Transformations and R applications applied to data with different distributions

This study investigates the effects of data transformation techniques, frequently used to address distribution abnormalities in statistical analyses, on the validity of analysis results. It specifically examines how applying transformations enhances the reliability of parametric tests in situations where data fails to meet the normal distribution assumption. The methodology section of the study introduces various distribution types (normal, skewed, multimodal, heavy/light-tailed) and discusses their impact on the analysis process. It explains why data characteristics such as right or left skewness, the presence of outliers, and variance heterogeneity pose problems in analyses, demonstrating with examples how these issues can be resolved using appropriate transformation techniques. Following theoretical explanations, the study covers fundamental transformation methods like logarithmic, square root, reciprocal, Box-Cox, and Yeo-Johnson, and also evaluates lesser-known techniques such as hyperbolic and probability integral transformations. Practical examples, implemented using the R programming language, illustrate in detail how these transformations are applied, visualized, and reflected in analysis results. Comparative analyses, particularly supported by normality test results, QQ plots, histograms, and density curves after transformation, highlight the effects of the transformations. In conclusion, this study demonstrates the significant importance of selecting and correctly applying appropriate data transformation techniques when the normality assumption cannot be met in statistical analyses. The research not only reinforces statistical theory but also provides a practical and applicable guide for researchers through examples implemented in the R programming environment. In this regard, the thesis contributes to studies aiming to improve the accuracy of statistical analyses across various fields, from biological and social sciences to engineering and health research.