A novel sample variance formula and Sv-plot3 for testing hypotheses

Abstract

Sample variance plots, also called Sv-plots, Sv-plot1 and 2, illustrate the deviations from the sample variance, identifying properties of the distribution. Sv-plot2 is exceptionally appealing in testing hypotheses outperforming both histogram and boxplot. In this work, a novel form of independent deviation is introduced, exploring its properties for normally distributed data. The relationship among these deviations, sample average, and variance is established. Further, a novel formula for sample variance is derived. Besides these results, a statistical plot, Sv-plot3 is innovated, that detects outliers, including characteristics of the data distribution such as symmetry and skewness. Remarkably, Sv-plot3 can also be employed to illustrate testing hypotheses over single and two population means comparable to Sv-plot2. Finally, simulated data with hypothetical examples are utilized for illustrations of Sv-plot3. As an efficient graphical tool, Sv-plot3 competitively contributes an attractive visualization for identifying distributional characteristics and testing hypotheses.