We have studied the size dependence of the exciton g factor in self-assembled InAs/InP quantum dots. Photoluminescence measurements on a large ensemble of these dots indicate a multimodal height distribution. Cross-sectional scanning tunneling microscopy measurements have been performed and support the interpretation of the macrophotoluminescence spectra. More than 160 individual quantum dots have systematically been investigated by analyzing single dot magnetoluminescence between 1200 and 1600 nm. We demonstrate a strong dependence of the exciton g factor on the height and diameter of the quantum dots, which eventually gives rise to a sign change of the g factor. The observed correlation between exciton g factor and the size of the dots is in good agreement with calculations. Moreover, we find a size-dependent anisotropy splitting of the exciton emission in zero magnetic field. © 2009 The American Physical Society.