STATISTICS

Course Credits: 3 Units

Prerequisites: Stat 123

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STAT 132 - Nonparametric Statistical Inference

Course Description

Levels of measurement; goodness-of-fit tests; sign and signed ranks tests; distribution tests; association test; tests for independence.

Course Learning Outcomes

By the end of this course, the student must be able to:

  1. Distinguish when to use nonparametric procedures;
  2. Determine the nonparametric techniques that are appropriate under various research problems and designs;
  3. Perform the nonparametric procedures (both manually and with the use of computer) and correctly interpret the results;
  4. Apply appropriate statistical concepts, tools, and technologies in the solution to various conceptual and real-world problems.
Course Outline

UNIT 1. Introduction

  1. Review of Terms in Statistical Inference
  2. The Statistical Model
  3. Efficiency
  4. Levels of Measurement
  5. Parametric versus Nonparametric Tests
  6. Monte Carlo Simulation

UNIT 2. Single Sample Tests

  1. Inferences About a Location Parameter
  2. Inferences about a Population Proportion
  3. Runs Test for Randomness
  4. Cox-Stuart Test for Trend.

UNIT 3. Two Independent Samples

  1. Inferences about Two Location Parameters
  2. Inferences about Two Dispersion Parameters
  3. The Wald-Wolfowitz Runs Test
  4. Hollander Test of Extreme Reactions
  5. Fisher’s Exact Test

UNIT 4. Two Related Samples Test

  1. Inferences about Location Parameters
  2. Confidence Interval for the Median Difference
  3. McNemar Test for Related Proportions

UNIT 5. Chi-Square Tests of Independence and Homogeneity

  1. Properties of Chi-Square Distribution
  2. Chi-Square Test of Independence
  3. Chi-Square Test of Homogeneity

UNIT 6. Three or More Independent Samples Test

  1. Extension of the Median Test
  2. Kruskal-Wallis ANOVA by Ranks
  3. Jonckheere-Terpstra Test for Ordered Alternatives
  4. Multiple Comparisons

UNIT 7. Three or More Related Samples Test

  1. Friedman Two-Way ANOVA by Ranks
  2. Multiple-comparison Procedure for Friedman Test
  3. Page’s Test for Ordered Alternatives
  4. Cochran’s Test for Related Observations

UNIT 8. Goodness-of-Fit Tests

  1. Chi-square Goodness-of-fit Test
  2. Kolmogorov-Smirnov One-sample Test
  3. Kolmogorov-Smirnov Two-sample Test
  4. Shapiro-Wilks Test