The influence of shape on apparent area: a new demonstration

Scaled rectangle diagrams can be used to visualize clinical and epidemiological data

OBJECTIVE

To illustrate scaled rectangle diagrams as a method for displaying clinical and epidemiological attributes (such as symptoms, signs, results of marker tests, disease, or risk factors). These are quantitative Venn diagrams, but using rectangles instead of circles.

STUDY DESIGN AND SETTING

The method is illustrated through examples from various data sets with different types of clinical information.

RESULTS

Examples drawing on studies of lung disease, rheumatic fever, blood pressure, lipid levels, sudden infant death syndrome, and low birth weight illustrate the different types of relationships between variables that the scaled rectangle approach can reveal (e.g., high- and low-risk groups; dependent, independent, or co-occurring attributes; effects from choice of cutoff; cumulative distributions; and case-control attributes).

CONCLUSION

Scaled rectangle diagrams are a novel way to display clinical data. They show clearly the relative frequency of clinical attributes and the extent to which they are shared characteristics. Features are revealed that might otherwise not have been appreciated.

Displaying clinical data relationships using scaled rectangle diagrams

A method is presented to draw rectangles to represent categorical data relationships. The idea is an adaptation of a scaled Venn diagram. Rectangles are drawn with area proportional to the frequency of categories and the rectangles are positioned to overlap each other so that the areas of overlap are in proportion to the joint frequencies of the characteristics. The diagrams are especially useful to illustrate symptom co-occurrence.

Apparent relative size in the judgment of apparent distance

In experiment 1 judgments of the apparent distance of comparison figures (squares or triangles) were obtained under reduction conditions. These comparison figures were either shaped the same as or different from equidistant standard figures, and were half, equal to, or double the area of the standard figures. Apparent distance was found to be a linear function of the relative area of the comparison figure both in same-shape and different-shape stimulus pair conditions. In addition, apparent distance was found to be a function of perceived area, because in different-shape conditions triangles were generally seen to be closer than squares even when the real area of the standard and comparison was equal. The results of experiment 2 and 3 provide some evidence that the effect of different shapes of standard and comparison on apparent distance is due to the observers' perception of the height rather than the area of figures. The series of experiments shows that the traditional transactionalists' explanation of relative size as a cue for distance is inadequate.