Sv-plots for identifying characteristics of the distribution and testing hypotheses

Abstract

The histogram and boxplot are effective and simple graphical tools, which are broadly used to explore the characteristics of the distribution of univariate data. In this proposed work, two statistical plots called sample variance plots (Sv-plots), are defined which illustrate squared deviations from the sample variance. Sv-plots exhibit the contribution of each data value toward the sample variability with profound insight. Besides capturing symmetry and skewness of the distribution, these plots can detect outliers in the data based on two novel bounds introduced on each plot analogous to a boxplot. In comparison with histogram and boxplot, for actual and simulated data, Sv-plots firmly lead in revealing more information. Displaying the exact data values, Sv-plots improve visual sensation for detecting masked atypical values and asymmetry of the data. Remarkably, one version of the Sv-plots can be employed to display the testing hypotheses for a single and two population means and discovers a graphical method to make the decision. It is found that the Sv-plots outperform both histogram and boxplot, and have additional benefits beyond identifying characteristics of the distribution.

Keywords:

• Data visualization
• Hypothesis testing
• Outlier detection
• Sample variance
• Skewness
• Squared deviations

Acknowledgments

Constructive comments by reviewers and the associated editor are greatly appreciated and have led to a substantial change. Also, the author gratefully acknowledges the partial support of the Early Career Faculty Grant provided by the University of Southern Indiana.

Additional information

Funding

This work was partially supported by the University of Southern Indiana under Early Career Faculty Grant.