In order to solve the problems that the averaging time of Allan variance can only reach half of total data length, and confidence at long averaging time is lower, according to the random errors properties of the optic gyroscope at time and frequency domains, a new method for analyzing the random error properties of the optic gyroscope based on theoretical variance #1 is proposed. By comparing the performance of the Allan and theoretical variance #1, identifying the noise types and noise levels, applying Allan variance and theoretical variance #1 methods, it is shown that the values of the theoretical variance #1 are consistent with the power law noises in estimating long-term τ-values, which improves the confidence efficiently and has higher evaluation precision than the conventional Allan method.