Statistical Models and Methods

The statistical procedures used in this thesis are summarized in this subsection together with hints for further literature. PASW Statistics 18 and Microsoft Office Excel were used for computations. T-tests and Mann-Whitney tests were performed to assess internal relationships between binary and continuous explanatory variables, particularly vehicle impact speed. Pearson and Spearman correlations were used to assess possible correlations among continuous variables. 

The t-test is a parametric method for comparing two mean values, e.g., for the difference in means between two groups or one mean value with an expected value [33, 34], T-tests require a random sample, normally distributed and metric raw data, and homogeneous variances [33-35], 

The Mann-Whitney test is a non-parametric rank test, which compares two independent samples [34, 35]. The Mann-Whitney test is used here, if some prerequisites for the t-test, e.g., the homogeneity of variances, are not given. 

Possible correlations between continuous variables and vehicle impact speed were tested using Pearson and Spearman correlations. The Pearson correlation can find a correlation between variables independent of their scaling [34, 35]. Prerequisite are two continuous variables [34]. Spearman correlation uses the Bravais-Pearson correlation coefficient applied to ranks [34, 36]. As a consequence, it is also applicable to ordinal data [36], 

A binary logistic regression model estimates the effect of one or several factors on the probability of a defined binary outcome [37]. The estimate can be interpreted as a group membership or the risk associated with the explanatory factors contained in the model [37, 38]. The explanatory factors can be continuous, discrete or dichotomous [38]. 

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Lawless, J. F. 2003. Statistical models and methods for lifetime data, 2nd edition. New York John Wiley Sons. 

Lisnianski, A., Frenkel, I., Khvatskin, L. Ding Yi. 2007. Markov Reward Model for Multi-State System Reliability Assessment. In F. Vonta, M. Nikulin, N. Limnios, C. Huber-Carol (eds). Statistical Models and Methods for Biomedical and Technical Systems. Birkhaiiser Boston, 153-168. 

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