Preterm birth is a major contributor to infant mortality worldwide. Cervical length and previous history of preterm birth are the only two indicators which can help in identifying preterm birth but have a low positive identifying rate. Quantitative ultrasound parameters like attenuation can provide additional details about the tissue microstructure besides the diagnostic image. Attenuation can be used to detect preterm cases as the attenuation decreases with the increasing gestation age and this decrease can be seen earlier in cases of preterm birth. The algorithm and the size of the region of interest (ROI) play a vital role in calculating valid estimates of attenuation. In this paper, we compared the ability of the Spectral log difference algorithm and the Spectral difference algorithm to detect changes in the cervix leading to delivery for both full term and preterm births under varying ROI sizes. Spectral log difference yields a more consistent decrease in the attenuation as we approach delivery for both the preterm and full term patients. ROI size doesn't significantly alter the observed trends for this study. For preterm birth a maximum decreases of 0.35dB/cm-MHz was observed. The bias in attenuation algorithms can be removed by selecting homogenous regions inside the cervix, but the cervix is a heterogeneous tissue. Gamma mixture model is used to segment the cervix into different tissue types and attenuation algorithm are then applied to individual tissue type to get an estimate of attenuation. The area under the receiver operating characteristic curve increases from 56% to 80% when gamma mixture model is used for segmentation.