Increased importance is being placed on statistics at both the K-12 and undergraduate level. Research divulging effective methods to teach specific statistical concepts is still widely sought after. In this paper, we focus on best practices for teaching topics in nonparametric statistics at the undergraduate level. To motivate the work, we consider the problem of "n" rankings: "m" alternatives are fully ranked by a sample of "n" judges. Through this problem, we addresses how to teach nonparametric methods under a unifying framework that connects nonparametric methods to their parametric counterparts, utilizes basic techniques from linear algebra, and can empower students to make their own statistical tests.