STAT 705 FINAL EXAM REVIEW SHEET

(The final exam will include new material and questions from Exam 1 
and Exam 2 material.  Also study the review sheets for Exams 1 and 2.)

MORE LINEAR MODELS
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I. Analysis of Advanced Designs

  A. Latin Square Designs
    1. When do we need a Latin Square Design?
      a. Row factor and column factor
    2. Properties of a Latin Square
    3. Advantages and disadvantages of a Latin Square
    4. Randomization Scheme for Latin Square Design
    5. Model for Latin Square
    6. ANOVA Table for Latin Square
    7. Inference (F-tests, Multiple Comparisons, etc.) and Diagnostics
  B. Repeated Measures Designs
    1. When is this appropriate?
    2. Role of subjects in the model
    3. Assumptions about variances and covariances for Y-values
      a. "Compound symmetry" assumption
      b. How can we check this? 
    4. Analysis (ANOVA table, F-tests)
 C. Analysis of Covariance
    1. In what situation is the ANCOVA approach used?
    2. Role of the Covariate in the ANCOVA model
      a. Principles for Choosing the Covariate
      b. "Symbolic Scatter Plot"
      c. Why / why not use ANCOVA instead of blocks?
    3. Single-Factor ANCOVA model
      a. Meaning of the (differences between) Treatment Effects
      b. F-test for significant treatment effects
      c. Test for significant covariate effect
    4. Diagnostic Plots
    5. Testing for Unequal Slopes in the ANCOVA model
      a. Role of Interaction Terms

II. Piecewise Regression
  A. Meaning of changepoint
  B. Two-Piece Continuous Piecewise Regression Model
    1. Mean response function at each piece
    2. Testing whether piecewise regression is needed
    3. Interpretation of estimated coefficients
  C. Multi-Piece Continuous Piecewise Regression Model
  D. Two-Piece Discontinuous Piecewise Regression Model
    1. Mean response function at each piece
    2. Testing whether discontinuous function is needed

III. Nested Designs
  A. Meaning of Nested Factors (as opposed to Crossed Factors)
  B. Notation and Model for Nested Design
  C. ANOVA table for Nested Design
    1. F-tests for Factor A and for Factor B(A)
    2. Partition of SSB(A) into components
  D. Diagnostic Plots
  E. Further Analysis of Treatment Means

DISTRIBUTION-FREE ALTERNATIVES IN ANOVA
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I.  Kruskal-Wallis Test
  A. When is it needed?
  B. Model for Data
  C. Hypotheses for K-W Test
  D. Procedure to Calculate Ranks and Test Statistic
  E. Bonferroni Multiple Comparisons
II. Friedman Test
  A. When is it needed?
  B. Model for Data
  C. Hypotheses for Friedman Test
  D. Procedure to Calculate Ranks and Test Statistic
  E. Similar Tests and Relationships to Other Tests

CATEGORICAL DATA ANALYSES
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I. One-Way Tables
  A. Summarizing Categorical Data with Contingency Table
  B. Modeling Success Counts with Binomial
  C. Inference about Binomial Probability pi
    1. Sampling distribution of pi-hat
    2. CI for pi (Wald & score)
    3. z-test about pi
    4. Large-sample checks
    5. Small-sample alternative
  D. Chi-square goodness-of-fit Test (1 by c table)
    1. Calculating Observed and expected counts
    2. Test statistic and its null distribution
    3. Large-sample checks
II. Two-Way Tables
  A. Comparing Two Proportions (Independent Samples)
    1. Representation as 2 by 2 table
    2. Sampling distribution of (pi_1-hat - pi_2-hat)
    3. CI for difference of two proportions
    4. z-test to compare two proportions
    5. Large-sample checks
  B. Small-sample Alternative:  Fisher's Exact Test
    1. Assumptions of test
    2. Rationale behind P-value
    3. Odds ratio
  C. Comparing Two Proportions (Paired Samples)
    1. Difference between paired and independent samples
    2. Test statistic for McNemar's Test
    3. McNemar-type CI for (pi_1 - pi_2)
    4. Large-sample checks
    5. Small-sample alternative
  D. Chi-square Test for Independence (r by c table)
    1. Model for Cell Counts
    2. Structure of table of cell counts and of cell probabilities
    3. Calculating Observed and expected counts
    4. Test statistic and its null distribution
    5. Large-sample checks
    6. Small-sample alternative
  E. Chi-square Test for Homogeneity (r by c table)
    1. Difference in sampling process compared to test for independence
    2. Difference in hypotheses compared to test for independence
    3. Large-sample checks
    4. Small-sample alternative