Students will disseminate the outcomes from their statistics capstone project in this course. Students will be required to create a professional poster, create and deliver a professional quality presentation, and write a detailed report of their capstone project outcomes.

Provides the student with experience and training in statistical techniques. The student will work a minimum of 100 hours (3 credits) or a minimum of 200 hours (6 credits) on a job utilizing statistics. 

A mathematical approach to probability and statistics.

1. Parametric Inference: Parametric inference focuses on making inferences about population parameters based on assumptions about the underlying probability distribution. Students learn about methods for estimating parameters using maximum likelihood estimation (MLE) and method of moments estimation. They also study properties of estimators, such as unbiasedness, efficiency, and consistency.

2. Nonparametric Inference: Nonparametric inference relaxes the assumptions about the underlying probability distribution and focuses on distribution-free methods. Students learn about nonparametric methods for hypothesis testing, such as the Wilcoxon signed-rank test, Mann-Whitney U test, and Kruskal-Wallis test. They also study nonparametric methods for estimation, such as kernel density estimation and nonparametric regression.

3. Bayesian Inference: Bayesian inference is a statistical paradigm based on Bayes' theorem, which updates prior beliefs about the parameters of interest in light of observed data to obtain posterior distributions. Students learn about Bayesian methods for parameter estimation, hypothesis testing, and model comparison. They study concepts such as prior distributions, likelihood functions, posterior distributions, and Bayesian decision theory.

4. Multivariate Analysis: Multivariate analysis deals with the analysis of datasets with multiple variables. Students learn about multivariate probability distributions, such as the multivariate normal distribution, and methods for analyzing relationships between variables, such as multivariate analysis of variance (MANOVA), principal component analysis (PCA), and factor analysis.

5. Statistical Computing: Statistical computing involves the use of computational tools and algorithms to implement statistical methods and analyze data. Students learn about programming languages such as R and Python, as well as software packages for statistical computing and data analysis. They study techniques for simulation-based inference, resampling methods (e.g., bootstrapping and permutation tests), and numerical optimization algorithms.

A mathematical approach to probability and statistics.

1. Probability Distributions: Students learn about various probability distributions, including discrete distributions such as the binomial and Poisson distributions, and continuous distributions such as the normal and exponential distributions. They study their probability mass functions (PMFs) or probability density functions (PDFs), cumulative distribution functions (CDFs), moments, and properties.

2. Random Variables: Random variables are central to probability theory and statistics. Students learn about different types of random variables, including discrete and continuous random variables, as well as their probability distributions. They study concepts such as expected value, variance, moment generating functions, and transformations of random variables.

3. Sampling Distributions: Sampling distributions play a crucial role in statistical inference. Students learn about the sampling distribution of sample statistics such as the sample mean and sample proportion. They study properties of sampling distributions, including their mean, variance, and distributional characteristics, particularly in the context of large samples and the central limit theorem.

4. Estimation Theory: Estimation theory deals with methods for estimating unknown parameters from sample data. Students learn about point estimation, where a single value is used to estimate a parameter, and interval estimation, where a range of values (confidence interval) is used to estimate a parameter with a certain level of confidence. They study properties of estimators, such as bias, efficiency, and consistency, and methods for constructing confidence intervals.

5. Hypothesis Testing: Hypothesis testing is a fundamental concept in statistical inference. Students learn about null and alternative hypotheses, test statistics, p-values, Type I and Type II errors, significance levels, and power of tests. They study common hypothesis tests for means, variances, proportions, and differences between means, as well as the principles of hypothesis testing in various contexts.

This course will develop skills necessary to become a working professional in the field of statistics. Students will critique, analyze, and evaluate several statistics research projects. A student's presentation, writing, and professional skills will be enhanced in this course.

In this course, the student will gain an understanding of the nature of applied consulting and the scientific philosophies and skills required to be successful as a statistical consultant. This course will continue to develop the student's oral and written communication skills that are necessary for communicating often technical statistical content with non-statisticians. Students will provide statistical consulting service to the university as time permits.

