Medical Image Quality Assessment (IQA) plays an important role in assisting and evaluating the development of any new hardware, imaging sequences, pre-processing or post-processing algorithms. We have performed a quantitative analysis of the correlation between subjective and objective Full Reference - IQA (FR-IQA) on Magnetic Resonance (MR) images of the human brain, spine, knee and abdomen. We have created a MR image database that consists of 25 original reference images and 750 distorted images. The reference images were distorted with six types of distortions: Rician Noise, Gaussian White Noise, Gaussian Blur, DCT compression, JPEG compression and JPEG2000 compression, at various levels of distortion. Twenty eight subjects were chosen to evaluate the images resulting in a total of 21,700 human evaluations. The raw scores were then converted to Difference Mean Opinion Score (DMOS). Thirteen objective FR-IQA metrics were used to determine the validity of the subjective DMOS. The results indicate a high correlation between the subjective and objective assessment of the MR images. The Noise Quality Measurement (NQM) has the highest correlation with DMOS, where the mean Pearson Linear Correlation Coefficient (PLCC) and Spearman Rank Order Correlation Coefficient (SROCC) are 0.936 and 0.938 respectively. The Universal Quality Index (UQI) has the lowest correlation with DMOS, where the mean PLCC and SROCC are 0.807 and 0.815 respectively. Student's T-test was used to find the difference in performance of FR-IQA across different types of distortion. The superior IQAs tested statistically are UQI for Rician noise images, Visual Information Fidelity (VIF) for Gaussian blur images, NQM for both DCT and JPEG compressed images, Peak Signal-to-Noise Ratio (PSNR) for JPEG2000 compressed images.