Teaching Causal Inference in an Introductory Statistics or Data Science Course and Beyond

Teaching Causal Inference in an Introductory Statistics or Data Science Course and Beyond Rosanna Overholser Department of Mathematics, California Polytechnic State University, Humboldt Abstract. People routinely encounter causal claims in news, health, and policy but may not have sufficient practice with the tools needed to evaluate these claims critically. While we think in terms of cause and effect, introductory statistics or data science classes sometimes avoid this type of thinking, only introducing randomized controlled trials and basic confounding identification as possible tools. This gap can leave students unprepared to assess the validity of a comparison. This paper presents a one-week, classroom-tested module that introduces causal directed acyclic graphs (DAGs) for identifying confounders and performing simple comparisons. The module is anchored by an example comparing calculus pass rates between two universities and demonstrates that conclusions can change depending on what assumptions are made. Developed using backward design, the module prepares students for an authentic project, designing a study to answer a peer’s research question, by teaching them to draw causal DAGs, identify valid adjustment sets, and understand the necessary assumptions. The module is compatible with both traditional and simulation-based inference curricula and includes complete materials: a list of learning outcomes, lecture notes, in-class activities, quiz questions, and a structured project. Designed for college level courses, the module provides a foundation that prepares students for advanced causal reasoning in future coursework and professional practice. The module has been refined through 7 years of teaching experience at two non-selective public polytechnic institutions. 1. Why teach causal diagrams? 1.1 Why add Causal DAGs to an already full course? Causal directed acyclic graphs (DAGs), developed and popularized by Judea Pearl and colleagues, can serve two roles in the undergraduate curriculum: they are both an accessible tool for reasoning about fair comparisons and a foundation for advanced methods in statistics, data science, and machine learning. They provide a visual, intuitive framework for thinking clearly about confounding, and a student who can draw a simple three-node DAG and identify a back-door path gains a transferable mental model for critiquing claims in news articles, evaluating published research, and planning their own analyses. This skill requires no calculus, minimal probability background, and no programming beyond basic data manipulation—making it appropriate for the first statistics or data science course at the college level. For students who continue in quantitative fields, causal DAGs are not a pedagogical simplification to be unlearned, they are an entry point to modern causal inference: • Causal DAGs can be combined with Donald Rubin’s formalization of the potential outcomes framework via single-world intervention graphs (SWIGs), providing a graphical bridge between structural and counterfactual approaches. (Richardson and Robins 2013) 1 • DAGs underpin recent developments in causal discovery (learning graph structure from data) and causal machine learning (e.g., counterfactual fairness, off-policy evaluation), areas of active research and industry application. (Spirtes, Glymour, and Scheines 2000; Kusner et al. 2017) • DAGs organize the g-methods (g-formula, inverse-probability weighting, g-estimation) taught in upper-division or graduate-level coursework in applied statistics across a variety of disciplines, ensuring continuity from the introductory module to advanced training. Introductory statistics and data science courses traditionally cover elementary probability, distributions, descriptive statistics, inference for one or two means or proportions, sampling methods, study design, and simple regression. These topics are foundational and, in many academic programs, are not up to an individual teacher to choose. The one-week causal DAG module presented here is designed to integrate with (not replace) this standard curriculum. The module fits naturally within a study design unit (randomization vs. observational studies; confounding) and descriptive statistics. The learning goals of the module support two key objectives: enabling students to evaluate the quality of statistical evidence in published research, and to perform simple descriptive and inferential analyses. 1.2 Confounding in the big data era: from inference to description Traditional statistics courses sometimes motivate confounding as a threat to inference, that is, as an obstacle to valid hypothesis tests or confidence intervals. But as datasets grow larger, the balance of concerns shifts dramatically. With millions of observations, sampling variability shrinks toward zero, yet bias from confounding remains unchanged (or may even worsen if data-collection mechanisms introduce new selection effects). A misleading comparison in a dataset of n = 10 6 will produce a statistically significant result with an impressively narrow confidence interval—and be entirely wrong. This reality elevates confounding from an “inference problem” to a data literacy problem that pervades every stage of analysis: • Descriptive statistics: a crude mean or proportion computed on