In this paper, we investigate the dynamical properties of electroencephalogram (EEG) signals of humans in sleep. By using a modified random walk method, we demonstrate that scale-invariance is embedded in EEG signals after a detrending procedure is applied. Furthermore, we study the dynamical evolution of the probability density function (PDF) of the detrended EEG signals by nonextensive statistical modeling. It displays a scale-independent property, which is markedly different from the usual scale-dependent PDF evolution and cannot be described by the Fokker-Planck equation.