Appendix C: Principles of Statistical Testing

Chapter
Part of the Computational Biology book series (COBO, volume 18)

Abstract

Here, we will briefly recap the basic principles of statistical testing. For an in depth treatment we recommend, for example, . We will start with the classical examples of the Z-test and t-test to assess statistical hypotheses concerned with sample means. We then describe the classical approaches to ANOVA and multiple regression, before we show how these procedures can be described using the unifying framework of general linear models (GLMs). After briefly discussing generalized linear models, we will cover the nonparametric counterparts of the t-test, ANOVA and regression. The chapter will conclude with the chi-square test and Fisher’s exact test as primary examples of statistical tests adapted to the analysis of qualitative variables.

Keywords

Design Matrix Good Linear Unbiased Predictor Rejection Region Rank Regression Canonical Parameter
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References

1. 1.
Famoye, F., Singh, K.P.: Zero-inflated generalized Poisson model with an application to domestic violence data. J. Data Sci. 4, 117–130 (2006)Google Scholar
2. 2.
Lehmann, E.L., D’Abrera, H.J.M.: Nonparametrics: Statistical Methods Based on Ranks. McGraw-Hill, New York (1975)
3. 3.
Lehmann, E.L., Romano, J.P.: Testing Statistical Hypotheses. Springer, New York (2005)
4. 4.
McCulloch, C.E., Searle, S.R., Neuhaus, J.M.: Generalized, Linear and Mixed Models, 2nd edn. John Wiley and Sons (2008)Google Scholar
5. 5.
Nelder, J.A., McCullagh, P.: Generalized Linear Models. Chapman and Hall, London (1991)Google Scholar
6. 6.
Neyman, J., Pearson, E.: On the problem of the most efficient tests of statistical hypotheses. Phil. Trans. Roy. Soc. Ser. A 231, 289–337 (1933)Google Scholar
7. 7.
Puri, M.L., Sen, P.K.: Nonparametric Methods in General Liner Models. John Wiley and Sons, New York (1985)Google Scholar
8. 8.
Seber, A.F., Lee, A.J.: Linear Regression Analysis. John Wiley and Sons (2003)Google Scholar
9. 9.
Shao, J.: Mathematical Statistics. Springer, New York (1999)

Authors and Affiliations

• Florian Frommlet
• 1
Email author
• Małgorzata Bogdan
• 2
• David Ramsey
• 3
1. 1.Center for Medical Statistics, Informatics, and Intelligent Systems Section for Medical StatisticsMedical University of ViennaViennaAustria
2. 2.Institute of MathematicsUniversity of WrocławWrocławPoland
3. 3.Department of Operations ResearchWrocław University of TechnologyWrocławPoland