ABSTRACT We use new 144 MHz observations over 5634 deg2 from the LOFAR (Low Frequency Array) Two-metre Sky Survey (LoTSS) to compile the largest sample of uniformly selected, spectroscopically confirmed quasars from the 14th data release of the Sloan Digital Sky Survey (SDSS-DR14). Using the classical definition of radio loudness, R = log (L1.4GHz/Li), we identify 3697 radio-loud (RL) and 111 132 radio-quiet (RQ) sources at 0.6 < z < 3.4. To study their properties, we develop a new rest-frame spectral stacking algorithm, designed with forthcoming massively multiplexed spectroscopic surveys in mind, and use it to create high signal-to-noise composite spectra of each class, matched in redshift and absolute i-band magnitude. We show that RL quasars have redder continuum and enhanced [O ii] emission than their RQ counterparts. These results persist when additionally matching in black hole mass, suggesting that this parameter is not the defining factor in making a quasi-stellar object (QSO) RL. We find that these features are not gradually varying as a function of radio loudness, but are maintained even when probing deeper into the RQ population, indicating that a clear-cut division in radio loudness is not apparent. Upon examining the star formation rates (SFRs) inferred from the [O ii] emission line, with the contribution from active galactic nucleus removed using the [Ne v] line, we find that RL quasars have a significant excess of star formation relative to RQ quasars out to z = 1.9 at least. Given our findings, we suggest that RL sources either preferably reside in gas-rich systems with rapidly spinning black holes, or represent an earlier obscured phase of QSO evolution.