In this paper, we introduce various graphical methods that can be used to represent data in mixed research. First, we present a broad taxonomy of visual representation. Next, we use this taxonomy to provide an overview of visual techniques for quantitative data display and qualitative data display. Then, we propose what we call "crossover" visual extensions to summarize and integrate both qualitative and quantitative results within the same framework. We provide several examples of crossover (mixed research) graphical displays that illustrate this natural extension. In so doing, we contend that the use of crossover (mixed research) graphical displays enhances researchers' understanding (i.e., increased Verstehen) of social and behavioral phenomena in general and the meaning that underlies these phenomena in particular. Key Words: Graphic Methods, Visual Techniques, Graphical Displays, Crossover Graphical Displays, and Mixed Research
Mixed Methods Analysis and Information Visualization: Graphical Display for Effective Communication of Research Results
Overview of Graphical Display
As knowledge increases among mankind, and transactions multiply, it
becomes more and more desirable to abbreviate and facilitate the
modes of conveying information from one person to another, and from
one individual to many.
While written by William Playfair in 1801, the idea of conveying information still is regarded as timely and valuable in today's world. Images can be visual renditions or representations of ideas, dimensions, and events (Dickinson, 2001). Representing statistical ideas and information is a complex task, and as Tufte (1990) stated, "all communication between the readers of an image must take place on a two-dimensional surface" (p. 12).
Historically, quantitative data have facilitated graphical display techniques, offering a visual one-to-one correspondence of number to graphical element. A typical example of this one-to-one correspondence is the scatterplot, with each Cartesian coordinate pair represented by a plotted point, providing a visual summary of the measure of association among the variables of interest.
Visual methods of quantitative data display have been extensively developed for more than 200 years (Chernoff, 1973; Friendly, 1995; Playfair, 1801/2005; Tufte, 1990, 1997a, 1997b, 2001, 2006; Tukey, 1972, 1989; Wainer, 1992, 2005). Playfair, a prolific graphical innovator, developed techniques such as divided surface area charts, bar charts, time series line charts, gridlines, and differentiated line qualities (broken and solid lines, and line weight [thickness]). In fact, Playfair developed or improved all four major types of graphical display: data maps, time series, space-time-narrative, and relational graphics (Tufte, 2001). After Playfair, "graphs popped up everywhere, being used to convey information in the social, physical, and natural sciences" (Wainer, 2005, p. 9).
Chernoff (Chernoff, 1973; Chernoff & Rizvi, 1975) developed a multivariate display technique known as Chernoff's Faces, whereby each facial feature reflected a corresponding numeric variable value. Tukey developed stem-and-leaf plots, while Wainer often and eloquently described the inherent pictorial connections between graphical display techniques and effective communication. Wainer (2005) wrote, "an efficacious way to add context to statistical facts is by embedding them in a graphic" (p. 86). The challenge remains to develop and apply new methods of graphical exploration and display in order to translate effectively qualitative data into a visual format, thereby providing a powerful visual tool for effective communication of research results. Unfortunately, although there is a myriad of literature on graphical displays of statistical data, with the exception of Miles and Huberman (1994), scant attention has been paid regarding graphical displays of qualitative data. …