  We perform the first statistical combined analysis of the diffuse neutrino
flux observed by ANTARES (nine-year) and IceCube (six-year) by assuming a
single astrophysical power-law flux. The combined analysis reduces by a few
percent the best-fit values for the flux normalization and the spectral index.
Both data samples show an excess in the same energy range (40--200 TeV),
suggesting the presence of a second component. We perform a goodness-of-fit
test to scrutinize the null assumption of a single power-law, scanning
different values for the spectral index. The addition of the ANTARES data
reduces the $p$-value by a factor 2$\div$3. In particular, a single power-law
component in the neutrino flux with the spectral index deduced by the six-year
up-going muon neutrinos of IceCube is disfavored with a $p$-value smaller than
$10^{-2}$.
