New evidence very strongly favor a "normal" neutrino mass hierarchy over an "inverted" neutrino mass hierarchy. The inverted hierarchy is disfavored by this new evidence at a 93% confidence level.
This determination is reached using a methodology based upon the "coherent forward scattering of the neutrino beam with electrons in the Earth". This much more direct method of measuring the neutrino mass hierarchy is entirely independent of the other evidence strongly favoring a "normal" neutrino mass hierarchy over an inverted.
The other main method that is used to determine the neutrino mass hierarchy compares the estimated sum of the masses of the three neutrino mass eigenstates based upon cosmology observations to the minimum masses of the sum in the "normal" and "inverted" mass hierarchy cases based upon differences between the mass eigenstates inferred from neutrino oscillation data.
The most recent results using that methodology exclude an inverted hierarchy with a confidence level that ranges from 64% to 96% depending upon the assumptions made in estimating this probability.
The fact that two independent experimental methods both strongly favor the normal hierarchy over the inverted one, makes the combined conclusion from this experimental data, that the neutrino hierarchy is very likely to be "normal" rather than "inverted" much more robust, and probably exclude the inverted hierarchy at a 95% confidence level or more.
The abstract to the paper and the citation to the pre-print are as follows:
Results are reported from an improved measurement of νμ→νe transitions by the NOvA experiment. Using an exposure equivalent to 6.05×10^20 protons-on-target 33 νe candidates were observed with a background of 8.2±0.8 (syst.). Combined with the latest NOvA νμ disappearance data and external constraints from reactor experiments on sin^2(2θ13), the hypothesis of inverted mass hierarchy with θ23 in the lower octant is disfavored at greater than 93% C.L. for all values of δCP.P. Adamson, et al., "Constraints on oscillation parameters from νe appearance and νμ disappearance in NOvA" (March 9, 2017).
UPDATE March 13, 2017: Another study favors a normal over inverted hierarchy by a 42:1 ratio by combining cosmology and oscillation data. In more conventional terms, this is two-sigma evidence in favor of a normal hierarchy over an inverted one.