MATH 672: Advanced Statistical Methods

Course Description

Objectives

1. Acquaint students with techniques used to test models used for large data sets using several factors.
   
   
2. Develop techniques and processes for designing experiments to extract optimal information.
   
   
3. Develop methods for fitting data to linear and non-linear regression curves and test the appropriateness of the model.
   
   
4. Gain experience in using a high level computer statistical program package to analyze large data sets.

Text

Grading Procedure

Attendance Policy

Course Outline

• Review

  Since students are assumed to have experience with statistical methods, Chapters 1 and 2 are briefly reviewed as needed.
  • Chapter 1: The Experiment, the Design, and the Analysis
    
  • Chapter 2: Review of Statistical Inference
  
  
  

• Chapter 3: Single Factor Experiments with no Restrictions on Randomization (9 days)

  Introduction, analysis of variance rationale, after anova- what?, tests on means, confidence limits on means, components of variance, checking the model
  
  

• Chapter 4: Single-Factor Experiments: Randomized Block and Latin Square Designs (9 days)

  Introduction, randomized complete block design, anova rationale, missing values, Latin squares, interpretations, assessment the model, Greco-Latin squares, extensions Introduction, factorial experiments: an example, interpretations, the model and its assessment, anova rationale, one observation per treatment
  
  

• Chapter 6: Fixed, Random, and Mixed Models (9 days)

  Introduction, single factor models, two factor models, ems rules, ems derivations, the pseudo F-test, expected mean squares by statistical computer packages
  
  

• Chapter 7: Nested and Nested Factorial Experiments (9 days)

  Introduction, nested experiments, anova rationale, nested-factorial experiments, repeated measure experiments and nested factorial experiments
  
  

• Chapter 8: Experiments of Two or More Factors: Restrictions on Randomization (5 days)

  Introduction, factorial experiments in a randomized block design, factorial experiments in a Latin square design
  
  

• Chapter 15: Regression (4 days)

  Introduction, linear regression, curvilinear regression, multiple linear regression
  
  
• Note:
  1. At appropriate places in this course, time should be allotted to elaborate on the historical aspects relevant to the subject.
  2. Most instructors for this course require the use of statistical calculators in addition to using the provided statistical computer package.