# Inference by Signal Strength

The top panel plots how much subjects over- or underinfer from signals as a function of the true signal.

Subjects start with a prior of 1/2, and are given binary symmetric signals of different strengths. The x-axis measures what a Bayesian's posterior would be. The y-axis measures how much weight subjects put on the signal, relative to a Bayesian. Values greater than 1 indicate overinference; values less than 1 indicate underinference.

The bottom panel relabels the axes to plot subjects' perceived signal *strength*, defined by the log odds ratio* *log(posterior / (1 - posterior)), as a function of the true signal strength. Data are shown on a log-log scale. As shown by the best-fit line, subjects' perceptions are roughly linear in logs, a hallmark of models of psychophysics and cognitive imprecision.

Error bars indicate 95% confidence intervals.