STAT 518 EXAM 1 REVIEW SHEET

I.  Basic Inference
  A. Population and Sample
    1. Definition of Random Sample
    2. Multivariate Data
  B. Measurement Scales
    1. Nominal Scale
    2. Ordinal Scale
    3. Interval Scale
    4. Ratio Scale
  C. Estimation
    1. Parameters and Statistics
    2. Order Statistics
    3. Sample mean, sample variance, sample standard deviation
    4. Cumulative distribution function
    5. Empirical distribution function
    6. Bootstrap method
  D. Hypothesis Testing
    1. Null and alternative hypothesis
    2. Test statistic
    3. Decision rule and critical region
      a. One-tailed test
      b. Two-tailed test
    4. Simple and composite hypotheses
    5. Type I and Type II errors
    6. P-values
      a. Lower-tailed
      b. Upper-tailed
      c. Two-tailed 
  E. Properties of Hypothesis Tests
    1. Assumptions of Test
    2. Power Function
      a. Finding Power for a simple null and a simple alternative
    3. Significance Level
    4. Unbiasedness and Consistency
    5. Relative Efficiency and A.R.E.
    6. Actual Significance Level vs. Nominal Significance Level
      a. Conservative test
  F. Nonparametric Statistical Methods
    1. Robust methods
    2. Performance of parametric methods
      a. When do they perform well?
      b. When do they perform poorly?
    3. Definition of Nonparametric Method

II. Tests Based on the Binomial Distribution
  A. The Binomial Test
    1. Definition of Binomial Experiment
    2. Null and alternative hypotheses of binomial test
    3. Test statistic and null distribution
    4. Decision Rules for each alternative
    5. P-values for each alternative
    6. Using Table A3
  B. Interval Estimation of p
    1. Idea behind Clopper-Pearson CI
    2. Using Table A4
    3. Difference between C-P and Wilson score intervals
  C. The Quantile Test
    1. Definition of Quantile
    2. Null and alternative hypotheses of quantile test
    3. Test statistics T1 and T2
    4. Decision Rules for each alternative
    5. P-values for each alternative
    6. Using Table A3
  D. Confidence Interval for a Quantile
    1. Order Statistics
    2. Using Table A3 to pick appropriate values of r and s
    3. Finding ACTUAL confidence level of interval
  E. Comparison of Quantile Test to t-test (Relative Efficiency)
  F. The Sign Test
    1. Definition of Paired Data
    2. Null and alternative hypotheses of sign test
    3. Test statistic and null distribution
    4. Decision Rules for each alternative
    5. P-values for each alternative
    6. Using Table A3
    7. When is the sign test appropriate?
    8. Comparison of Sign Test to t-test and Signed-rank test
  G. Variations of the Sign Test
    1. McNemar's Test
    2. Paired binary data
    3. Null and alternative hypotheses of McNemar's test
    4. Test statistic and null distribution
    5. P-value
    6. Large-sample test statistic and its null distribution
    7. Cox-Stuart Test for Trend
    8. Null and alternative hypotheses of Cox-Stuart test