Lumen’s new Introductory to Statistics course will be delivered in Lumen One, a new platform that brings together the best of Lumen’s teaching & learning solutions including a full suite of professional development resources to support evidence-based teaching. Designed for the Introductory Statistics course, it can also be used in a co-requisite course model, as it includes extensive additional support for those students struggling with prerequisite skills.

**Designed to Support Equity**

This Introductory Statistics course is built with support from the Bill & Melinda Gates Foundation to promote equitable outcomes in gateway courses. Putting equity at the center of course design allows us to focus on the research-backed practices and approaches that have a real and measurable positive impact on outcomes for all students, especially Black, Latino/a/x, Indigenous, and low-income students.

**The platform and content of the course are built to:**

- Create and foster connections between faculty and students.
- Support students’ sense of belonging and engagement.
- Provide early & timely intervention when students face challenges.
- Surface student performance and actionable data for faculty to quickly see who’s struggling and help them.
- Include sample data sets and problems that are relevant and culturally diverse.
- Provide worked problem videos that make students feel represented and included.

Working closely with both student and faculty groups, Lumen’s principles of co-design and collaboration also extend to the course content, which comes from our partnership with The Dana Center at UT Austin.

**Key features include:**

- A simplified, highly-actionable Faculty Engagement Center that enables timely intervention when students are struggling
- Class-wide performance analytics on pre-requisite skills and learning objectives so you can flex your instruction to better support your students
- A suite of support resources, including evidence-based teaching practices to help faculty quickly identify and action student support needs
- Facilitation of peer-to-peer learning and engagement
- A design that is built from the ground up to promote equitable outcomes through research-backed instruction

**Content **

*(Subject to minor changes prior to course release)*

**Data Types and Organizations – What is Statistics?**

- Statistical Investigative Process
- Subjects, Cases, and Experimental Units
- Variable Classifications: Categorical and Quantitative Variables
- Data Collection and Organization
- Good Statistical Questions

**Statistical Studies and Sampling**

- Population vs. Sample; Parameters vs. Statistics
- Simple Random Sampling
- Sampling Methods
- Observational Study Design
- Confounding Variables
- Experimental Design
- Sampling Bias, Variabilities, and Limitations

**Describing Data Graphically**

- Descriptive Statistics
- Displays of Categorical Data: Pie Chart, Bar Graph, Side-by-Side Bar Graph, Stacked Bar Graph
- Display of Quantitative Data: histogram, dotplot
- Distributions of Quantitative Variables: Shape, Center, Spread, Unusual Observations/Outliers

#### Describing Data Numerically

- Measure of Center
- Measure of Variability
- Five-Number Summary and Boxplots
- Distribution and Variabilities of the Datasets
- Outliers
- Standardized Scores and Empirical Rule

**Displaying and Describing Bivariate Data**

- Displays of Bivariate Data: scatterplots
- Trend, Relationship, and Outliers of Bivariate Data
- Association of Bivariate Data
- Correlation Coefficient
- Complex Graphical Displays
- Visual Displays in the Media

**Modeling Bivariate Data**

- Least Square Regression Analysis
- Regression Lines
- Line of Best Fit
- Estimated Slopes and y-Intercepts
- Coefficient of Determination
- Model Adequacy and Residuals
- Limit of Extrapolation
- Calculating Predicted Values

**Probability**

- Empirical and Theoretical Probabilities
- Probability of Compound Events: Union, Intersections, and Complements
- Basic Rules of Probability
- Mutually Exclusive and Independent Events
- Conditional Probability
- Bayes Theorem

**Probability Distribution**

- Probability Model and Distributions
- Discrete Probability Distributions
- Expected Value
- Binomial Distribution
- Normal Distribution

**Sampling Distributions**

- Population and Parameter of Interest
- Sample and Statistics of Interest
- Sampling Distribution of a Sample Proportion
- Conditions for a Sampling Distribution of a Sample Proportion
- Standard Error of a Sampling Distribution of a Sample Proportion

**Confidence Intervals for Population Proportions**

- Confidence Level vs. Confidence Interval
- Confidence Intervals for a Population Proportion
- Confidence Intervals for a Difference Between Two Proportions
- Sample Size of a Sampling Distribution of a Sample Proportion
- Interpretation and Misinterpretation of Confidence Intervals

**Hypothesis Testing for a Population Proportion**

- Hypothesis Testing
- Null and Alternative Hypotheses
- Conditions for a Hypothesis Test for a Population Proportion
- Test Statistics
- P-Values
- One-Sample z-test for a Population Proportion
- Two-sample z-Test for Proportions
- Errors in Hypothesis Testing
- Logic of Inference
- Inference using Confidence Intervals and Hypothesis Testing

**Confidence Intervals for Population Means**

- Sampling Distribution of a Sample Mean
- Mean, Standard Deviation, and Standard Error of a Sampling Distribution of a Sample Mean
- Conditions for a Sampling Distribution of a Sample Mean: Central Limit Theorem
- The t-distribution
- One-sample t Confidence Intervals for a Population Mean
- Two-sample t Confidence Intervals for a Difference in Population Means
- Interpretation and Misinterpretation of Confidence Intervals

**Hypothesis Testing for Population Means**

- One-sample t-test for a Population Mean
- Two-sample t-test for Independent Population Means
- Paired (Two-sample) t-test for Dependent Population Means
- Errors in Hypothesis Testing
- Logic of Inference
- Inference using Confidence Intervals and Hypothesis Testing

**Inference Concerning Two Population Means***

- One-way ANOVA
- Conditions for One-way ANOVA
- Multiple Pairwise Comparisons
- Inferences using One-way ANOVA

**Chi-Squared Statistics*******

- Chi-Squared Test and Statistics
- Chi-Squared Test for Goodness of Fit
- Chi-Squared Test of Homogeneity
- Chi-Squared Test of Independence
- Fisher’s Exact Test
- Two-sample Inference
- Standardized Residuals from a Chi-Squared Test

**Analysis of Variance*******

- Test for Significance of Slope
- ANOVA for Regression
- Confidence Intervals and Prediction Intervals
- Data Transformations for Regression Analysis

**Multiple Linear Regression***

- Multiple Linear Regression
- Multiple Linear Regression: Indicator Variables
- Multiple Linear Regression: Interpretations

**Bootstrap and Simulation-Based Statistics***

- Bootstrap Distribution and Confidence Intervals
- Simulation-Based Hypothesis Tests
- Randomization Tests

*Topic List by Module – subject to minor changes prior to course release.*