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 & 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), Good (2006), Edgington & Onghena (2007) or Beasley & Rodgers (2009). 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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———. (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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———. (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.
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.tb00023.x.
Schrausser, D. G. (1996). Permutationstests: Theoretische und praktische Arbeitsweise von Permutationsverfahren beim unverbundenen 2 Stichprobenproblem. Universität Graz: Naturwissenschaftliche Fakultät. https://zenodo.org/records/11529663.
———. (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.