Statistical graphics play an important role in exploratory data analysis, model checking and diagnostics, but they are not usually associated with statistical inference. Recent developments allows inference to be applied to statistical graphics. A new method, called the lineup protocol, enables the data plot to be compared with null plots, in order to obtain estimates of statistical significance of structure. With the lineup protocol observed patterns visible in the data can be formally tested. The research conducted and described in this thesis validates the lineup protocol, examines the effects of human factors in the application of the protocol, and explains how to implement the protocol. It bridges the long existing gulf between exploratory and inferential statistics. In the validation work, additional refinement of the lineup protocol was made: methods for obtaining the power of visual tests, and p-values for particular tests are provided. A head-to-head comparison of visual inference against the best available conventional test is run for regression slope inference, using simulation experiments with human subjects. Results indicate that the visual test power is higher than the conventional test when the effect size is large, and even for smaller effect sizes, there may be some super-visual individuals who yield better performance than a conventional test. The factors that may influence the individual abilities are examined, and results suggest that demographic and geographic factors have statistically significant but practically insignificant impact. This work provides instructions on how to design human subject experiments to use Amazon's Mechanical Turk to implement the lineup protocol.