  Using a sample of 2922 z<0.2, spectroscopically-identified Active Galactic
Nuclei (AGN) we explore the relationship between radio size and the prevalence
of extreme ionised outflows, as traced using broad [O III] emission-line
profiles in Sloan Digital Sky Survey (SDSS) spectra. To classify radio sources
as compact or extended, we combine a machine-learning technique of
morphological classification with size measurements from two-dimensional
Gaussian models to data from all-sky radio surveys. We find that the two
populations have statistically different [O III] emission-line profiles, with
the compact sources tending to have the most extreme gas kinematics. When the
radio emission is confined within 3" (i.e., within the spectroscopic fibre or
~<5kpc at the median redshift), there is twice the chance of observing broad [O
III] emission-line components, indicative of very high velocity outflows, with
FWHM>1000 km/s. This difference is most enhanced for the highest radio
luminosity bin of log[L(1.4GHz)/(W/Hz)]=23.5-24.5 where the AGN dominate the
radio emission; specifically, >1000 km/s components are almost four-times as
likely when the radio emission is compact in this subsample. Our follow-up
~0.3"-1" resolution radio observations, for a subset of targets in this
luminosity range, reveal that radio jets and lobes are prevalent, and suggest
that compact jets might be responsible for the enhanced outflows in the wider
sample. Our results are limited by the available, relatively shallow, all-sky
radio surveys; however, forthcoming surveys will provide a more complete
picture on the connection between radio emission and outflows. Overall, our
results add to the growing body of evidence that there is a close connection
between ionised outflows and compact radio emission in highly accreting
`radiative' AGN, possibly due to young or frustrated, lower-power radio jets.
