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Hypothesis Testing

  • Thomas Cleff
Chapter

Abstract

Among the most important techniques in statistics is hypothesis testing. A hypothesis is a supposition about a certain state of affairs. It does not spring from a sudden epiphany or a long-standing conviction; rather, it offers a testable explanation of a specific phenomenon. A hypothesis is something that we can accept (verify) or reject (falsify) based on empirical data.

References

  1. Backhaus, K., Erichson, B., Plinke, W., Weiber, R. (2016). Multivariate Analysemethoden. Eine anwendungsorientierte Einführung, 14th Edition. Berlin, Heidelberg: SpringerGabler.Google Scholar
  2. Bortz, J. (1999). Statistik für Sozialwissenschaftler, 5th Edition. Berlin, Heidelberg: Springer.Google Scholar
  3. Bortz, J., Lienert, G. A., Boehnke, K. (2000). Verteilungsfreie Methoden der Biostatistik, 2nd Edition. Berlin, Heidelberg: Springer.CrossRefGoogle Scholar
  4. Brown, M. B., Forsythe, A. B. (1974). Robust tests for the equality of variances. Journal of the American Statistical Association, 69, 364–367.CrossRefGoogle Scholar
  5. Conover, W.J. (1980). Practical nonparametric statistics. New-York: Wiley.Google Scholar
  6. Dixon, W.J. (1954). Power under normality of several nonparametric tests. The Annals of Mathematical Statistics, 25: 610-614.CrossRefGoogle Scholar
  7. Field, A. (2005). Discovering Statistics Using SPSS. London: Sage.Google Scholar
  8. Fisher, R.A., Yates, F. (1963). Statistical tables for biological, agricultural, and medical research. London: Oliver and Boyed.Google Scholar
  9. Hair, J.F., Anderson, R.E., Tatham, R.L., Black, W.C. (1998). Multivariate Data Analysis, 5th Edition. London: Prentice Hall.Google Scholar
  10. Kolmogorov, A. N. (1933). Sulla determinazione empirica di una legge di distribuzione. Giornale dell’ Istituto Italiano degli Attuari, 4, 83–91.Google Scholar
  11. Kruskal, W. H., Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47, 583–621.CrossRefGoogle Scholar
  12. Kruskal, W. H., Wallis, W. A. (1953). Errata: Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 48, 907–911.CrossRefGoogle Scholar
  13. Mann, H.B., Whitney, D.R. (1947). On a test whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics, 18, 65-78.CrossRefGoogle Scholar
  14. Neyman, J. (1937). Outline of a theory of statistical estimation based on the classical theory of probability. Philosophical transactions of the Royal Society, Series A, 236.Google Scholar
  15. Neyman, J. & Pearson, E. S. (1928a). On the use and interpretation of certain test criteria for purposes of statistical inference, part i. Biometrika, 20A, 175–240.Google Scholar
  16. Neyman, J. & Pearson, E. S. (1928b). On the use and interpretation of certain test criteria for purposes of statistical inference, part ii. Biometrika, 20A, 263–294.Google Scholar
  17. Popper, K. (1934). Logik der Forschung. Tübingen: Mohr.Google Scholar
  18. Satterthwaite, F. E. (1946). An approximate distribution of estimates of variance components. Biometrics Bulletin 2: 110-114.CrossRefGoogle Scholar
  19. Scheffé, H. (1953). A method for judging all contrasts in the analysis of variance. Biometrika, 40, 87-104.Google Scholar
  20. Shapiro, S. S., and R. S. Francia (1972). An approximate analysis of variance test for normality. Journal of the American Statistical Association, 67, 215–216.CrossRefGoogle Scholar
  21. Shapiro, S. S., and M. B. Wilk (1965). An analysis of variance test for normality (complete samples). Biometrika, 52, 591–611.CrossRefGoogle Scholar
  22. Smirnov, N. V. (1933). Estimate of deviation between empirical distribution functions in two independent samples. Bulletin Moscow University, 2, 3–16.Google Scholar
  23. Spearman, C.E. (1904). The proof and measurement of association between two things. American Journal of Psychology, 15(1), 72–101.CrossRefGoogle Scholar
  24. Stevens, J. P. (1972). Four Methods of Analyzing between Variations for the k-Group MANOVA Problem, Multivariate Behaviorial Research, 7, 442-454.Google Scholar
  25. Welch, B. L. (1947). The generalization of Student’s problem when several different population variances are involved. Biometrika, 34, 28–35.Google Scholar
  26. Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics, 1, 80-83.CrossRefGoogle Scholar
  27. Wilcoxon, F. (1947). Probability tables for individual comparisons by ranking methods. Biometrics, 3, 119-122.CrossRefGoogle Scholar
  28. Witting, H. (1960). A generalized Pitman efficiency for nonparametric tests. The Annals of Mathematical Statistics, 31, 405-414.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Thomas Cleff
    • 1
  1. 1.Pforzheim Business SchoolPforzheim University of Applied SciencesPforzheimGermany

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