confounded data misrepresents the underlying causal difference, regardless of sample size. For example, if we compare average test scores between two schools without accounting for differences in student backgrounds, we might mistakenly attribute those differences to the schools themselves rather than the students they enroll. The descriptive summary is misleading before we even consider confidence intervals. • Data visualization: a bar chart or scatterplot that ignores confounders can suggest relationships that reverse or disappear upon stratification (Simpson’s paradox). Students who learn to “just plot the data” without considering confounding structure are at risk of routinely produce and share misleading graphics. • Automated summaries and dashboards: modern tools (including AI-driven analytics) can compute and display any summary statistic requested. Without human oversight about what to condition on, these summaries are at risk of propagating confounded comparisons at scale. • Inference and decision-making: only after ensuring the descriptive comparison is meaningful (i.e., properly adjusted) does it make sense to quantify uncertainty or test hypotheses. A p -value or confidence interval for a confounded effect estimate is formally correct as a statement about sampling variability but substantively meaningless as a guide to action. 2 Tools for addressing confounding should not be postponed until upper-division or graduate level courses, but introduced alongside data summarization and visualization: every graph and summary table is a potential site of confounding bias. By introducing causal DAGs early, we give students a tool to ask, “Should I stratify or adjust before summarizing?” and to communicate which comparisons are—and are not—meaningful. Modern tools already automate large parts of the analysis pipeline. AutoML systems can train, tune, and ensemble strong predictive models with minimal human input, and generative AI tools like ChatGPT’s Data Analyst can write and execute code, join files, and generate tables and charts in-session. What these systems do not supply are the causal ingredients: a well-posed estimand, a defensible adjustment set, and plausible assumptions. Those pieces remain inherently human and teachable within the confines of a traditional first and second course in statistics. 2. The one-week module for a college level introductory statistics or data science course Executive Summary • Who it’s for: Instructors of introductory statistics or data science courses for any major, including non-STEM. • Time required: Three 50-minute class periods and six to eight hours of student time outside of class. • What students can do afterward: Draw a causal DAG for a comparative question, identify a valid adjustment set using the back-door criterion, design a simple observational study with appropriate confounding control, and compute appropriate descriptive statistics. • Materials provided: Learning outcomes, lecture notes, in-class activities, quiz questions, and a short project. All materials are available at https: //roverhol.github.io/teaching-overview/. This module was developed using backward design: I started with the end goal of students completing a realistic project and worked backward to identify what students need to learn to achieve that goal. Every element of the module (learning outcomes, examples, activities, and assessments) is designed to prepare students for this authentic assessment of their causal reasoning skills. 2.1 Course context and curricular placement The module presented here was developed for an introductory statistics or data science course serving all majors, including non-STEM students. My version of such a course covers standard topics that are often mandated by departmental or institutional requirements: •Definition and basic rules of probability •Binomial and normal distributions •Descriptive statistics for one and two variables •Hypothesis tests and confidence intervals for one or two means/proportions •Sampling methods •Study design (observational vs. experimental; randomization; confounding) •Simple linear regression 3 This module integrates into rather than replacing this standard curriculum, appearing in my course immediately after the study design unit and before simple regression. It provides students with practical tool for reasoning about and controlling for confounding and prepares them for more advanced coursework. 2.2 Learn by doing projects in an introductory statistics or data science course My course uses a project-based assessment model in which students complete five “miniprojects” over the semester, each tied to a major course topic and requiring students to apply concepts to self-selected or peer-generated research questions. The five projects are: 1. Binomial test for probability of success: Students formulate a hypothesis and test it using data they collect from a binomial random process. 2. Estimation from a simple random sample: Students create a sampling frame, collect data from a simple random sample, and compute a confidence interval for a single mean or proportion. 3. Descriptive statistics: Students choose a dataset with at least four variables, compute appropriate descriptive statistics, and share their most interesting findings. 