  Recently we have presented the analytical relationship between choice
probabilities, noise correlations and read-out weights in the classical
feedforward decision-making framework (Haefner et al. 2013). The derivation
assumed that behavioral reports are distributed evenly between the two possible
choices. This assumption is often violated in empirical data - especially when
computing so-called grand CPs combining data across stimulus conditions. Here,
we extend our analytical results to situations when subjects show clear biases
towards one choice over the other, e.g. in non-zero signal conditions.
Importantly, this also extends our results from discrimination tasks to
detection tasks and detect probabilities for which much empirical data is
available. We find that CPs and DPs depend monotonously on the fraction, p, of
choices assigned to the more likely option: CPs and DPs are smallest for p
equal to 0.5 and increase as p increases, i.e. as the data deviates from the
ideal, zero-signal, unbiased scenario. While this deviation is small, our
results suggest a) an empirical test for the feedforward framework and b) a way
in which to correct choice probability and detect probability measurements
before combining different stimulus conditions to increase signal/noise.
