Fig 1.
Scientists have measured the concentration of two chemical solutes (A and B, each measured in parts per million) in many vials of sea water. Horizontal blue lines are the means, dashed vertical bars capture 95% of the measurements for each solute, and you may assume independence. Question: in what percentage of vials is there more of solute B than A (Probability(B > A)? Answer below.
Fig 2.
An illustration of our different study conditions.
Error bars convey the mean of a distribution of measurements (outcomes) along with a vertical “error bar” capturing a 95% confidence interval. Violin plots extend this idea by showing the distribution in a mirrored histogram. Hypothetical Outcome Plots (HOPs) present the same distribution as animated frames (that can be played in sequence or manually flipped through). Each frame contains a horizontal bar representing one outcome. An animated version of this figure is available in the animated manuscript (S1 File).
Table 1.
One-Variable Distribution Types.
Fig 3.
Violin plots showing the four one-quantity tasks, four two-quantity tasks, and single three-quantity task summarized in Tables 1–3.
An animated version of this figure is available in the animated manuscript (S1 File).
Table 2.
Two-Variable Distribution Types.
Table 3.
Three-Variable Distribution Types.
Table 4.
Mean Absolute Error by Treatment and Task Parameters.
The * indicates a significant difference between the starred treatment and at least one other (padj < 0.001). Fig 3 illustrates the violin plot for each Type.
Fig 4.
Stimuli (left) and absolute error (right) of estimates of μ.
Error bars indicate a 95% confidence interval. Error bars in the results plot show a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).
Fig 5.
Stimuli (left) and absolute error (right) of estimates of Pr(A ≥ k).
Both locations of the red dot (above and below mu) are shown, though subjects saw only one of the dots in each trial. Error bars in the results plot indicate a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).
Fig 6.
Stimuli (top) and absolute error (bottom) of estimates of Pr(k2 < = A< = k3).
Error bars indicate a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).
Fig 7.
Stimuli (left) and absolute error (right) of estimates of Pr(B > A).
Error bars indicate a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).
Fig 8.
Stimuli (top) and absolute error (bottom) of estimates of Pr(B > A, B > C).
Error bars in the results plot indicate a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).
Fig 9.
A gradient plot, where probability density of each possible outcome is encoded using mark opacity.