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We perform the first statistical combined analysis of the diffuse neutrinoflux observed by ANTARES (nine-year) and IceCube (six-year) by assuming asingle astrophysical power-law flux. The combined analysis reduces by a fewpercent 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-fittest to scrutinize the null assumption of a single power-law, scanningdifferent values for the spectral index. The addition of the ANTARES datareduces the $p$-value by a factor 2$\div$3. In particular, a single power-lawcomponent in the neutrino flux with the spectral index deduced by the six-yearup-going muon neutrinos of IceCube is disfavored with a $p$-value smaller than$10^{-2}$.

Use of ANTARES and IceCube data to constrain a single power-law neutrino flux