4. Comparison of two groups (the project described in this paper): Students design a study, thinking through both a Randomized Controlled Trial (RCT) and an Observational Study, to answer a peer’s causal question. They draw a DAG, identify confounders, and write an analysis plan. 5. Prediction: Students find the “best” simple linear regression model to predict a numerical outcome. Project 4 is related to the material covered in the one-week causal DAG module described here. It synthesizes study design, confounding, and DAG reasoning, and it leverages authentic student-generated research questions collected on the first day of class. 2.3 Project: Designing a study to answer a peer’s causal question This project is a realistic application of material on study design and drives the entire module. Students must design a study, considering both an randomized controlled trial (RCT) and an observational study in order to to answer a peer’s causal question. They are asked draw a DAG, identify confounders, write an analysis plan, simulation data and present sample results. This project requires students to synthesize all the causal reasoning skills developed throughout the module and builds on material previously covered in the course on descriptive statistics. Here is how I implement the project in my courses: Day 1: Collecting authentic causal questions (setup for the project) On the first day of class, after introducing the syllabus, defining “Statistics”, and sharing examples of statistics in action, I ask students to write a few research questions they are interested in answering on notecards. These questions are typically causal, reflecting students’ natural curiosity about interventions and comparisons. Here are some examples from my courses: • Are people with older siblings who attended college more likely to attend college than people without older siblings who attended college? •Does the quality of sleep cause people to be successful or not? •Will upgrading to 5G affect people’s brain function? •Do students learn more when sitting at small group tables than when sitting in rows? 4 •Does assigning homework improve student achievement? •Do high school students learn more if their school has a later start time? •Does doing work on Apple devices instead of Windows devices improve productivity? •Do video games affect academic performance? These questions are set aside until project 4, by which time students have learned basic probability, sampling methods, descriptive statistics, hypothesis testing, confidence intervals, and the basics of study design. I then randomly assign each student a causal question written by a classmate, ensuring that students engage with questions they did not generate and cannot cherry-pick for simplicity. Also ensuring that everyone is working on answering a question that at least one person cares about answering! The project then has two main components: Part A: Eight guiding questions for study design. These eight questions are designed to lead students step by step through the process of choosing and justifying an appropriate study design for their assigned causal question. By answering them, students build a plan for both an RCT and an observational study, consider potential confounders, and decide how best to generate strong evidence in their project report. 1. Identify the explanatory variable and response variable for the research question. Make sure both are well-defined (for example, if the response is “good” or “bad,” define “good” with a specific measure and cutoff). 2. Identify the observational units (people or objects) from whom you could collect data on these variables. 3. Decide whether results should be summarized by a difference in means or a difference in proportions (hint: consider the type of response variable). 4. Describe how a randomized controlled trial (RCT) would be carried out to answer the research question (don’t worry about feasibility, just explain what would need to happen to conduct a true RCT). 5. If the RCT shows a difference between treatment groups, state two main possible explanations for this difference (e.g., causation versus chance). 6. Describe how an observational study could be carried out to answer the research question. 7. If the observational study shows a difference between groups, state three main possible explanations (e.g., causation, confounding, or chance). 8. Identify a potential confounding variable for the observational study. Draw a DAG (Directed Acyclic Graph) and explain how this variable could impact both the explanatory and outcome variables. Part B: Summary report with simulated data. Students synthesize their answers into a one-page report addressed to their classmate, describing the study design they recommend as the best balance between feasibility and providing strong evidence of a cause-and-effect relationship. The report must include: 1. Simulated data and summary table: students create hypothetical data for the explanatory and response variables (and the confounding variable, if applicable), summarize the data, and present the results in a table. For students without programming experience, this can be done in a spreadsheet, with simulated data created by entering plausible numbers into the spreadsheet. Students with programming skills or those comfortable using AI tools may use ChatGPT’s Data Analyst or similar tools to simulate data under a specified scenario. The table should show the relationship between treatment and response, stratified by the confounder if appropriate. 