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Schematic eye models have typically been used to explain the average monochromatic and chromatic imaging properties of the eye. Both monochromatic aberrations and transverse chromatic aberration are known to vary widely across subjects. However, to our knowledge, the ability of schematic eye models to predict these individual variations has not been tested experimentally. We used a spatially resolved refractometer to measure the monochromatic aberrations and the optical transverse chromatic aberration (oTCA) in a group of 15 eyes. By recording the 1st and 4th Purkinje images for five directions of gaze, we also estimated the tilt, misalignment of ocular surfaces (front surface of the cornea and back surface of the lens) and off-axis position of the fovea (angle alpha), as well as pupil centration. We conclude that, contrary to expectations none of those factors are major contributors to the variability in monochromatic aberrations and oTCA in this group of eyes. Simulations show that corneal curvature and corneal conicity are also unlikely to account for the observed relation between monochromatic aberrations and oTCA. Our results suggest an important contribution of corneal irregularities to those aberrations.