The ultrasonic attenuation coefficient (ACE) can be used to classify tissue state. Pulse-echo spectral-based attenuation estimation techniques, such as the spectral-log-difference method (SLD), account for beam diffraction effects using a reference phantom having a sound speed close to the sound speed of the sample. Methods like SLD assume linear propagation of ultrasound and do not account for potential acoustic nonlinear distortion of the backscattered power spectra in both sample and reference. In this study, the ACE of a sample was computed and compared using the SLD with two independent references (high attenuating and low attenuating phantoms but with similar B/A values) and over several pressure levels. Both numerical and physical tissue-mimicking phantoms were used in the study. The results indicated that the biases in ACE increased when using a reference having low attenuation, whereas the high attenuating reference produced more consistent ACE. Furthermore, increments in ACE vs input pressure were correlated to the log-ratio of Gol'dberg numbers between the sample and reference (R2=0.979 in simulations and R2=0.734 in experiments). Therefore, the results suggest that to reduce bias in ACE using spectral-based methods, both the sound speed and the Gol'dberg number of the reference phantom should be matched to the sample.