Figure 1. Simulations using sinusoidal tuning curves provide intuition into the attenuation and inflation of estimated signal, that is, tuning curve, correlation (r̂s). A, Sinusoidal tuning curves (solid lines, blue and orange) show theoretical expected value (ti,x and ti,y) for responses of two neurons to repeated stimulation. Their relative phase shift sets a fixed rs = 0.5. Simulating an experiment, single-trial responses are drawn and averaged for each neuron at each point on the tuning curves (dots and bars show expected value and variance, open circles indicate the sample mean). Signal correlation is typically estimated across such trial averages (open circles), which often have a lower correlation (here r̂s=0.32) than do the expected values (solid lines). Thus, sample signal correlation is downwardly biased compared with the correlation between the true tuning curves. B, A schematic distribution of single-trial simultaneous responses of both neurons plotted against each other. The lack of noise correlation is reflected by the circular contour lines. C, Simulation showing how signal correlation can be inflated by noise correlation. Here, deviations of the dotted lines around the means (solid lines) are correlated across the two neurons, that is, at a given x value, both dashed lines often lie above or below their means. D, Noise correlation is indicated in the joint distribution of simultaneous single-trial responses by the tilted ellipsoids around expected values. This positive tilt inflates the estimated signal correlation.