Academic journal article Perception and Psychophysics

The Perception of Scatterplots

Academic journal article Perception and Psychophysics

The Perception of Scatterplots

Article excerpt

Four experiments investigated the perception of correlations from scatterplots. All graphic properties, other than error variance, that have been shown to affect subjective but not objective correlation (r) were held constant. Participants in Experiment 1 ranked 21 scatterplots according to the magnitude of r. In Experiments 2 and 3, participants made yes/no judgments to indicate whether a scatterplot was high (signal) or low (noise). Values of r for signal and noise scatterplots varied across participants. Differences between correlations for signal and for noise scatterplots were constant in r in Experiment 2, and constant in r^sup 2^ in Experiment 3. Standard deviations of the ranks in Experiment 1 and d' values in Experiments 2 and 3 showed that discriminability increased with the magnitude of r. In Experiment 4, faculty and graduate students in psychology and sociology made point estimates of r for single scatterplots. Estimates were negatively accelerated functions of objective correlation.

The research literature on the perception of scatterplots is reviewed below. However, it is first necessary to distinguish between the two fundamentally different forms of judgments made in the research, discriminative judgments and absolute judgments, or point estimates. They can be operationally distinguished in a straightforward way. Discriminative judgments are those that call for the organism to make greater than/less than judgments, whereas absolute judgments call for participants to make point estimates on a scale.

Discriminative Judgments

In a study commonly cited as the first investigation of scatterplot perception, Pollack (1960) had participants make discriminative judgments about scatterplots presented on an oscilloscope. He described his scatterplots as a "dazzling dancing parade of correlation patterns" (p. 352). Using the classical psychophysical method of constant stimulus differences (Guilford, 1936, pp. 186ff), Pollack assessed two-choice difference thresholds in eight different experiments, or, in his terms, eight series, that varied the duration of the display, frequency range, size of the scatterplot sign of the correlation represented, and characteristics of the pulses that generated the points. In each experiment participants judged whether a scatterplot represented a higher or lower correlation than a reference scatterplot by pressing a lever up or down, and were provided immediate confirmation of the correctness or incorrectness of their judgments. The number of standard stimuli, or reference correlations, varied in given experiments from five to ten, with from four to six variable stimuli associated with each one. Threshold levels for 60%, 75%, and 90% correct were assessed for each reference correlation. The results were presented as the minimum difference between r^sup 2^ for the reference scatterplots and r2 for the judged scatterplots required to achieve the desired level of discriminability.

Pollack (1960) interpreted the participant's task "as that of testing alternative statistical hypotheses" (p. 359), and found that the difference thresholds diminished markedly as the magnitude of the correlations increased. He suggested that "we might profitably search for an appropriate metric of confusability such as the d' measure of the theory of signal detectability" (pp. 359-360). He went on to speculate that r^sup 2^ might be the appropriate metric for the "representation of the visual scatterplot in discrimination space."

Pollack's suggestion that d' be considered as a possible metric for the confusability of scatterplots has not been pursued, nor have there been further investigations of the discriminability, as such, of scatterplots. There has, however, been considerable research, reviewed below, on point estimates of correlations exhibited in scatterplots. The first three experiments in the present paper were designed primarily to pursue Pollack's suggestion to investigate scatterplot confusability. …

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