I have performed a study where 50 patients underwent a computerized tomography (CT) scan. Each scan was reconstructed using 3 different algorithms (no noise reduction, medium noise reduction, high noise reduction). These reconstruction algorithms create noise reduction which is an issue when trying to reduce radiation dose. Since all 50 patients had 3 reconstruction, there were 150 studies total. These studies were then anonymized and randomized. 8 separate radiologists then read each study and graded them on a Likert scale of 1-5 (1-awful, 5-ideal) for numerous qualitative categories including diagnostic confidence, perceived image noise, perceived contrast enhancement, and perceived image artifacts. I want to compare the readers scores between the different reconstructions. For instance, does the high noise reduction algorithm lead to improved diagnostic confidence compared to the other reconstructions. Also, in general, most studies were subjectively graded as either a 4 or 5, leading to negatively skewed data. So long story short, what test would you recommend for analyzing this data. I am thinking a Friedman test. Is this correct? If so, would you run a post-test of any kind. Any help would be great appreciated.