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Description: Our understanding of how the brain makes decisions has benefited greatly from behavioral and neural findings that have identified close links between neural computations and normative decision theory. Among the most well-studied decisions that exhibit this link are simple perceptual decisions that are thought to transform sensory observations into likelihoods, which are the probabilities of obtaining the sensory evidence given particular hypotheses about the state of the world (Gold & Shadlen, 2001, 2007). According to normative theory, likelihoods for different hypotheses can be compared to each other (e.g., via their ratio) to make optimal decisions (in terms of maximizing accuracy) about which hypothesis about the world is most probable given the evidence. This procedure is central to numerous models, such as the widely used drift-diffusion model (DDM), that have successfully accounted for a host of decision-related neural and behavioral findings. However, many of these models include “fudge factors” that are used to account for the fact that true likelihoods can be difficult to compute and thus must often be approximated. This difficulty arises because true likelihoods require information about not just the given sensory observation but also the (possibly long-term) statistics of the process that generated that observation in the world and then represented it in the brain. Previous studies have shown that these fudge factors (e.g., the drift rate in the DDM, often fit as a free parameter) can vary considerably across individuals and conditions. Because these fudge factors govern the difference between true likelihoods, which are needed for optimal decisions, and merely approximate ones, this variability can play a key role in governing decision accuracy, speed, biases, and other factors related to optimality. Although these sub-optimalities have been identified for certain conditions, a more general treatment, including identifying how different statistical environments affect decision-making via their impact on how (and how easily) likelihoods can be computed or approximated from sensory observations, is lacking and is the focus of this study. In particular, most prior work focused on decision-making based on single streams of evidence or based on multiple sources that were assumed to be statistically independent. However, in the real world, we often must base decisions on evidence that comes from multiple sources that are not independent. Ignoring correlations among sources of evidence distorts the computation of likelihoods and posteriors, leading to them to over- or underestimate the probability of particular hypotheses. When accumulating evidence over time to form decisions based on a fixed decision rule, such distortions result in unintended shifts of the speed-accuracy tradeoff. However, the extent to which human decision-makers take correlations into account is not well-understood. Here we developed a novel evidence accumulation paradigm that allows precise control of the correlations between sources of evidence to ask whether and how humans take correlations into account in simple two-alternative perceptual decisions.