We present a statistical analysis of the big blue bump (BBB) feature for a large heterogeneous sample of 95 optically selected and soft X-ray bright, low redshift active galactic nuclei (AGNs). This sample covers a sufficiently broad luminosity range, allowing us to test the luminosity dependence of the spectral energy distribution in the BBB region. Following the works of Zheng et al., Laor et al. and Kriss et al., we introduce the broad band spectral index from 1050 A to0.5 keV (α UV-SX ), compare its distribution with that of the soft X-ray spectral index (α SX ) obtained by ROSAT PSPC, and find that the two indices have equal average-values within 1 ∼ 2σuncertainties, whether in the whole sample, in luminosity divisions or in subsamples. These equalities also have no obvious luminosity dependence. This indicates that a single power law can describe the overall UV toX-ray spectrum in a statistical sense, or the broad band UV to soft X-ray spectrum is the soft X-ray spectral extension on an average. Thus, our results support Laor et al.'s conjecture about the BBB peak aroundFUV 1050 A from a statistical viewpoint. As we further test whether the equality holds for individual objects within measure errors, χ2 test refuse to accept it. In addition, our statistical results, from the luminosity divisions and on the correlation of spectral indices with luminosity (M B), imply that the luminosity dependence of α UV and α UV-SX is mainly due to absorption in low luminosity AGNs.