1. Consulting Process: The consulting process involves a series of steps from understanding the client's problem to delivering actionable recommendations. Students learn about the importance of establishing clear objectives, defining the scope of work, collecting relevant data, conducting analyses, and presenting findings in a way that addresses the client's needs.

2. Client Interaction and Communication: Effective communication skills are essential for successful statistical consulting. Students learn how to communicate with clients from various backgrounds, including non-statisticians, and how to explain complex statistical concepts in clear and understandable terms. This may involve using visual aids, such as graphs and charts, to convey key messages.

3. Ethical Considerations: Ethical considerations play a significant role in statistical consulting, particularly regarding issues such as confidentiality, conflict of interest, and integrity in data analysis and reporting. Students learn about ethical guidelines and best practices for maintaining professional standards and integrity in their consulting work.

4. Project Management: Statistical consulting projects often involve managing multiple tasks, deadlines, and stakeholders. Students learn project management skills, including time management, resource allocation, and prioritization, to ensure that consulting projects are completed on time and within budget.

5. Real-world Case Studies: Case studies and practical examples are used to illustrate the application of statistical methods in consulting projects across different industries and domains. Students analyze real-world datasets, identify relevant statistical techniques, and develop solutions to address clients' needs. This hands-on experience helps students develop problem-solving skills and gain insights into the challenges and opportunities of statistical consulting.

One-way Analysis of Variance, planned comparisons, post-hoc procedures, two- and three-way Analysis of Variance, experimental design, Analysis of Covariance. Interpretation of computer output will be emphasized.

1. Randomization and Control: Randomization is a fundamental principle in experimental design that involves randomly assigning subjects to different treatment groups or conditions. This helps to minimize the effects of confounding variables and ensures that any observed differences between groups are due to the treatment. Control involves keeping other factors constant or controlling for them to isolate the effect of the treatment.

2. Factorial Designs: Factorial designs involve studying the effects of multiple factors (independent variables) simultaneously. This allows researchers to investigate main effects (individual effects of each factor) as well as interactions between factors. Factorial designs are efficient for studying complex relationships and interactions.

3. Blocking and Randomized Complete Block Designs: Blocking involves grouping experimental units (subjects) into blocks based on certain characteristics that may influence the response variable. Randomized complete block designs ensure that each treatment is applied within each block, thereby reducing variability and increasing the precision of estimates.

4. Analysis of Variance (ANOVA): ANOVA is a statistical method used to analyze experimental data by comparing means between two or more groups. It helps to determine whether there are statistically significant differences among the treatment groups and which groups differ from each other. ANOVA can be applied to various experimental designs, including completely randomized designs, randomized block designs, and factorial designs.

5. Response Surface Methodology (RSM): RSM is a collection of statistical and mathematical techniques used to optimize processes and improve product quality by studying the relationship between multiple independent variables and a response variable of interest. RSM involves designing experiments to systematically explore the response surface and identify optimal operating conditions.

Simple linear regression, multiple regression, hypothesis testing, analysis of residuals, stepwise regression. Interpretation of computer output will be emphasized. 

1. Simple Linear Regression: Simple linear regression involves modeling the relationship between two variables: one independent variable (predictor) and one dependent variable (response). The goal is to fit a linear equation to the data that best describes the relationship between the variables.

2. Multiple Linear Regression: Multiple linear regression extends simple linear regression to cases where there are multiple independent variables. It allows for the analysis of how several predictors collectively influence the dependent variable while controlling for the effects of other variables.

3. Model Assumptions and Diagnostics: Regression analysis relies on several assumptions, such as linearity, independence of errors, constant variance (homoscedasticity), and normality of errors. Understanding these assumptions and diagnosing violations is crucial for interpreting regression results accurately.

