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Approved by Faculty Senate.

University Studies Course Approval Proposal

Unity and Diversity – Critical Analysis

The Department of Mathematics and Statistics proposes the following course for inclusion in University Studies, Unity and Diversity, Critical Analysis at Winona State University. This was approved by the full department on Thursday, January 4, 2001.

Course: Intermediate Statistics (STAT 310) 3 s.h.

Catalog Description: A second course in statistics covering regression, measures of association, and analysis of variance. Interpretation of computer output and applications will be emphasized throughout. This is a University Studies course satisfying requirements for Critical Analysis. Prerequisite: STAT 110, STAT 210, STAT 303, STAT 305, PSY 231, or equivalent. Credit will not be given for STAT 310 if the student has completed STAT 360 or STAT 365.

This is an existing course, previously approved by A2C2.

Department Contact Person for this course:

Carol J. Blumberg; email cblumberg@winona.edu

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General Discussion of Each Objective in Critical Analysis as it relates to learning activities in STAT 310

**a. evaluate the validity and reliability of information**

Chi-square, correlation coefficients, multiple linear regression, stepwise regression, and Analysis of Covariance are used extensively when evaluating the validity and reliability of information statistically. Explicit connections between the terms validity and reliability and these techniques are made in lectures. Explicit questions relating to reliability and validity are included in homework assignments and tests. Reliability and Validity questions are also included as part of the term project.

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**b. analyze modes of thought, expressive works, arguments, explanations, or theories**

Several methods for statistically analyzing arguments, explanations, and theories are Chi-square, multiple linear regression, post-hoc procedures, and multiple factor designs. It is discussed in class how each of these methods can be used to help support and refute various arguments, explanations, and theories. Also, the limitations and incorrect uses of each technique are strongly emphasized. Examinations and homework assignments are given that make the students consider alternative arguments, explanations, and theories and decide which ones are plausible from a statistical (as well as logical) point of view. For example, if a proposed model for predicting weights based on height, age, and bone density predicts negative weights for certain classes of people, then it has both statistical and logical problems. Also, one of the requirements of the term project is that the students discuss the theory behind the statistical models that they have built or others have built (depending on the option chosen for the term project).

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c. recognize possible inadequacies or biases in the evidence given to support arguments or conclusions AND

**d. advance and support claims**

For each of the statistical techniques discussed in this course, extensive discussion is made of how it helps the researcher discover inadequacies and biases in their proposed models. Once they discover inadequacies and biases, they can then propose new models and test these new models using these same statistical techniques. Both the examinations and homework have many problems where the students must discuss both numerically and verbally the adequacies, inadequacies, biases, and lack of bias in the models that they are asked to analyze or create themselves. A major focus of the term project is for students to discuss these same issues for models developed by others or for models they develop.

**Statistics 310--Intermediate Statistics—3 s.h**.

**Course Description**: A second course in statistics covering regression, measures of
association, and analysis of variance. Interpretation of computer output and applications
will be emphasized throughout. This is a University Studies course satisfying requirements
for Critical Analysis. Prerequisite: STAT 110, STAT 210, STAT 303, STAT 305, PSY 231, or
equivalent. Credit will not be given for STAT 310 if the student has completed STAT 360 or
STAT 365.

**Possible Textbooks**:

Berenson, Mark L. & Levine, David L. __Basic Business Statistics: Concepts and
Applications__ (Fourth Edition). Prentice-Hall, 1989. Mendenhall, William & Sincich,
Terry. __Statistics for Engineering and the Sciences__ (Fourth Edition). Prentice-Hall,
1995.

**Unity and Diversity--Critical Analysis: **Critical Analysis courses in the University
Studies program are devoted to teaching critical thinking or analytic problem-solving
skills. These skills include the ability to identify sound arguments and distinguish them
from fallacious ones. The objective of these courses is to develop students’
abilities to effectively use the process of critical analysis. Disciplinary examples
should be selected to support the development of critical analysis skills.

These courses must include requirements and learning activities that promote students' abilities to...

a. evaluate the validity and reliability of information;

b. analyze modes of thought, expressive works, arguments, explanations, or theories;

c. recognize possible inadequacies or biases in the evidence given to support arguments or conclusions; and

d. advance and support claims.

In the description of class topics and requirements below, these objectives in this list are referred to by a-d.

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**Topics Covered**:

I. Measures of Association

A. Review of Chi-square/Contingency Table Analysis **(a, b. c, d)**

B. Other Measures including Pearson and Spearman Correlation Coefficients **(a, c, d)**

II. Regression

A. Simple Linear Regression **(c. d)**

B. Multiple Linear Regression **(a, b, c, d)**

C. Stepwise Regression **(a, b, c, d)**

III. Analysis of Variance

A. One-way Analysis of Variance **(c, d)**

B. Use of Planned Comparisons **(c, d)**

C. Post-hoc Procedures **(b, c, d)**

D. Multiple Factor Designs** (a, b, c, d)**

E. Analysis of Covariance **(a, c, d)**

IV. Additional Topics as time permits. Some possibilities are Discriminant Analysis, Factor Analysis, and Introduction to Log-linear Models

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**Method of Instruction**: Lecture, group work, case studies, and/or discussion of
examples and computer output.

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**Evaluation Procedures**: Possible methods include examinations, quizzes, homework,
computer assignments, and/or a final examination. **(a, b, c, d)** A term project may
also be assigned. **(a, b, c, d)**

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**Approval/Disapproval Recommendations**

Department Recommendation: Approved Disapproved Date

Chairperson Signature Date

Dean's Recommendation: Approved Disapproved Date

Dean's Signature Date

*In the case of a Dean's recommendation to disapprove a proposal, a written rationale for the recommendation

to disapprove shall be provided to USS.

USS Recommendation: Approved Disapproved Date

University Studies Director's Signature Date

A2C2 Recommendation: Approved Disapproved Date

A2C2 Chairperson Signature Date

Faculty Senate Recommendation: Approved Disapproved Date

FA President's Signature Date

Academic VP's Recommendation: Approved Disapproved Date

VP's Signature Date

President's Decision: Approved Disapproved Date

President's Signature Date