Research on the effects of the spatial correlation between signal and response key has shown a clear relationship between signal/response spatial correlation and reaction time (RT) for signals and response keys that are in a linear relationship (Morin and Grant 1955; Hoffmann 2010). By means of a reanalysis of previous data of Chan and Chan (2009a, 2009b, 2011a, 2011b, 2010), the equivalent relationships for two-dimensional (2D) and three-dimensional (3D) display/control relationships are established. In a 2D array of signals with a corresponding 2D array of response keys, RT is dependent on spatial correlation, with arrangements having transverse compatibility reacting faster than those with longitudinal compatibility. 3D arrangements show a similar effect, with up/down compatibility being a major factor in determination of RT and with similar effects of transverse compatibility. The results indicate the best arrangements of signal/key arrangements where complex designs are necessary.Practitioner Summary: Design of complex display/control arrangements requires high compatibility in order to minimise reaction times. This work extends previous research to cases where displays and controls are in two-dimensional and three-dimensional arrangements, and indicates how reaction time is affected by these more complex arrangements. © 2013 Taylor & Francis.