This dissertation focuses on a human operator's ability to perform rotational control of a three-dimensional object using two-degrees of freedom (DOF) interface devices. Although input devices designed specifically for 3D interaction exist, devices traditionally used for two-dimensional user interaction, such as a mouse or joystick, have become ubiquitous to computer tasks. This research examines a particular human-computer interaction issue that arises from stimulus-response compatibility between three-dimensional stimuli spaces and 2-DOF response sets. The focal point of this research is a phenomenon referred to here as accidental inversion. Accidental inversions occur when an operator erroneously moves a three-dimensional object in a direction opposite than was intended. Thus, the effect of accidental inversion results from a mismatch between the operator's intended and actual input. A key assumption in diagnosing the causal factors involved in the accidental inversion effect is contribution from both internal (i.e., having to do with the individual) and external (i.e., having to do with the environment) influences. Three experiments were conducted to study accidental inversion. The first examined population stereotype, a measure of a target population's natural response tendencies to particular stimuli for a particular task. Results indicated a strong population stereotype for horizontal rotations (i.e., yaw) and weak stereotype for vertical rotations (i.e., pitch). This effect was mediated by whether the task was in the context of flight or ground-based movement. The second experiment analyzed the subjective preference for two opposite input-response (I-R) mappings (i.e., how the system responds to different input into the controlling device) for a task requiring control over vertical rotation. Results indicated that subjective preferences for I-R mappings were not heavily polarized. The third experiment also focused on vertical rotational control and examined how subjective preference for a particular I-R mapping affected performance. Furthermore, this experiment also examined performance when interference was introduced in the form of a temporary interruption where the participant had to conduct the task using an opposite I-R mapping. Results indicated that, upon being interrupted with the opposite I-R mapping, the group who used the mapping they subjectively preferred did worse than the group who used the mapping they did not prefer. This research has implications for the design of human-machine systems requiring human-in-the-loop three-dimensional rotational control. Some human-machine systems can have significant consequences from even a single mistake caused by a human-operator accidentally providing the wrong input. Findings from this research lead to two primary recommendations to the design of human-machine systems: a) an easily accessible and clearly indicated method to select input-response mapping which is provided before beginning the actual task, b) be informed of the current input-response mapping in use.