Transcranial direct current stimulation (tDCS) is a well-established technique for non-invasive brain stimulation (NIBS). However, the technique suffers from a high variability in outcome, some of which is likely explained by the state of the brain at tDCS-delivery but for which explanatory, mechanistic models are lacking. Here, we tested the effects of bi-parietal tDCS on perceptual line bisection as a function of tDCS current strength (1 mA vs 2 mA) and individual baseline discrimination sensitivity (a measure associated with intrinsic uncertainty/signal-to-noise balance). Our main findings were threefold. We replicated a previous finding (Giglia et al., 2011) of a rightward shift in subjective midpoint after Left anode/Right cathode tDCS over parietal cortex (sham-controlled). We found this effect to be weak over our entire sample (n = 38), but to be substantial in a subset of participants when they were split according to tDCS-intensity and baseline performance. This was due to a complex, nonlinear interaction between these two factors. Our data lend further support to the notion of state-dependency in NIBS which suggests outcome to depend on the endogenous balance between task-informative ‘signal’ and task-uninformative ‘noise’ at baseline. The results highlight the strong influence of individual differences and variations in experimental parameters on tDCS outcome, and the importance of fostering knowledge on the factors influencing tDCS outcome across cognitive domains.