Graphic Comparisons of Several Linked Aspects: Alternatives and Suggested Principles

Abstract

The graphical display of two or more numerical aspects, in comparing several circumstances, has widespread applications. Like almost all graphic display, emphasis is on comparison and on phenomena (on appearances describable in nonnumerical words). Impact of the highest quality attainable is important. Digital information can, and should, be included when helpful.

A variety of schemes—linkages—for displaying first two and then several numerical aspects are explored. Circular forms for the elements involved do relatively well.

Next we look at linkages in a substantial and moderately diversified field of applications. Individual (inCI) and simultaneous (siCI) confidence intervals for individual values (determinations), and related but different structures (interference notches) for (pairwise) comparisons provide an important area of application for linkages, both simple and of moderate complexity. The same desire to simplify the viewer's task that contributed to the introduction of (simple) simultaneous intervals leads to the introduction of multiple simultaneous confidence intervals (musiCI). Three siCI's usually suffice. Possible styles of all of these kinds of confidence intervals are explored to a limited degree, and a consistent set of choices is proposed. (By analogy to a dialect, such a consistent set may well be called a diaglypt.) Confidence apertures offer another, often desirable approach to displaying confidence intervals.

When we come to all pairwise comparisons, we need to deal with notches, conveniently called interference notches or IN's (sometimes called partial intervals or PI's). Again, we can have individual (inIN), simultaneous (siIN, naturally expanded to simIN), or multiple simultaneous (musiIN, naturally contracted to musIN) interference notches. After a little exploration of style, a diaglypt is proposed for IN's that is consistent with our earlier proposals for CI's.

We then turn to boxplots, where an essentially simple idea was (usefully) complicated by the inclusion of (interference) notches. The techniques and attitudes developed earlier allow a satisfactory resolution of an uncomfortable problem.

We turn next to the question of what general principles are suggested by the detailed implementations that we have studied. These include:

•	Balancing impact across a linkage, which often requires more intrinsic impact near the center of the linkage than toward its ends.
•	Alternating emphasis from one aspect to another, which may be necessary when several aspects are shown.
•	“The dog in the night time”—who was noticeable because he did not bark—is the analogy of the intrinsically weak element (of a linkage, character array, or curve system), which gains impact by being the only intrinsically weak element in a sea of intrinsically strong elements.
•	The conflict between desires for sharp indication but restrained busyness, which is often ameliorated by the use of circular elements.
•	The need, where several related kinds of display form a diaglypt (whether we will or not), for care in “regular inflections” in making logical parallels also visually parallel.

An appendix suggests some useful calculations—about the relation of confidence intervals to endogenous fits—that do not seem to be available.

Key Words:

• Confidence intervals
• Diaglypts
• Display
• Interference notches
• Multiple confidence intervals