Optimising line graph aspect ratio

Abstract

The aim of these studies was to find a way of selecting aspect ratios for line graphs so that they would provide the data analyst using graphical methods with the most information with the least distortion. If an ideal aspect ratio could be discovered it would help scientist make the best possible use of their research data. Cleveland and McGill (1987) theorised that the ideal aspect ratio could be selected by adjusting the aspect ratio until the line segments that make up a graph’s data path were positioned as close as possible to 45°. Cleveland and McGill went on to report a study which supported their theory. Experiments 1-3 here failed to replicate the results of Cleveland and McGill. Further analysis showed that the measure of accuracy used by Cleveland and McGill (1987) and in Experiments 1- 3 was corrupted by a confounding. This confounding was between response bias and accuracy, and as a result nothing could be concluded about Cleveland and McGill’s theory from the data. Given the problems with the previous accuracy measure, a new technique was required to test Cleveland and McGill’s theory of ideal aspect ratio. A “signal detection” style procedure called the “behavioural detection model” was used which produced separate measures of accuracy (log d) and response bias (log c). Using these measures it was found that, as the angle of a pair of lines increased from 0° to 45°, accuracy improved. For all angles greater than 45° accuracy was poor. These results partially support the theory of ideal aspect ratio suggested by Cleveland and McGill (1987). Like Cleveland and McGill’s theory it seems the data path should be positioned as close as possible to 45°; Unlike Cleveland and McGill’s theory the results here suggest that the data path should never be greater than 45°. These conclusions still need further testing to see if the results here apply to lines with negative slopes, as well as positive slopes, and how well the theory works in applied settings.