The Effective Use of Statistics

Statistical independence is one of the most important statistical ideas and is required in order to generalize a conclusion from a sample to a population. The estimated differences between averages for phenomena of interest take center stage and much less attention is devoted to variation, however. The study of variation is a key aspect to generalizing results and making predictions. This paper addresses concepts of variation in statistics and attempts to simplify various statistical ideas. Two cases will be presented for the need of statistical understanding in day-to-day life garnered by an enhanced understanding of statistical independence and variation. An industrial example and a lithographic example are used to demonstrate the steps needed to analyze seemingly innocuous dataset and how the application of these concepts is crucial.