Discuss each of the following topics in class or review the topics on your own. Then write a brief but complete essay in which you summarize the main points. Please include formulas and graphs as appropriate.
1. (a) What do we mean by the term nonparametric statistics? What do we mean by the term parametric statistics? How do nonparametric methods differ from the methods we studied earlier?
(b) What are the advantages of nonparametric statistical methods? How can they be used in problems to which other methods we have learned would not apply?
(c) Are there disadvantages to nonparametric statistical methods? What do we mean when we say that nonparametric methods tend to waste information? Why do we say that nonparametric methods are not as sensitive as parametric methods?
(d) List three random variables from ordinary experience to which you think nonparametric methods would definitely apply and the application of parametric methods would be questionable.
2. Outline the basic logic and ideas behind the sign test. Describe how the binomial probability distribution was used in the construction of the sign test. What assumptions must be made about the sign test? Why is the sign test so extremely general in its possible applications? Why is it a special test for “before-and-after” studies?

3. Outline the basic logic and ideas behind the rank-sum test. Under what conditions would you use the rank-sum test and not the sign test? What assumptions must be made in order to use the rank-sum test? List two advantages the ranksum test has that the methods of Section 9.5 do not have. List some advantages the methods of Section 9.5 have that the rank-sum test does not have.
4. What do we mean by a monotone relationship between two variables x and y? What do we mean by ranked variables? Give a graphic example of two variables x and y that have a monotone relationship but do not have a linear relationship.
Does the Spearman test check for a monotone relationship or a linear relationship? Under what conditions does the Pearson product moment correlation coefficient reduce to the Spearman rank correlation coefficient? Summarize the basic logic and ideas behind the test for Spearman rank correlation. List variables x and y from daily experience for which you think a strong Spearman rank correlation coefficient exists, although the variables are not linearly related.
5. What do we mean by a runs test for randomness? What is a run in a sequence? How can we test for randomness about the median? Why is this an important concept? List at least three applications from your own experience.