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Human Perception of Exponentially Increasing Data Displayed on a Log Scale Evaluated Through Experimental Graphics Tasks

Emily Anna Robinson, University of Nebraska - Lincoln

Abstract

Log scales are often used to display data over several orders of magnitude within one graph. We conducted a series of three graphical studies to evaluate perception of exponentially increasing trends on log and linear scales. Each study required a different level of interaction and cognitive use of the data being presented. Experiment 1 evaluated whether our ability to perceptually notice differences in exponentially increasing trends is impacted by the choice of scale. Participants were shown a set of plots and asked to identify which plot appeared to differ most from the other plots. Results indicated the choice of scale changes the contextual appearance of the data leading to slight perceptual advantages for both scales depending on the curvatures of the trend lines being compared. Experiment 2 validated a new method for testing statistical graphics and introduced an appropriate statistical analysis method for comparing visually fitted trend lines to statistical regression results. This method was then used to assess our ability to forecast exponentially increasing trends on both scales. The results from the analysis showed a clear underestimation of forecasting trends with high exponential growth rates when participants were asked to make predictions on the linear scale; improvements in forecasts were made when participants were asked to make predictions on the log scale. Experiment 3 evaluated graph comprehension as it relates to the contextual scenario of the data shown. Overall, our results suggested that log logic is difficult and that anchoring and rounding biases result in a sacrifice in accuracy in estimates made on the log scale for large magnitudes. The studies conducted in this research relied on graphical tasks of varying complexity to help us understand the perceptual and cognitive advantages and disadvantages of displaying exponentially increasing data on the log scale. The results are instrumental in establishing guidelines for making design choices about scale which result in data visualizations effective at communicating the intended results.

Subject Area

Statistics

Recommended Citation

Robinson, Emily Anna, "Human Perception of Exponentially Increasing Data Displayed on a Log Scale Evaluated Through Experimental Graphics Tasks" (2022). ETD collection for University of Nebraska - Lincoln. AAI29257475.
https://digitalcommons.unl.edu/dissertations/AAI29257475

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