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.

摘要

直方图和箱线图是有效且简单的图形工具，广泛用于探索单变量数据的分布特征。在这项拟议的工作中，定义了两个称为样本方差图（Sv-plots）的统计图，它们说明了样本方差的平方偏差。Sv-plots 以深刻的洞察力展示了每个数据值对样本变异性的贡献。除了捕获分布的对称性和偏度外，这些图还可以基于类似于箱线图的每个图上引入的两个新边界来检测数据中的异常值。与直方图和箱线图相比，对于实际数据和模拟数据，Sv-plots 在揭示更多信息方面稳居领先地位。显示确切的数据值，Sv-plots 改善了检测掩蔽的非典型值和数据不对称性的视觉感觉。值得注意的是，可以使用一个版本的 Sv-plots 来显示单个和两个总体均值的检验假设，并发现一种图形方法来做出决定。结果发现，Sv 图优于直方图和箱线图，并且除了识别分布特征外还有其他好处。