We analyze a series of full-Sun observations performed with the SoHO/SUMER instrument between March and October 1996. Some parameters (radiance, shift and width) of the S vi 93.3 nm , S vi 94.4 nm , and Ly \varepsilon line profiles were computed on board. Radiances and line-of-sight velocities in a large central region of the Sun are studied statistically: distributions of solar structures, field Fourier spectra and structure functions are obtained. The structures have distributions with power-law tails, the Fourier spectra of the radiance fields also display power laws, and the normalized structure functions of the radiance and velocity fields increase at small scales. These results support the idea of the existence of small scales, created by turbulence, and of intermittency of the observed fields. These properties may provide insight into the processes needed for heating the transition region, or, if confirmed in the corona, the corona itself. The difficulties encountered in this analysis, especially for the velocity data, underline the need for sensitive ultraviolet imaging spectrometers.