The shifting boxplot. A boxplot based on essential summary statistics around the mean.

Abstract

Boxplots are a useful and widely used graphical technique to explore data in order to better understand the information we are working with. Boxplots display the first, second and third quartile as well as the interquartile range and outliers of a data set. The information displayed by the boxplot, and most of its variations, is based on the data’s median. However, much of scientific applications analyse and report data using the mean. In this paper, we propose a variation of the classical boxplot that displays information around the mean. Some information about the median is displayed as well.

Getting the most from your curves: Exploring and reporting data using informative graphical techniques

“…This information is supported also by essential summary statistics like the confidence intervals around the mean. Given that the mean is the statistic most frequently reported in psychological research and other sciences, future work should propose graphical techniques which represent essential summary statistics around the mean and give information about the data's distribution (e.g., Marmolejo-Ramos & Tian, 2009).…”

The visualisation of data in a digital context

“…[ Figure 3: An interactive dashboard that provides a range of visualisaion and analysis options (Ellis & Merdian, 2015)] In response to the digitalisation of psychological research methods, data figures have and will continue to evolve in order to maximise their expressive power, both with regards to conveying the content and structure of the data as well as informing the analysis process (Campitelli & Macbeth, 2014;Marmolejo-Ramos, 2014). So far, this has included computational developments, such as the expansion of boxplots to include information about both distribution and density of the data (Marmolejo-Ramos & Matsunaga, 2009;Marmolejo-Ramos & Tian, 2010) or explorations of different data visualisations for particularly skewed data sets (Ospina et al, 2014).…”

Visualization of Skewed Data

“…A vertical shifting boxplot is a compound of nine quantities about a normally distributed batch of data (Marmolejo & Tian 2010): (1) Smallest outlying observation, (2) Minimum value within the ±2s range, where s is the sample standard deviation, Observations that fall below −2s and above 2s are represented by dashes. Observations that are equal to or above −2s and equal or below 2s are enclosed by the innermost box, which covers approximately 95% of the data and is similar to the whiskers in the traditional boxplot.…”

“…Modifications to the shifting boxplot incorporate more accurate confidence intervals and robust estimators of central tendency to explore non-normal data (Marmolejo & Tian 2010). …”