1. A radiation oncologist is looking at the potential for a new radiation therapy treatment to reduce the size of tumors. She carries out PET scans of 50 patients prior to treatment and rescans each of them after two months of intensive treatment. From each scan, she classifies the tumor in the following way: 1 = early stage (small and contained), 2 = progressing (larger and beginning to extend along axon pathways), 3 = invasive (large with many extensions), and 4 = integrated (very large, with growth clusters in multiple brain regions). 
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3. Following treatment, she finds that the integrated tumors were reduced, such that she classified them in the progressing category (she finds the median post-treatment classification to be 2). She concludes from this that radiation therapy cuts the size of integrated tumors in half. From a statistical standpoint, is this a valid conclusion? Why or why not?