Variability of spectral estimates is examined with respect to the nonlinearity of the wave field considered. Both measured field data and numerical simulations are used for checking the extent of variations, which are quantified as histograms that closely follow the chi-square distribution. An absolute assessment of the variations over the entire frequency band of a spectrum is also made and found to approach to a mean of 70% regardless of the frequency concerned. Finally, it is observed that a nonlinearly evolving wave field of initially constant spectral shape, assumes a spectral variability, which is characterized by the chi-square distribution. The last finding provides a clue for a possible cause of the variations observed in the estimates of spectra.