Sensory decision-making is frequently studied using categorical tasks, even though the feature space of most stimuli is continuous. Recently, it has become more common to measure feature perception in a gradual fashion, say when studying motion perception across the full space of directions. However, continuous reports can be contaminated by perceptual or motor biases. Here, we examined such biases on perceptual reports by comparing two response methods. With the first method, participants reported motion direction in a motor reference frame by moving a trackball. With the second method, participants used a perceptual frame of reference with a perceptual comparison stimulus. We tested biases using three different versions of random dot kinematograms. We found strong and systematic biases in responses when reporting the direction in a motor frame of reference. For the perceptual frame of reference, these systematic biases were not evident. Independent of the response method, we also detected a systematic misperception where subjects sometimes confuse the physical stimulus direction with its opposite direction. This was confirmed using a von Mises mixture model that estimated the contribution of veridical perception, misperception, and guessing. Importantly, the more sensitive perceptual reporting method revealed that, with increasing levels of sensory evidence, perceptual performance increases not only in the form of higher detection probability, but under certain conditions also in the form of increased precision.