In this paper, correlation coefficients between the five objective estimates of speech quality and the Speech Transmission Index were calculated. This comparison was performed using binaural room impulse responses corresponded to different points of the three university auditoriums of different sizes. Speech quality was assessed using intrusive speech quality measures: Segmental Signal-to-Noise Ratio, Logarithmic Spectral Distortion, Frequency-Weighted Segmental Signal-to-Noise Ratio, Perceptual Evaluation of Speech Quality, and Bark Spectral Distortion. The formation of signals distorted by reverberation was performed by convolving of pure signals with binaural room impulse responses of the premises. A high level of correlation (0.6-0.99) of Bark Spectral Distortion estimates with estimates of the Speech Transmission Index for rooms of different sizes was revealed. Correlation of estimates (0.65-0.98) of Frequency-Weighted Segmental Signal-to-Noise ratio with Speech Transmission Index estimates was observed for medium and large rooms. Significant correlation (0.96-0.99) of Perceptual Evaluation of Speech Quality with Speech Transmission Index estimates was observed only for large audiences. At the same time, estimates of the Segmental Signal-to-Noise Ratio and Logarithmic Spectral Distortion turned out to be practically uncorrelated with Speech Transmission Index estimates for all studied premises.