  We examine how dark energy constraints from current observational data depend
on the analysis methods used: the analysis of Type Ia supernovae (SNe Ia), and
that of galaxy clustering data. We generalize the flux-averaging analysis
method of SNe Ia to allow correlated errors of SNe Ia, in order to reduce the
systematic bias due to weak lensing of SNe Ia. We find that flux-averaging
leads to larger errors on dark energy and cosmological parameters if only SN Ia
data are used. When SN Ia data (the latest compilation by the SNLS team) are
combined with WMAP 7 year results (in terms of our Gaussian fits to the
probability distributions of the CMB shift parameters), the latest Hubble
constant (H_0) measurement using the Hubble Space Telescope (HST), and gamma
ray burst (GRB) data, flux-averaging of SNe Ia increases the concordance with
other data, and leads to significantly tighter constraints on the dark energy
density at z=1, and the cosmic curvature \Omega_k. The galaxy clustering
measurements of H(z=0.35)r_s(z_d) and r_s(z_d)/D_A(z=0.35) (where H(z) is the
Hubble parameter, D_A(z) is the angular diameter distance, and r_s(z_d) is the
sound horizon at the drag epoch) by Chuang & Wang (2011) are consistent with SN
Ia data, given the same pirors (CMB+H_0+GRB), and lead to significantly
improved dark energy constraints when combined. Current data are fully
consistent with a cosmological constant and a flat universe.