4. Variable Selection and Model Building: Selecting the appropriate variables to include in a regression model is an important aspect of regression analysis. Techniques such as stepwise regression, forward selection, backward elimination, and regularization methods (e.g., Lasso and Ridge regression) are used to identify the most influential predictors and build parsimonious models.

5. Model Interpretation and Inference: Once a regression model is fitted, interpreting the coefficients of the model and making inferences about the relationships between variables are essential tasks. This involves assessing the significance of individual predictors, evaluating the overall fit of the model, and interpreting the coefficients in the context of the problem domain.

This course will provide an introduction to study design and proper methods of data collection. Students will gain an overview of the research cycle, basic principles of experimental design, observational studies, effective design of survey instruments, examples of study bias, and ethical considerations in the conduct of research. 

1. Randomization: Randomization is a crucial principle in study design that involves randomly assigning subjects to different treatment groups or conditions. It helps to ensure that any observed differences between groups are due to the treatment and not to other factors.

2. Controlled Experiments: Controlled experiments involve manipulating one or more variables to observe the effect on another variable while controlling for potential confounding factors. This allows researchers to establish causality and make valid inferences about the relationship between variables.

3. Bias and Confounding: Bias refers to systematic errors in study design, data collection, or analysis that can lead to incorrect conclusions. Confounding occurs when the effect of an extraneous variable is mixed with the effect of the variable of interest, making it difficult to attribute observed differences to the variable being studied.

4. Sample Size Determination: Determining the appropriate sample size is essential for ensuring that a study has sufficient statistical power to detect meaningful effects. Factors such as the desired level of significance, effect size, and variability in the data influence sample size calculations.

5. Ethical Considerations: Ethical principles play a critical role in study design, particularly when human subjects are involved. Researchers must consider factors such as informed consent, privacy, confidentiality, and the potential risks and benefits of participation in the study.

A second course in statistics covering regression, measures of association, and analysis of variance. Interpretation of computer output and applications will be emphasized throughout.

1. Multiple Regression Analysis: Building upon simple linear regression, multiple regression allows for the analysis of the relationship between a dependent variable and multiple independent variables. It enables the examination of how several factors collectively influence an outcome.

2. Analysis of Variance (ANOVA): ANOVA is a statistical method used to compare means between two or more groups. It helps in determining whether there are statistically significant differences among the means of the groups and which groups differ from each other.

3. Nonparametric Statistics: While parametric statistics assume specific distributions for the data, nonparametric statistics make fewer assumptions about the underlying population distribution. Methods like the Wilcoxon signed-rank test, Mann-Whitney U test, and Kruskal-Wallis test are examples of nonparametric tests used for various purposes.

4. Experimental Design: Understanding how to design experiments is crucial in statistics. This involves considerations such as selecting appropriate sample sizes, randomization, and controlling for confounding variables to ensure the validity and reliability of experimental results.

5. Time Series Analysis: Time series data involves observations collected over time. Time series analysis includes methods for modeling, forecasting, and understanding patterns and trends in such data. Techniques like autoregressive integrated moving average (ARIMA) modeling and exponential smoothing are commonly used in this context.

First course in statistics for students with a strong mathematics background.

1. Probability: This concept deals with the likelihood of events occurring. It forms the foundation of statistical inference and helps in understanding uncertainty and randomness in data.

2. Sampling Distributions: Understanding how sample statistics vary from one sample to another is crucial. Sampling distributions help in making inferences about population parameters based on sample statistics.

3. Hypothesis Testing: This involves making decisions or inferences about population parameters based on sample data. Hypothesis testing allows statisticians to evaluate the strength of evidence in favor of or against a particular claim.

4. Confidence Intervals: These provide a range of values within which a population parameter is likely to lie. They are useful in estimating population parameters with a certain degree of confidence based on sample data.

5. Regression Analysis: Regression is used to model the relationship between one or more independent variables and a dependent variable. It helps in understanding how changes in the independent variables affect the dependent variable and is widely used in predictive modeling and forecasting.