Is Detecting Discontinuity Difficult? Evidence from the Visual Trend Classification of Scatterplots

Abstract

Abstract Visualization of data comes with the promise that even unexpected aspects of the data can be detected. For instance, viewers might discover that patterns in a scatterplot follow a non-linear trend. Using two experiments, we examined whether and when scatterplots depicting different types of mathematical functions are classified correctly and confidently. In Experiment 1, 237 participants categorized scatterplots that depicted more or less noisy linear, negative exponential, or discontinuous step functions. Results indicated a classification advantage for the continuous linear and negative exponential functions over the discontinuous step function. Generalizing from these findings, in Experiment 2, 231 participants categorized scatterplots that depicted more or less noisy versions of a broader range of functions, including rising continuous linear, quadratic (half parabola), and discontinuous linear (kinked) functions and rising and falling continuous quadratic (full parabola), sine wave, and discontinuous linear (inverted-v) functions. Generally, results suggested that scatterplots based on discontinuous functions are difficult to classify. Overall, the results indicated a classification advantage for the continuous functions over the discontinuous functions and underscore the need for scientists and practitioners to be extremely careful when developing theory and making decisions based on exploration of raw data visualizations.