We study the radio–far-infrared (FIR) correlation in a sample of faint dwarf irregular galaxies using NRAO VLA Sky Survey (NVSS) data for 1.4-GHz radio flux, Spitzer Multiband Imaging Photometer (MIPS) 70-μm data for FIR flux and GALEX far-ultraviolet data to estimate the star formation rates (SFRs). Since our target galaxies are extremely faint, we stack images of many galaxies together to estimate the average radio and FIR fluxes. We find that for a given SFR both 70-μm and 1.4-GHz fluxes are low compared to the calibration for large spirals. None the less, the ratio of 70 μm to 1.4 GHz flux agrees within error bars with that seen for large galaxies. The radio–FIR correlation thus appears to be the result of a ‘conspiracy’. We use the SFR to estimate the non-thermal fraction of the 1.4-GHz radio emission and find it to be around 50 per cent, much smaller than the 90 per cent typical for spirals. We also estimate the equipartition magnetic field and find it to be ∼2 μG, about five times smaller than that typical for spirals.