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  [NOT ON FALL 2015 EXAM]
    1. Several 2 X 2 Tables [NOT ON FALL 2015 EXAM]
    2. Test Statistic, Hypotheses, Decision Rules for each alternative [NOT ON FALL 2015 EXAM]
  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  [NOT ON FALL 2015 EXAM]
    1. When is it appropriate? [NOT ON FALL 2015 EXAM]
    2. Relationship to McNemar Test and Friedman/Quade Tests [NOT ON FALL 2015 EXAM]
    3. Test Statistic, Hypotheses, Decision Rule  [NOT ON FALL 2015 EXAM]

III. Other Topics
  A. Loglinear Models [NOT ON FALL 2015 EXAM]
    1. Method for analyzing three-way tables [NOT ON FALL 2015 EXAM]
    2. Types of dependence represented by interaction terms in model [NOT ON FALL 2015 EXAM]
    3. Interpretation via odds ratios [NOT ON FALL 2015 EXAM]
    4. Comparing potential models using chi-square tests [NOT ON FALL 2015 EXAM]
  B. Nonparametric Density Estimation
    1. Histograms
      a. Idea of bin width and its effect on estimated density curve
    2. Kernel Density Estimators 
      a. Smoothness property
      b. Weighted averaging of observations through use of kernel 
      c. Idea of bandwidth and its effect on estimated density curve