After fixing the Higgs boson mass to the best fit value mh = 125 GeV, the SM does not have any free parameter left to vary. Therefore all the anomalies in the present data must be statistical fluctuations and disappear with more statistics. This interpretation is supported by the fact that the average of all data agrees with the SM prediction [...] and the global χ2 is good: 16 for 15 dof (we recall that with n>>1 degrees of freedom one expects χ2 = n+-sqrt(n) ).
On the other hand, our best fit [...] has a signicantly lower χ2 = 5.5 for 13 dof: a bigger reduction than what is typically obtained by adding two extra parameters (one expects Δχ2 = -Δn +- sqrt(Δn) when adding Δn >> 1 parameters). The SM is disfavoured at more than 95% CL in this particular context, but of course we added the two parameters that allow to fit the two most apparent anomalies in the data, the γγ excess and the WW* deficit.
Only more data will tell if this is a trend, or if we are just fitting a statistical fluctuation.
P.P. Giardino, K. Kannike, M. Raidal, and A. Strumia, "Reconstructing Higgs Boson Properties from the LHC and Tevatron Data", arxiv/1203.4254