STAT 518 FINAL EXAM REVIEW SHEET

I.  Goodness-of-Fit Tests
  A. Kolmogorov Test
    1. Empirical distribution function
    2. Test statistics T, T+, T- and null distribution
    3. Decision Rules for each alternative
    4. Confidence Band for True Population c.d.f.
    5. Properties of Kolmogorov test
  B. Lilliefors Test
    1. When is it appropriate?
    2. Test for normality
      a. Test statistic and decision rule
    3. Test for exponential distribution
      a. Test statistic and decision rule
  C. Smirnov Test
    1. When is it appropriate?
    2. Test statistics T1, T1+, T1- 
    3. Three possible sets of hypotheses
    4. Decision Rules for each alternative
    5. Comparison of Smirnov Test to M-W test

II. Contingency Tables
  A. Chi-square Goodness-of-Fit Test
    1. One-Way Table
    2. Test statistic, null distribution, and decision rule
    3. Rule of Thumb for validity of large-sample test
    4. Chi-square Goodness-of-Fit Test with Unknown Parameters
      a. Adjusting the degrees of Freedom
    5. Testing Goodness-of-Fit with discrete distributions
    6. Testing Goodness-of-Fit with continuous distributions
  B. Z-test to Compare Two Probabilities
    1. Test statistic to compare p1 and p2
    2. Three possible sets of hypotheses
    3. Decision Rules for each alternative
    4. Fisher's Exact Test with 2 X 2 Tables
      a. Fixed Marginal Totals as opposed to random marginal totals
      b. Finding P-values depending on the alternative hypothesis
      c. Fisher's Exact Test as a small-sample alternative to the Z-test
  C. Mantel-Haenszel Test 
    1. Several 2 X 2 Tables 
    2. Test Statistic, Hypotheses, Decision Rules for each alternative
  D. Tests for r X c Tables
    1. Two Types of sampling schemes
    2. Test for Homogeneity:   Comparing Multinomial Probabilities
      a. Test Statistic, Hypotheses, Decision Rule
      b. Rule of Thumb for validity of large-sample test
    3. Test for Independence:  Testing for association between categorical variables
      a. Test Statistic, Hypotheses, Decision Rule
      b. Random Row Totals and Column Totals
    4. Fisher's Exact Test with r X c Tables
  E. Median Test 
    1. When is it appropriate?
    2. Creating the 2 X c table
    3. Test Statistic, Hypotheses, Decision Rule 
    4. Comparison of Median Test to ANOVA F-test
  F. Measures of Dependence for Contingency Tables
    1. Use of Chi-square test statistic T to measure dependence
    2. Cramer's Contingency Coefficient
      a. Interpretation (strength of association)
    3. Phi Coefficient
      a. When is it appropriate?
      b. Interpretation (strength and type of association)
  E. Cochran's Test 
    1. When is it appropriate?
    2. Relationship to McNemar Test and Friedman/Quade Tests
    3. Test Statistic, Hypotheses, Decision Rule 

III. Other Topics
  A. Loglinear Models
    1. Method for analyzing three-way tables
    2. Types of dependence represented by interaction terms in model
    3. Interpretation via odds ratios
    4. Comparing potential models using chi-square tests
  B. Nonparametric Density Estimation [NOT ON FALL 2017 FINAL EXAM]
    1. Histograms [NOT ON FALL 2017 FINAL EXAM]
      a. Idea of bin width and its effect on estimated density curve [NOT ON FALL 2017 FINAL EXAM]
    2. Kernel Density Estimators [NOT ON FALL 2017 FINAL EXAM]
      a. Smoothness property [NOT ON FALL 2017 FINAL EXAM]
      b. Weighted averaging of observations through use of kernel [NOT ON FALL 2017 FINAL EXAM]
      c. Idea of bandwidth and its effect on estimated density curve [NOT ON FALL 2017 FINAL EXAM]