To investigate the statistical errors inherent in this classical process and its influence on PSDT measurements， based on the perturbation technique， the mean and variance of the quotient of the random variables are approximately expressed with the application of the statistical moment method. Then， the statistical moments of two response spectral estimates are substituted to derive the formulae for the mean and variance of the PSDT’s amplitude regarding the coherence function of the response and the number of averaging segments in spectrum analysis. Based on this， the error law in the amplitude of the PSDT estimate at the resonance frequency is revealed to quantify the estimation error of the mode shape. It is found that the error in the PSDT’s amplitude estimate at the resonances tends to a local minimum value， and the coefficient of variation is smaller than the counterparts of two associated response power spectrum densities. Finally， the accuracy of the derived error formulation in the paper is verified by vibration data from one numerical frame. Moreover， a parameter study regarding the influence of the selection of reference response， the time duration of measurements， and the type of window function on the PSDT and mode shape estimates is performed. The results show that using two basic responses of PSDT as the reference responses is beneficial to reduce the error in PSDT estimates and outcomes of modal analysis， and the standard variance of the estimate also decreases with the increasing time duration of measurements and finally to a specific limit.