5 2. Sample interpretation and conclusion: students write a brief interpretation of the simulated results (e.g., “The table shows that among students who took AP Calculus, 90% passed at Timber Ridge compared to 80% at Wild Horse. . . ”) and state all relevant potential explanations for the observed difference (e.g., causation, confounding by other, unmeasured variables, or chance). 3. Recommendation for study design: students recommend either the RCT or the observational study based on feasibility and strength of evidence, justifying their choice. 2.4 Learning outcomes for the causal DAG module Working backward from the study design project, I identified specific skills students would need to successfully complete it. The one-week module adds the following learning outcomes to the study design and confounding unit of my course. Outcomes 1, 7, 8, and 9 (marked with †) represent content that is not yet typically covered in introductory statistics or data science courses; the remaining outcomes related to standard study-design topics. Learning outcomes related to study design and confounding: 1. †Distinguish between causal and non-causal research questions. Students should recognize that questions like “Does homework improve achievement?” are causal (asking about an intervention or comparison), while “What is the average GPA?” is descriptive, and “Can we predict stock price from social media?” is a situation where mere correlation might suffice. 2. Identify the explanatory variable and the response variable in a comparative question. Students should be able to parse a causal question into the possible cause (explanatory) and the effect of interest (response), ensuring both are well-defined and measurable. 3. Identify a randomized controlled trial (RCT) study design and assess its feasibility. Students should be able to recognize how random assignment would be implemented for a given question (e.g., “randomly assign students to receive homework or no homework”) and evaluate whether such a design is ethical and practical. 4. Identify an observational study design and assess its feasibility. Students should be able to describe how data could be collected without random assignment (e.g., “survey students about whether they were assigned homework and measure their achievement”) and recognize when an observational study is a viable approach. 5. Assess the internal validity of data collected in an RCT or observational study by listing possible explanations of the analysis results. Students should be able to articulate that an RCT showing a difference generally has two potential explanations (causation or chance), while an observational study has three (causation, confounding, or chance). 6. Identify a possible confounding variable for a given pair of explanatory and response variables. Students should be able to propose a third variable that plausibly influences both treatment choice and the outcome of interest (e.g., “geographic location could affect both university choice and calculus success”). 7. †Draw a Directed Acyclic Graph (DAG) for a causal research question involving three variables. Students construct a DAG with nodes for an explanatory variable X , response variable Y , and a third variable C , placing arrows to represent causal influence (e.g., C→X,C→Y,X→Y). 6 8. †Use a DAG to determine if a third variable is a confounding variable. Students apply the graphical criterion: a variable C is a confounder of X→Y if there are arrows C→X and C→Y , creating a back-door path from X to Y . They distinguish confounders from mediators (where X→C→Y ) and colliders (where X→C←Y). 9. †Use the method of subclassification (stratification) to determine whether there is evidence of a causal relationship when one confounding variable is present. Students compute the treatment effect separately within each level of the confounder (e.g., “among AP Calculus students” and “among non-AP students”), compare these stratum-specific effects, and optionally combine them via the g-formula to estimate the average causal effect. Prerequisite knowledge. Students should have already covered descriptive statistics for one and two variables (e.g. means, proportions, cross-tabulations, and correlation coefficient). Hypothesis tests and confidence intervals for one or two means/proportions can be covered either before or after the DAG module; the module itself focuses on design and confounding control rather than formal inference, making it flexible with respect to the inference sequence. 2.5 The university example: Wild Horse Tech vs. Timber Ridge Tech I use the Wild Horse Tech vs. Timber Ridge Tech example as my central pedagogical anchor for the one-week module. This example is adapted from Pearl and Mackenzie’s The Book of Why (2018), modified to use a relatable context for my students: two polytechnic universities in the same state, and a Chancellor’s Office trying to decide which does a better job teaching calculus to incoming freshmen. (Pearl and Mackenzie 2018) I present the example in lecture as follows: The scenario: Each university has a calculus class of 200 students. A comparison of passage rates shows: University Passed Calculus Timber Ridge 150/200 (75%) Wild Horse 154/200 (77%) The central question: More students passed overall at Wild Horse. But is this a fair comparison? Should the Chancellor’s Office conclude that Wild Horse does a better job teaching