Function estimation: Quantifying individual differences of hand-drawn functions

Graphical perception is an important part of the scientific endeavour, and the interpretation of graphical information is increasingly important among educated consumers of popular media, who are often presented with graphs of data in support of different policy positions. However, graphs are multidimensional and data in graphs are comprised not only of overall global trends but also local perturbations. We presented a novel function estimation task in which scatterplots of noisy data that varied in the number of data points, the scale of the data, and the true generating function were shown to observers. 170 psychology undergraduates with mixed experience of mathematical functions were asked to draw the function that they believe generated the data. Our results indicated not only a general influence of various aspects of the presented graph (e.g., increasing the number of data points results in smoother generated functions) but also clear individual differences, with some observers tending to generate functions that track the local changes in the data and others following global trends in the data.