Two statistics are proposed for testing the homogeneity of signals, when these are noisy and repeatedly recorded. The distribution of the statistics is well approximated by the $\chi^2$ and the normal distribution, respectively, as shown by theoretical and simulation results. Power and insensitivity to other types of variation are discussed. The approach is developed in the context of analysing recordings of electric brain potentials being evoked by some stimulation, as traditionally investigated in neurophysiology and psychophysiology. In particular, applications to visual potentials evoked by light flashes of a group of 41 children are given.