Techniques for graphing paired data are considered. A conventional method frequently used when reporting scientific results, particularly in medical journals, involves representing pairs of measurements by straight line segments titled at different angles related to the differences between the components of the data pairs. However when the sample size is only moderately large, this type of display can become cluttered and thus uninformative due to overlap. It is suggested that a new graph that combines features of ANOVA plots and multivalued dot charts may provide a more effective visual display of paired data. A designed experiment in data perception using simulated data provides some evidence in favor of this parallel line plot.