This is a rather common belief among amateur radio operators, but is it true? A NEC analysis provides some insight on this concept.
Below is a NEC4.2 study comparing the fields radiated by an eighth-wave, series-fed vertical monopole driven against sets of thirty buried radials of 1/4 and 1/8 wavelength (other things equal).
The X axis shows field intensity (E), and the Y axis shows elevation (Z) above a flat Earth ground plane, at a horizontal distance of 100 meters from the base of the monopole.
The antenna system with 1/4-wave radial lengths generates a maximum field intensity 12.5% greater than the system with 1/8-wave radials.
The corresponding improvement in radiated power is 1.125² x 100% = 26.6% (approximately).
The increased radiation efficiency is the result of collecting more of the r-f currents flowing on and below the surface of the earth within a 1/2-wavelength radius from the base of the monopole, as a result of its radiation. The r-f resistance of the set of buried radials is a series circuit element whose I^2R loss reduces the r-f current that flows along the monopole, itself.