Boxplot for circular variables |
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Authors: | Ali H Abuzaid Ibrahim B Mohamed Abdul G Hussin |
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Institution: | 1. Institute of Mathematical Sciences, University of Malaya, 50603, Kuala Lumpur, Malaysia 2. Center for Foundation Studies in Science, University of Malaya, 50603, Kuala Lumpur, Malaysia
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Abstract: | A boxplot is a simple and flexible graphical tool which has been widely used in exploratory data analysis. One of its main applications is to identify extreme values and outliers in a univariate data set. While the boxplot is useful for a real line data set, it is not suitable for a circular data set due to the fact that there is no natural ordering of circular observations. In this paper, we propose a boxplot version for a circular data set, called the circular boxplot. The problem of finding the appropriate circular boxplot criterion of the form ν × CIQR, where CIQR is the circular interquartile range and ν is the resistant constant, is investigated through a simulation study. As might be expected, we find that the choice of ν depends on the value of the concentration parameter κ. Another simulation study is done to investigate the performance of the circular boxplot in detecting a single outlier. Our results show that the circular boxplot performs better when both the value of κ and the sample size are larger. We develop a visual display for the circular boxplot in S-Plus and illustrate its application using two real circular data sets. |
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