Comments on the Statistical Analysis of Excess Variance in the COBE Differential Microwave Radiometer Maps

Cosmic anisotropy produces an excess variance σ_sky_^2^ in the {DELTA}T maps produced by the Differential Microwave Radiometer (DMR) on CO8E that is over and above the instrument noise. After smoothing to an effective resolution of 10^deg^, this excess, σ_sky_(10^deg^), provides an estimate for the amplitude of the primordial density perturbation power spectrum with a cosmic uncertainty of only 12%. We employ detailed Monte Carlo techniques to express the amplitude derived from this statistic in terms of the universal rms quadrupole amplitude, <Q_RMS_^2^>^0.5^. The effects of monopole and dipole subtraction and the non-Gaussian shape of the DMR beam cause the derived <Q_RMS_^2^>^0.5^ to be 5%-10% larger than would be derived using simplified analytic approximations. We also investigate the properties of two other map statistics: the actual quadrupole and the Boughn-Cottingham statistic. Both the σ_sky_(10^deg^) statistic and the Boughn-Cottingham statistic are consistent with the <Q_RMS_^2^>^0.5^ = 17 +/- 5 microK reported by Smoot et al. (1992) and Wright et al. (1992).