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The time and polarization resolved ultrasonic technique which we previously developed has been demonstrated to simultaneously provide measurements of the wave velocity in the coupling liquid, and the leaky surface wave and leaky longitudinal wave velocities in solid samples. To document the measurement precision associated with this technique, a statistical method is employed for the data fit and error analysis. With the help of statistical analysis, the simple ray model used to determine wave velocities in this technique is first confirmed by theoretical data which are predicted by the Green's function. Error analysis is then applied to the experimental data. The results show that this technique has a relative expanded uncertainty (equal to twice the standard deviation) of 0.03% for the wave velocity in water, and an uncertainty less than 0.2% and 2%, respectively, for the leaky surface and leaky longitudinal wave velocities in a crown glass sample. The uncertainty in the repeatability for leaky surface wave measurements is observed to be much less than the expanded uncertainty of a single measurement set. This methodology also has been applied to a set of steel samples. The results allow that the expanded uncertainty for leaky surface wave velocities is less than 0.07%, enabling a correlation of the measured velocities with specific sample heat treatments.