In the clinical setting, image quality is most commonly evaluated by the visual observation of images of test objects and/or phantoms. Because of the uncertainties in such results (either large variance or bias or both), more precise quantitative measures based on statistical decision theory should be investigated. A series of simulations and experiments were conducted to investigate the statistical properties, i.e., the bias and variance, of the estimate of the square of the SNR of the 'ideal' observer (SNRPWMF). Several methods of bias reduction were compared including one due to Fukunaga and Hayes. Good agreement was obtained between the results of simulations and the theoretical predictions for the bias and variance. The different methods of bias reduction have the same applicability for both 'ideal' and 'quasi-ideal' observers for the series of SKE/BKE tasks investigated in the present study. This work also provides some new avenues for additional investigation. First, the techniques can lead to protocols for making the evaluation of imaging system performance with a limited number of sample images, which is an important issue for any clinical implementation. Second, since selective spatial frequency channels can be used in estimating the SNRPWMF, the method has potential utility for imaging tasks beyond SKE/BKE tasks such as those with clinically relevant backgrounds but possessing stationary statistics.