calculus? Students quickly recognize the comparison may not be fair if the two universities enroll different types of students. This leads to my suggestion that including AP Calculus background might be helpful: Wild Horse enrolls many more students who took AP Calculus in high school (170 of 200 = 85%) compared to Timber Ridge (50 of 200 = 25%). A stratified comparison, adjusting for AP Calculus background: University AP Calculus No AP Calculus Combined Timber Ridge 45/50 (90%) 105/150 (70%) 150/200 (75%) Wild Horse 136/170 (80%) 18/30 (60%) 154/200 (77%) When we stratify by AP Calculus background, the conclusion reverses: Timber Ridge actually has higher success rates in both strata (90% vs. 80% among AP students; 70% 7 vs. 60% among non-AP students), even though Wild Horse appears better in the overall comparison. This is a classic example of Simpson’s paradox, where the marginal association contradicts the conditional associations within every stratum. The g-formula can optionally be applied to reweight these stratum-specific effects to estimate the true causal effect (see Section 5 for the full calculation). A second comparison: should we adjust for tutoring center usage? To reinforce the distinction between confounders and other third variables, I next introduce another variable and ask if we should adjust for it. I chose Tutoring center usage, a variable measured after students enroll at the university: University Used Tutoring Center Didn’t Use Tutoring Center Combined Timber Ridge 86/120 (71%) 64/80 (80%) 150/200 (75%) Wild Horse 65/90 (72%) 89/110 (81%) 154/200 (77%) Within each stratum, Wild Horse still has similar or slightly higher pass rates, and the crude comparison (77% vs. 75%) is roughly maintained. Unlike AP Calculus, stratifying by tutoring center usage does not reverse the conclusion. Crucially, we should ignore this breakdown entirely because tutoring center usage is a mediator: it is part of the university’s effect on student success. Going to the tutoring center happens after students enroll and is influenced by the university’s resources, culture, and support systems. If Wild Horse provides better tutoring access or encourages more students to use it, that is part of the treatment, not a confounder. After the students and I puzzle out the appropriate rates to compare based on context, I offer to teach the students a simple visual tool for deciding when comparisons should should be adjusted: this is the causal DAG. I proceed as follows: • Drawing a 3-node DAG C→X→Y with C→Y (where C =AP Calc, X =University, Y=Pass). • Explaining why AP Calc is a confounder of X→Y based on a visual inspection of the direction of the arrows. • Identifying that the minimal sufficient adjustment set is {C} , with a vague explanation that we can think of correlation existing on all paths from X to Y and that we need to “close” non-causal paths. • Drawing a 3-note DAG but with the third variable being tutoring center usage rather than AP Calc: this diagram has only causal paths so we should leave them all “open”. • Computing a simple g-formula estimate using stratified two-by-two tables (see Section 5 for the worked example) or just comparing rates within each level of the confounding variable and ignoring the non-confounding variable. The process does not end with simply comparing calculus pass rates across strata defined by AP Calculus background. At this stage in the lesson, I challenge students to consider the conditional validity of their conclusions: if the DAG structure (and the associated assumptions) accurately captures the relevant relationships, then subclassification by AP Calculus is appropriate, and under this adjustment Timber Ridge would appear superior. However, I encourage students to scrutinize the causal diagram: have all relevant variables, particularly those influencing both university choice and calculus success, been included? This highlights for students that DAGs serve as reasoning frameworks grounded in explicit assumptions rather than as automatic guarantees of causal validity. Students must confront 8 the possibility that omitted variables such as student motivation or socioeconomic status could undermine the analysis. To emphasize this, I explain that, contingent upon accepting the DAG and its assumptions, the necessary adjustment set can be identified either manually or with tools like DAGitty. Yet, the real answer to “which university is better?” remains uncertain without confidence in the diagram’s completeness and the availability of appropriate data. Making a fair comparison of calculus passage rates therefore requires collecting information not only on university attended and calculus passage but also on factors such as student motivation, SES, and AP Calculus background, assuming these are suggested by the DAG as confounders. When I have presented similar tables to students or even faculty and take a vote, the audience is usually equally split between which school is better. Causal DAGs provide an easy way to see that “AP Calculus” is a confounder (and should be acted upon) while “Tutoring Center” is not. The confounder in a DAG has arrows going out to both the potential cause and effect of interest: C→X and C→Y . Mediators and colliders don’t have this pattern: mediators have X→M→Y (part of the causal pathway), while colliders have arrows coming in from multiple sources. Students learn that*only variables on back-door paths (confounders) should be adjusted; variables on forward paths (mediators) and other graph structures (colliders) should not be conditioned on when estimating total causal effects. 