  A frequent task in exploratory data analysis consists in examining pairwise
dependencies between data variables. Popular approaches include visualizing
correlation or scatter plot matrices. However, both methods can be misleading.
The former is primarily limited because it reports a single value for a pair of
random variables. Furthermore, scatter plots can fail to convey the dependency
structure between variables properly. In this paper we discuss these
shortcomings and present alternative and richer visualizations based on copula
functions, which fully determine the dependency between continuous random
variables. Since copulas seldom appear in the data visualization literature we
first review essential theory, and propose alternative scatter plots and
several heatmaps for assessing the statistical association between two
continuous random variables. These visualizations not only allow users to
detect independence, but also increasing and/or decreasing trends in the data
through a color coding, which can also be applied in other methods such as
parallel coordinates.
