Mutually contradicting previously reported theoretical results on the effects of a dispersive active medium in a ring laser on its sensitivity to rotation are critically analyzed. A measure of the rotation rate in the active ring resonator is the beating frequency ∆ν between the counterpropagating waves whose frequencies are shifted in opposite directions due to the Sagnac effect. ∆ν is shown to be inversely proportional to the group index of the medium filling the cavity. A comparison of the results obtained considering the resting and rotating frames confirms the applicability of Fresnel's original expression for the optical drag effect to the analysis of the Sagnac effect in an active laser gyro. The frequency splitting ∆ν is sensitive to dispersion via the group refractive index.