STAT 518 EXAM 2 REVIEW SHEET

I.  One-, Two-, and k-Sample Inference based on Ranks
  A. Definition of Ranks
    1. Why use ranks rather than actual data?
    2. Definition of midranks
  B. Wilcoxon Signed-Rank Test
    1. When is it appropriate?
    2. What parametric test is it analogous to?
    3. Assumptions of Signed-Rank Test
    4. How to Check Assumptions using Normal Q-Q plot
    5. Carrying Out the Wilcoxon Signed-Rank Test
      a. Differences, Absolute Differences, and Signed Ranks
      b. How to Calculate Test Statistic
      c. Null and alternative hypotheses of Signed-Rank test
      d. Test statistic and null distribution
      e. Decision Rules for each alternative
      f. P-values for each alternative
      g. Using Table A12
    6. Wilcoxon Signed-Rank Test for a Single sample
    7. Confidence Interval for the Median Difference
    8. Comparison of Signed-rank test to its Competitors
  C. Mann-Whitney Test
    1. When is it appropriate?
    2. What parametric test is it analogous to?
    3. Assumptions of M-W Test
    4. Carrying Out the M-W Test
      a. How to Calculate Test Statistic
      b. Null and alternative hypotheses of M-W test
      c. Test statistic and null distribution
      d. Decision Rules for each alternative
      e. P-values for each alternative
      f. Using Table A7
    5. Confidence Interval for the Difference between Two Means
    6. Comparison of M-W test to its Competitors
  D. Kruskal-Wallis Test
    1. When is it appropriate?
    2. What parametric test is it analogous to?
    3. Assumptions of K-W Test
    4. Carrying Out the K-W Test
      a. How to Calculate Test Statistic
      b. Null and alternative hypotheses of M-W test
      c. Test statistic and null distribution
      d. Decision Rule
      e. Using Table A2
    5. Multiple Comparisons
    6. Comparison of K-W test to its Competitors

II. Other Rank-based Tests
  A. Tests Comparing Variances
    1. Idea behind Talwar-Gentle Test
      a. Other options: Conover and Fligner-Killeen
      b. Comparison to parametric Competitors
      c. Test statistic and null distribution
      d. Decision Rules for each alternative
      e. Using Table A3
  B. Measures of Rank Correlation
    1. Basics of Correlation
    2. Pearson Correlation coefficient
    3. Spearman Correlation coefficient
      a. Testing for Independence Using Spearman's Rho
      b. Hypotheses, Decision Rules, P-values for each alternative
      c. Using Table A10
    4. Kendall's Tau Correlation measure
      a. Testing for Independence Using Kendall's Tau
      b. Definitions of Concordant and Discordant Pairs
      c. Hypotheses, Decision Rules, P-values for each alternative
      d. Using Table A11
    5. Daniels Test for Trend
    6. Comparison to parametric Competitors
    7. Kendall's Tau for measuring association for ordinal binary variables
  C. Distribution-Free Inference in Regression
    1. Simple Linear Regression Model
    2. Least Squares Method of estimation
    3. Distribution-Free Testing about the Slope
    4. Distribution-Free CI for the Slope
    5. Theil's Method of estimation
    6. Comparison to parametric Competitors

III. Other Nonparametric Methods
  A. Nonparametric regression
    1. Model for nonparametric regression 
    2. Advantages/disadvantages of nonparametric regression approach 
    3. Kernel Regression Estimators 
      a. Idea of local averaging within a window 
      b. Weighted averaging through use of kernel 
      c. Idea of bandwidth and its effect on estimated curve 
  B. Block Designs
    1. Extension of matched pairs to blocks
    2. Friedman's test to Compare Treatment Effects
      a. Assumptions of K-W Test
      b. Null and alternative hypotheses of K-W test
      c. Test statistic and null distribution
      d. Decision Rule, Using Table A22
      e. Multiple Comparisons
    3. Comparison of Friedman's test to its Competitors
      a. Quade Test, Page Test, classical F-test  [PAGE TEST NOT ON EXAM FOR FALL 2017]
  C. Randomization Tests
    1. Idea behind Fisher's Approach
    2. Randomization Test with Two Independent Samples
      a. Similar to which Rank-based test?
      b. Test statistic, null distribution, P-value for each alternative
      c. Approximating null distribution via simulation
    2. Randomization Test with Two Paired Samples
      a. Similar to which Rank-based test?
      b. Test statistic, null distribution, P-value for each alternative
      c. Approximating null distribution via simulation
      d. Performing Randomization Test with a Single Sample
    8. Comparison of Randomization tests to Rank-based and Classical Competitors
  D. The Rank Transformation [NOT ON EXAM FOR FALL 2017]
    1. Why replace raw data with ranks?  [NOT ON EXAM FOR FALL 2017]
    2. Rank-transforming in Multivariate Analyses  [NOT ON EXAM FOR FALL 2017]