Prefix, Number and Name of Course: MAT 383 Applied Statistics

 

Credit Hours: 3

In Class Instructional Hours: 2       Labs: 1                             Field Work: 0             

 

Catalogue Description:

Prerequisite: MAT 382 or MAT 325 or (MAT 311 and MAT 381)

 

Categorical data analysis; simple linear regression and correlation; multiple linear regression; experimental design models (one, two or more factors); nonparametric statistics.

 

Reasons for addition:

1.                 To illustrate important concepts of the theory behind the application of probability and statistics.

2.                 To introduce statistical software suitable for problem solving in mathematical statistics.

3.                 To provide a foundation for more concentrated study using the computer for the solution of problems in applied mathematical statistics.

4.                 To increase studentsŐ awareness of the variety of applications of mathematical statistics beyond the scope of academia.

 

Student Learning Outcomes:

Students will:

Content Reference:

Assessment:
  1. conduct two-sample hypothesis testing for categorical data

 

I; VI

1. Homework assignments, problem sets, tests, exams, computer projects with assigned data sets
  1. demonstrate the ability to fit simple and multiple regression models to real- life data and test for the appropriateness of the models

II; III. A-E, G, H; VI

2. Homework assignments, problem sets, tests, exams, computer projects with assigned data sets
  1. demonstrate an understanding of the problem of multicollinearity and demonstrate the ability to use sequential methods for model selection

III. F; VI

3. Homework assignments, problem sets, tests, exams, computer projects with assigned data sets
  1. implement a variety of experimental design techniques to compare population means together with diagnostics and interaction in the higher order experiments

IV; VI

4. Homework assignments, problem sets, tests, exams, computer projects with assigned data sets
  1. use appropriate nonparametric methods for testing procedures that assume no knowledge about the distribution of the underlying population

V; VI

5. Homework assignments, problem sets, tests, exams, computer projects with assigned data sets
  1. apply statistical knowledge at an advanced level to diverse real-life fields by solving problems by hand as well as with standard statistical software

I; II; III; IV; V; VI

6. Problem sets, Term

computer project

 

 

Course Content:

 

I.            Tests of Hypotheses (Categorical data)

               A.          Goodness-of-Fit test

               B.          Test for independence

               C.          Test for homogeneity

               D.          Test for several proportions

 

II.          Simple Linear Regression and Correlation

A.               Least squares and the fitted model

B.                Properties of the least squares estimators

C.                Inferences concerning regression coefficients

D.               Prediction

E.                Analysis-of-Variance approach

F.                 Diagnostic plots of residuals

G.                Transformation of data

H.               Correlation

 

III.         Multiple Linear Regression

A.               Estimation of coefficients

B.                Properties of least squares estimators

C.                Inferences in multiple linear regression

D.               Analysis-of-variance in multiple regression

E.                Categorical or indicator variables

F.                 Sequential methods for model selection

G.                Study of residuals and violation of assumptions

H.               Polynomial regression

 

IV.        Design and Analysis of Experiments

A.               One-way analysis of variance

B.                Tests for the equality of several variances

C.                Multiple comparisons

D.               Comparing treatments with a control

E.                Randomized complete block designs

F.                 Diagnostics

G.                Latin square design

H.               Interaction in the two-factor experiment

I.                  Two-factor analysis of variance

J.                  Three-factor experiments

 

V.          Nonparametric Statistics

A.               Sign-test

B.                Signed-Rank test

C.                Wilcoxon Rank-Sum test

D.               Kruskal Wallis test

E.                Runs test

F.                 Rank correlation coefficient

 

VI.        Use of SPSS (Statistical Package for the Social Sciences)

 

 

Resources

 

Classic Scholarship in the Field:

 

               Andersen, E. B. Introduction to the Statistical Analysis of Categorical Data, Springer 1997.

 

               Agresti, A. Categorical Data Analysis, Wiley 1990.

 

               Brook, R. L. and Arnold, G. C. Applied Regression Analysis and Experimental Design, Dekker 1985.

 

               Draper, N. R. and Smith, H. Applied Regression Analysis, 3rd edition, Wiley 1998

              

               Hettmansperger, T. P. and McKean, J. W. Robust Nonparametric Statistical Methods, John Wiley & Sons 1998.

 

               Hinkelmann, K. and Kempthorne, O. Design and Analysis of Experiments, Wiley 1994.

 

               Hollander, M. and Wolfe, D. A. Nonparametric Statistical Methods, Wiley 1973.

 

               Kleinbaum, D. G., Kupper, L. L. and Muller, K. E. Applied Regression Analysis and other Multivariable Methods, 3rd edition, Duxbury Press 1998.

 

               Lehmann, E. L. Nonparametrics: Statistical Methods Based on Ranks, Holden Day 1975.

 

               Maritz, J. S. Distribution-free Statistical Methods, Chapman & Hall 1981.

 

               Neter, J., Wasserman, W. and Kutner, M. H. Applied Linear Statistical Models, 2nd edition, Richard D. Irwin 1985.

 

               Placket, R. L. The Analysis of Categorical Data, 2nd edition, Macmillan 1981.

 

               Rao, C. R. Linear Statistical Inference and its Applications, 2nd edition, Wiley Eastern 1973.

 

               Seber, G. A. F. Linear Regression Analysis, John Wiley & Sons 1977.

              

Current Scholarship in the Field:

 

Gibbons, J. D. Nonparametric Statistics: An Introduction, Sage publications, 2003.

              

Leonard, T. A Course in Categorical Data Analysis, Chapman & Hall 2000.

 

               Mason, R. L., Gunst, R. F. and Hess, J. L. Statistical Design and Analysis of Experiments: with Applications to Engineering and Science, 2nd edition, John Wiley 2003.

 

               Mickey, R. M. Applied Statistics: Analysis of Variance and Regression, 3rd edition, Wiley-Interscience 2004.

              

Miller, A. J. Subset Selection in Regression, 2nd edition, Chapman & Hall/CRC 2002.

              

Montgomery, D. C. and Runger, G. C. Applied Statistics and Probability for Engineers, 3rd edition, Wiley 2006.

 

               Montgomery, D. C. Design and Analysis of Experiments, 6th edition, John Wiley & Sons 2005.

 

               Weisberg, S. Applied Linear Regression, 3rd edition, Wiley-Interscience 2005.

 

Periodicals:

 

               The American Statistician

               The Annals of Probability

               The Annals of Statistics

               Bernoulli (Journal of the Bernoulli Society for Mathematical Statistics and Probability)

               Biometrika

               Journal of the American Statistical Association

 

Electronic and/or Audiovisual Resources:

 

Annals of Applied Probability (http://www.jstor.org.gate.lib.buffalo.edu/journals/10505164.html)

               Journal of Nonparametric Statistics (online: Taylor & Francis)

Journal of the Royal Statistical Society Series C, Applied Statistics (online: Blackwell Synergy)

Journal of Statistics Education

(http://www.amstat.org/publications/jse/)