Course Overview: Advanced Engineering Statistics (IE 4362)

Introduction

This course provides a comprehensive introduction to advanced statistical methods as applied in industrial engineering. Emphasis is placed on hypothesis testing, regression analysis, ANOVA, factorial experiments, and nonparametric methods, with practical implementation using statistical software (JMP).

• Prerequisite: IE 3302 or IE 3303

• Textbook: Probability & Statistics for Engineers & Scientists, 9th edition, Walpole et al.

• Software: JMP Student Edition

Course Outcomes

• Define and describe fundamental statistical concepts, including types of data, distributions, and statistical inference.

• Formulate and test statistical hypotheses, including goodness-of-fit and inference based on observed data.

• Construct and evaluate linear and nonlinear regression models, including model fit and data transformations.

• Estimate and interpret parameters in multiple regression models using statistical software.

• Apply one-way ANOVA to analyze single-factor experimental data.

• Design and analyze multi-factor experiments, interpret interactions, and assess statistical significance.

• Identify and apply appropriate nonparametric statistical methods.

Grading Breakdown

Grading Scale: Standard letter grades with plus/minus distinctions (A+, A, A-, B+, etc.).

Module Topics and Learning Objectives

Module 1: Hypothesis Testing and Inference

• Hypothesis Testing: Conduct tests for a single sample and for comparing two datasets, both manually and using JMP.

• Type I and Type II Errors: Understand and distinguish between these errors in hypothesis testing.

• Confidence Intervals: Calculate for means by hand and with JMP.

• Goodness-of-Fit and Independence: Assess using JMP.

Key Terms: Null hypothesis, alternative hypothesis, significance level (), p-value, test statistic, confidence interval.

Example: Testing whether the mean diameter of manufactured bolts differs from the specified value using a t-test.

Module 2: Simple Linear Regression (SLR)

• Scatter Plots: Visualize relationships between two variables.

• SLR Model: Develop and interpret the model .

• Model Fit: Evaluate using and residual analysis.

• Prediction: Use the model to predict outcomes and interpret prediction intervals.

• Assumptions: Linearity, independence, homoscedasticity, normality of errors.

Example: Predicting product strength based on temperature using SLR.

Module 3: Multiple Linear Regression (MLR)

• Purpose: Model the relationship between a response variable and multiple predictors.

• MLR Model:

• Model Building: Use JMP to fit models, interpret coefficients, and assess fit with and adjusted .

• Variable Selection: Apply stepwise regression to choose predictors.

• Categorical Variables: Incorporate using indicator (dummy) variables.

• Diagnostics: Identify outliers, non-constant variance, and non-normality.

Example: Modeling production time as a function of machine speed, operator experience, and material type.

Module 4: Analysis of Variance (ANOVA)

• Experimental Design: Identify designs suitable for one-way ANOVA.

• Assumptions: Independence, normality, and equal variances.

• F-Statistic: Calculate and interpret for both equal and unequal sample sizes.

• Output Analysis: Summarize findings from ANOVA tables.

• Contrasts and Post-Hoc Tests: Determine which group means differ significantly.

• Randomized Designs and Blocking: Apply to control for nuisance variables.

Example: Comparing mean yields from three different fertilizer treatments using one-way ANOVA.

Module 5: Factorial Experiments and Two-Way ANOVA

• Main and Interaction Effects: Define and interpret in factorial designs.

• Two-Way ANOVA: Perform and interpret results using JMP.

• 2k Factorial Designs: Apply full and fractional factorial designs.

• Graphical Methods: Use interaction plots to interpret effects.

• Fractional Factorial Designs: Explain purpose and determine test levels.

Example: Studying the effect of temperature and pressure on product quality using a 2x2 factorial design.

Module 6: Nonparametric Methods

• Definition: Statistical methods that do not assume a specific distribution for the data.

• When to Use: Appropriate when data do not meet parametric assumptions (e.g., normality).

• Test Selection: Choose based on data type and research question (e.g., Wilcoxon, Kruskal-Wallis).

• Implementation: Conduct tests using JMP.

Example: Comparing median customer satisfaction scores between two service centers using the Mann-Whitney U test.

Module 7: Communicating Statistical Results

• Presentation: Organize and present analyses for non-technical audiences.

• Interpretation: Translate statistical outcomes into actionable business or engineering decisions.

Example: Summarizing regression analysis findings for management to inform process improvements.

Additional Course Policies and Resources

• Academic Integrity: All work must be original or properly cited. Unauthorized use of materials or AI tools during assessments is prohibited.

• Use of AI: Permitted for learning and understanding, but not for direct submission unless disclosed and verified.

• Disability Services: Accommodations available through the Office of Disability Services.

• Support Resources: Academic success centers, communication workshops, and career planning services are available to students.

• Nondiscrimination and Title IX: LSU provides equal opportunity and support for all students. Resources are available for those experiencing discrimination or harassment.

Summary Table: Key Statistical Methods Covered

Additional info: This syllabus covers advanced topics that build on introductory statistics, including regression, ANOVA, factorial designs, and nonparametric methods, all of which are relevant to the core chapters of an Introductory Statistics course.