The ILL experiment, one of the "reactor anomaly" experiments, is re-examined. ILL's baseline of 8.78 m is the shortest of the reactor anomaly short baseline experiments, and it is the experiment that finds the largest fraction of the electron antineutrinos disappearing -about 20%. Previous analyses, if they do not ignore the ILL experiment, use functional forms for chisquare which are either totally new and unjustified, are the magnitude chisquare (also termed a "rate analysis"), or utilize a spectral form for chisquare which double counts the systematic error. We do an analysis which utilizes the standard, conventional form for chisquare as well as a derived functional form for a spectral chisquare. We find that when analyzed with a conventional chisquare that includes spectral information or with a spectral chisquare that is independent of the magnitude of the flux, the results are a set of specific values for possible mass-squared differences of the fourth neutrino and where the minimum chisquare difference values are significantly enhanced over previous analyses of the ILL experiment. For the Huber flux and the conventional chisquare, the two most preferred values are mass-squared differences of 0.90 and 2.36 eV 2 preferred at ∆χ 2 min values of -12.1 and -13.0 (3.5 and 3.6 σ), respectively. For the Daya Bay flux and conventional chisquare we find 0.95 and 2.36 eV 2 preferred at ∆χ 2 min of -8.22 and -9.45 (2.9 and 3.1 σ), respectively. For the spectral chisquare and either flux these values are 0.95 and 2.36 eV 2 preferred at ∆χ 2 min of -10.5 and -11.7(3.2 and 3.4 σ), respectively. These are to be compared to -4.4 (2.1 σ) found in the original reactor anomaly anaysis for all of the experiments excepting the ILL experiment.