Derived LoTSS-NVSS and in-band LoTSS spectral index measurements for isolated, compact, fully deconvolved LoTSS-DR2 sources overlaid with contours showing the density of points. The solid blue histograms show the in-band LoTSS spectral index distribution (top) and the LoTSS-NVSS spectral index distribution (right) for all sources where we have both measurements. The histograms outlined in black show the LoTSS-NVSS spectral index distribution of these sources overlaid on the in-band LoTSS spectral index distribution or vice versa. The solid and dashed red lines show the spectral index values derived from only bright (LoTSS S_I > 30 mJy beam⁻¹) LoTSS sources for in-band and LoTSS-NVSS (top) and LoTSS-NVSS and in-band (right) respectively. The dotted and the dashed yellow histograms (top) show the results from simulations where the LoTSS-NVSS spectral index values of bright (LoTSS S_I > 30 mJy beam⁻¹) sources, and associated errors, are used to simulate LoTSS in-band flux densities which are then fitted with a power law to give a spectral index. Here flux densities for each band and source are extrapolated from the LoTSS-NVSS spectral index and LoTSS continuum measurement plus a random error drawn from a Gaussian with a standard deviation equal to 10% (dotted) or 3% (dashed) of the flux density (mimicking a flux density scale alignment uncertainty) added in quadrature to the statistical uncertainty from the PYBDSF estimation of noise local to the source.