The impact of outlying observations on selected statistical analyses in R

This bachelor thesis is devoted to the issue of outlying observations in a dataset and their impact on selected statistical analyses, specifically regression and cluster analysis. Basic description of these statistical analyses is included in this bachelor thesis. However, the focus of this thesis is outlying observations. This thesis explores the properties of outliers at a theoretical level and presents the mechanisms of their occurrence. Different types of outlying observations are defined and illustrated with examples. Then, six outlier detection methods are introduced in the paper: the three-sigma rule, Tukey’s method, Mahalanobis distance, DFBETA, Cook’s distance, and cluster analysis detection. The procedure, suitability of use, advantages and disadvantages of each of these methods for outlier detection are explained. Finally, these theoretical insights are implemented in an experiment to demonstrate the impact of outlying observations on selected statistical analyses on a real data set. Potential outlying values are detected and removed using each outlier detection method. The regression and cluster analysis results are compared with respect to the statistical detection method used on the real dataset. The experiment is based on a regression analysis with one explanatory variable and two cluster analyses, the first using hierarchical cluster analysis method and the second using a non-hierarchical cluster analysis method. The whole practical part is carried out using the R programming language, with additional graphical representations of the analyses results.