We determine the gas-phase oxygen abundance for a sample of 695 galaxies and H II regions with reliable detections of [O III]4363, using the temperature-sensitive Te method. Our aims are to estimate the validity of empirical methods such as R23, R23-P, log([N II]/Halpha) (N2), log[([O III]/Hbeta)/([N II]/Halpha)] (O3N2), and log([S II]/Halpha) (S2), and especially to re-derive (or add) the calibrations of R23, N2, O3N2 and S2 indices for oxygen abundances on the basis of this large sample of galaxies with Te-based abundances. We select 531 star-forming galaxies from the SDSS-DR4, and 164 galaxies and H II regions from literature for such study. Their (O/H) abundances obtained from Te are within 7.1<12+log(O/H)<8.5 mostly. For roughly half of the SDSS samples, the Bayesian abundances obtained by the MPA/JHU group are overestimated by ~0.34 dex compared with the Te-based (O/H) measurements, possibly due to the treatment of nitrogen enrichment in the models they used. R23 and R23-P methods systematically overestimate the O/H abundance by a factor of ~0.20 dex and ~0.06 dex, respectively. The N2 index, rather than the O3N2 index, provides relatively consistent O/H abundances with the Te-method, but with some scatter. The relations of N2, O3N2, S2 with log(O/H) are consistent with the photoionization model calculations of Kewley & Doptita (2002), but R23 does not match well. Then we derive analytical calibrations for O/H from R23, N2, O3N2 and S2 indices on the basis of this large sample of galaxies, especially including the excitation parameter P as an additional parameter in the N2 calibration. These can be used as calibration references in the future studies about metallicities of galaxies.
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