Accumulated evidence as an additive performance measure based on confidence ratings

Perceptual evidence accumulation is a gradual process that is typically studied using drift diffusion models. A disadvantage of those models is that they treat accumulated evidence only in an indirect way. Here, we suggest to measure accumulated evidence more directly by utilizing participants’ confidence ratings together with their decisions. The resulting measure has the key advantage of being additive: For example, evidence accumulated during a first stimulus presentation interval E [ 0 , a ] adds up with evidence accumulated during a second interval E [ a , b ] to the total evidence accumulated during the whole presentation E [ 0 , a ] + E [ a , b ] = E [ 0 , b ] . Because it is experimentally only possible to measure evidence after the first interval ( E [ 0 , a ] ) or after the whole presentation ( E [ 0 , b ] ), but not selectively for the second interval ( E [ a , b ] ), we can exploit additivity to calculated this value E [ a , b ] = E [ 0 , b ] − E [ 0 , a ] . In two experiments, we demonstrate the strengths of our approach. In Experiment 1, we provide direct support for previous findings suggesting a deceleration in evidence accumulation ( E [ 0 , a ] > E [ a , b ] ). Moreover, we show an increased evidence accumulation rate for causal rather than anti-causal dot-motion stimuli. In Experiment 2, we quantify inter-dependencies of evidence accumulation in later stages ( E [ a , b ] ) on that of earlier stages ( E [ 0 , a ] ). Limitations of our approach arise from its reliance on confidence ratings. But when properly implemented, it allows the generation of more specific hypotheses than other approaches: Instead of only testing whether evidence accumulation changes, our measure supports precise point predictions and interpretations about the particular amount of accumulated evidence.