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.