed: |0| Zeitwert
[min] ........................... R Minimalwert
[max] ........................... R Maximalwert
[qq] ........................... Theta-Theta/
[qp] ........................... Theta P/
[qs1][qs2]....................... Theta S1, S2/
[qQ] ........................... Theta Q:
|0| Harmonisches Mittel (HM)
|1| Arithmetisches Mittel (AM)
|2| Summe (SUM)
|3| Standardabweichung (SD)
|4| Populationsvarianzschaetzung (VAR)
|5| Produktsumme(PSM)
|6| Geometrisches Mittel(GM)
|7| Schrausser's d (D)
|8| DvarO (DV)
[QQ] ........................... Theta Theta Q:
|1| Differenz
|2| Quotient
|3| Summe
|4| Produkt
|5| Korrelation
|6| Kovarianz
|7| Determinationskoeffizient
|8| Redundanz
[v] ........................... n zu Theta P (v)
[n] ........................... n zu Theta S1,S2 (n)
[s] ........................... n Subpopulationen (s)
[x] ........................... Vergleichswert x
[g] ........................... |1| Wertebereich ganzzahlig
Usage: Theta_rQ [sd][min][max][qq][qp][q11][q12][q21][q22][qr1][qr2][qQ][v][m][n][s] [[x]] [[g]]
[sd] ....................... Seed: |0| Zeitwert
[min] ....................... R Minimalwert
[max] ....................... R Maximalwert
[qq] ....................... Theta-Theta/
[qp] ....................... Theta P/
[q11][q12] .................. Theta S11, S12/
[q21][q22] .................. Theta S21, S22:
|0| Harmonisches Mittel (HM)
|1| Arithmetisches Mittel (AM)
|2| Summe (SUM)
|3| Standardabweichung (SD)
|4| Populationsvarianzschaetzung (VAR)
|5| Produktsumme(PSM)
|6| Geometrisches Mittel(GM)
|7| Schrausser's d (D)
|8| DvarO (DV)
[qr1][qr2] ...................Theta Regressionen 1,2/
|1| Korrelation (kor)
|2| Kovarianz (cov)
|3| Determinatinskoeffizient (det)
|4| Redundanz (red)
[qQ] ....................... Theta Q:
|1| Differenz (Diff)
|2| Quotient (Quot)
|3| Summe (Summ)
|4| Produkt (Prod)
[v] ....................... n zu Theta P (v)
[m] ....................... n zu Theta S11,S12 (m)
[n] ....................... n zu Theta S21,S22 (n)
[s] ....................... n Subpopulationen (s)
[x] ....................... Vergleichswert x
[g] ....................... |1| Wertebereich ganzzahlig
Usage: Theta_S [sd] [min] [max] [qq] [qp] [qs] [v] [m] [s] [[x]] [[g]]
[sd] ...................... Seed: |0| Zeitwert
[min] ...................... R Minimalwert
[max] ...................... R Maximalwert
[qq] ...................... Theta-Theta:
[qp] ...................... Theta P/
[qs] ...................... Theta S/
|0| Harmonisches Mittel (HM)
|1| Arithmetisches Mittel (AM)
|2| Summe (SUM)
|3| Standardabweichung (SD)
|4| Populationsvarianzschaetzung (VAR)
|5| Produktsumme(PSM)
|6| Geometrisches Mittel(GM)
|7| Schrausser's d (D)
|8| DvarO (DV)
[v] ..................... n zu Theta P (v)
[m] ..................... n zu Theta S (m)
[s] ..................... n Subpopulationen (s)
[x] ..................... Vergleichswert x
[g] ..................... |1| Wertebereich ganzzahlig
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/10.4135/9780857020994.n16
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———. (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
———. (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
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———. (1971). The Design of Experiments. 9th ed. New York: Hafner Press. https://home.iitk.ac.in/~shalab/anova/DOE-RAF.pdf
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———. (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
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———. (2009). ThetaWin Overview. Software. Academia. https://www.academia.edu/81800920
———.(2024). Schrausser/ConsoleApp_DistributionFunctions: Console applicationes for distribution functions (version v1.5.0). Zenodo. https://doi.org/10.5281/zenodo.7664141