This study manipulated the graphical representation of options by framing the physical characters in figures and found that preferences could be affected even when the words and numbers of the problem were constant. Based on attribute substitution theory and an equate-to-differentiate approach, we proposed a two-process model of graph-framing effects. In the first mental process, the graph-editing process, the physical features (e.g., distance, size) represented in the graph are visually edited, and the perceived numerical difference between the options is judged based on its physical features. The second mental process, the preferential choice process, occurs by an equate-to-differentiate approach in which people seek to equate the difference between options on the dimension on which the difference is smaller, thus leaving the greater other-dimensional difference to be the determinant of the final choice. Four experiments were tested for graph-framing effects. Experiment 1 found a graph-framing effect in coordinate graphs resting on the (de)compression of the scales employed in the figures. Experiment 2 revealed additional graph-framing effects in other question scenarios and showed that preference changes were mediated by perceived numerical distances. Experiment 3 further confirmed the presence of graph-framing effects in sector graphs similar to those found in coordinate ones. Experiment 4 suggested that such graph-framing effects could be eliminated when logical processing (e.g., introducing a mathematical operation before a choice task) was encouraged. This paper discusses related research and a possible substrate basis for graph-framing effects. Copyright © 2011 John Wiley & Sons, Ltd.