We present a deep study of the Neutrino-4 data aimed at finding the statistical significance of the large-mixing short-baseline neutrino oscillation signal claimed by the Neutrino-4 collaboration at more than 3σ. We found that the results of the Neutrino-4 collaboration can be reproduced approximately only by neglecting the effects of the energy resolution of the detector. Including these effects, we found that the best fit is obtained for a mixing that is even larger, close to maximal, but the statistical significance of the short-baseline neutrino oscillation signal is only about 2.7σ if evaluated with the usual method based on Wilks' theorem. We show that the large Neutrino-4 mixing is in strong tension with the KATRIN, PROSPECT, STEREO, and solar νe bounds. Using a more reliable Monte Carlo simulation of a large set of Neutrino-4-like data, we found that the statistical significance of the Neutrino-4 short-baseline neutrino oscillation signal decreases to about 2.2σ. We also show that it is not unlikely to find a best-fit point that has a large mixing, even maximal, in the absence of oscillations. Therefore, we conclude that the claimed Neutrino-4 indication in favor of short-baseline neutrino oscillations with very large mixing is rather doubtful.