Effects of inaccurate attenuation correction on quantitation in positron emission computed tomography were investigated by both computer simulation and theoretical analysis, followed by experimental verification with phantom measurements. It was found that, due to the finite width of detector responses, compensation of scan measurements by measured attenuation correction factors does not completely correct for attenuation. For FWHM greater than 1.8 cm, errors in object size and in activity levels of reconstructed images are more than 4%. Mismatches between true and assumed attenuation media are found to give large errors. These mismatches include object shift, incorrect size and shape, uniform and nonuniform mismatches in attenuation coefficients, and nonzero background levels. Errors as large as 14% in the reconstructed activity level can be introduced by a 5 mm shift in object position. A 5% error in the cylinder diameter can give differences between the total reconstructed activity and true value more than 12%. Strong image distortions, which could lead to incorrect interpretations of images are created by object shift and by nonuniform mismatches in attenuation coefficient. It was also found that statistical noise in measured attenuation correction factors can significantly increase noise levels in images, resulting in lower effective total counts for the emission scan. Effective total counts can be estimated as Neff = kNxmNem/(Nem + kNxm), where Nem and Nxm are total counts in emission and transmission scans, and k is a scanner dependent factor, which accounts for configuration differences.