Accidental coincidences (ACs) and methods of compensation for ACs were investigated in terms of their effect on quantitation in positron emission computed tomography (ECT). Formulations of basic expressions describing the physical factors, which cause true coincidences or ACs, are presented to provide a framework of contrasting the two phenomena. Correction of image data for attenuation of the annihilation radiation or nonuniformities in detector efficiency is shown to amplify errors caused by the presence of ACs in the data. It was shown that failure to compensate for ACs caused overestimates in measurements of isotope concentrations from image data and that in many cases the overestimate was significant for relatively modest percentages of ACs in the data. Three methods of compensation for ACs were evaluated as to their accuracy and effect on statistical noise in images. It was found that nonuniform detector efficiencies could cause prominent image artifacts if an inadequate method was employed in the determination and subtraction of ACs from image data. The additional statistical noise produced in images by subtraction of ACs from total coincidence data demonstrates the advisability of minimizing AC rates in spite of an ability to adequately measure and compensate for their presence in the data.