Serial femtosecond crystallography (SFX) is an emerging method for data collection at free-electron lasers (FELs) in which single diffraction snapshots are taken from a large number of crystals. The partial intensities collected in this way are then combined in a scheme called Monte Carlo integration, which provides the full diffraction intensities. However, apart from having to perform this merging, the Monte Carlo integration must also average out all variations in crystal quality, crystal size, X-ray beam properties and other factors, necessitating data collection from thousands of crystals. Because the pulses provided by FELs running in the typical self-amplified spontaneous emission (SASE) mode of operation have very irregular, spiky spectra that vary strongly from pulse to pulse, it has been suggested that this is an important source of variation contributing to inaccuracies in the intensities, and that, by using monochromatic pulses produced through a process called self-seeding, fewer images might be needed for Monte Carlo integration to converge, resulting in more accurate data. This paper reports the results of two experiments performed at the Linac Coherent Light Source in which data collected in both SASE and self-seeded mode were compared. Importantly, no improvement attributable to the use of self-seeding was detected. In addition, other possible sources of variation that affect SFX data quality were investigated, such as crystal-to-crystal variations reflected in the unit-cell parameters; however, these factors were found to have no influence on data quality either. Possibly, there is another source of variation as yet undetected that affects SFX data quality much more than any of the factors investigated here.