Distributions of the absolute difference in position angles between matched ILT and HSC sources. The top panel shows the overall distribution for all matched sources. The lower panels show distributions for sub-samples divided by radio flux density (middle) and by radio size (bottom). The shaded error band reflects the Poisson uncertainties. The solid grey line represents the scenario without a correlation between the radio and optical position angles. For all matched sources, the KS statistic relative to a uniform distribution is D = 0.10. For the three increasing flux bins, the KS statistics are D = 0.06, 0.12, and 0.12. For the three increasing size bins, the KS statistics are D = 0.06, 0.10, and 0.18. In all cases, the p-values are lower than 0.005.