Humans are often observed to make optimal sensorimotor decisions but to be poor judges of situations involving explicit estimation of magnitudes or numerical quantities. For example, when drawing conclusions from data, humans tend to neglect the size of the sample from which it was collected. Here, we asked whether this sample size neglect is a general property of human decisions and investigated its neural implementation. Participants viewed eight discrete visual arrays (samples) depicting variable numbers of blue and pink balls. They then judged whether the samples were being drawn from an urn in which blue or pink predominated. A participant who neglects the sample size will integrate the ratio of balls on each array, giving equal weight to each sample. However, we found that human behavior resembled that of an optimal observer, giving more credence to larger sample sizes. Recording scalp EEG signals while participants performed the task allowed us to assess the decision information that was computed during integration. We found that neural signals over the posterior cortex after each sample correlated first with the sample size and then with the difference in the number of balls in either category. Moreover, lateralized beta-band activity over motor cortex was predicted by the cumulative difference in number of balls in each category. Together, these findings suggest that humans achieve statistically near-optimal decisions by adding up the difference in evidence on each sample, and imply that sample size neglect may not be a general feature of human decision-making.