2.7 Common student challenges Successfully completing the project requires students to master three core ideas, each of which presents characteristic difficulties: 1. Random assignment vs. random selection (a persistent confusion). I’ve noticed that students often conflate random assignment (the mechanism that creates a valid RCT by balancing confounders across treatment groups) with random selection (a sampling method that ensures representativeness of a population). • Random assignment makes groups comparable (eliminates confounding) but does not guarantee the sample represents any larger population. • Random selection makes the sample representative (supports generalization) but does not eliminate confounding if treatment is observational. A study can have random selection without random assignment (e.g., a representative survey asking whether people chose to attend college; confounding remains), random assignment without random selection (e.g., a lab experiment with volunteer participants; no confounding, but limited generalizability), both, or neither. 2. Identifying a confounding variable (the central challenge). In my experience this is the hardest conceptual hurdle for students. A confounder must satisfy two conditions: (i) it influences treatment/exposure choice or assignment, and (ii) it influences the outcome. Students frequently propose variables that satisfy only one condition (e.g., “age is a confounder” without explaining how age affects both university choice and calculus success) or propose mediators (variables caused by the treatment) as confounders. The module addresses this by teaching students to: • Draw a 3-node DAG with the candidate confounder C , the treatment X , and the outcome Y . If arrows C→X and C→Y both belong in the graph, C is a confounder. • Justify each arrow with a concrete mechanism (e.g., “Students who took AP Calculus in high school ( C = 1) are more likely to choose a university known for strong STEM programs ( C→X ), and are also more likely to pass Calculus I regardless of which university they attend (C→Y)”). 9 with. That new baseline raises the value of explicitly taught causal skills: specifying the estimand, drawing and critiquing a DAG, identifying a valid adjustment set, and articulating the assumptions under which the estimate has a causal interpretation. 8. So your students have seen a one week module. What’s next? The one-week module was developed using backward design, starting with the end goal of students who can perform rigorous causal inference and working backward to identify prerequisite skills. This suggests three levels of implementation: Level 1: Within an intro stats/DS class (this paper’s focus) Students identify causal questions, draw simple DAGs, recognize and adjust for simple confounding, and design basic observational studies. Level 2: Within a standard course in regression or shallow ML Transition from causal DAGs to Potential Outcome Framework, interpret SUTVA, distinguish causal vs. predictive modeling. Level 3: One full course in causal inference Perform rigorous causal inference using various datasets with appropriate method selection and sensitivity analysis. For programs seeking comprehensive causal reasoning across STEM disciplines, a fourcourse pathway leverages existing courses with minimal modifications: (1) Intro stats/DS (modify ~1 week), (2) Probability Theory (use existing), (3) Regression/ANOVA (modify ~2 weeks), (4) Causal Inference (new). This requires minimal curricular disruption while providing comprehensive causal reasoning skills. For programs seeking or maintaining ABET accreditation, both the Computing Accreditation Commission (CAC) and the Applied & Natural Science Accreditation Commission (ANSAC) publish discipline-specific program criteria for Data Science, Data Analytics, and similarly named programs. The ABET Data Science program criteria explicitly require applied statistical and mathematical topics including inference, modeling, linear algebra, probability, and optimization, plus computing topics including data structures and algorithms. A causal inference sequence maps directly onto these requirements. Official sources: - CAC (Computing): Data Science, Data Analytics and Similarly Named Computing Programs, 2025–2026 Criteria. See Program Criteria under Criterion 5 (Curriculum). Available at: https://www.abet.org/accreditation/accreditation-criteria/criteria-foraccrediting-computing-programs-2025-2026/ - ANSAC (Applied & Natural Science): Data Science, Data Analytics and Similarly Named Programs, 2025–2026 Criteria (Baccalaureate, Curriculum section). Available at: https://www.abet.org/accreditation/accreditationcriteria/criteria-for-accrediting-applied-and-natural-science-programs-2025-2026/ Table 2. Minimal operationalization of ABET Data Science program criteria. ABET DS topic Typical course(s) that satisfy it Example program-level outcome you can assess Data acquisition & representativeness Intro DS; Data Wrangling “Explain sampling/coverage limits; justify representativeness.” Data management; preparation/integration Databases; Data Engineering “Design a pipeline; implement joins/ETL reproducibly.” Analysis; model development & deployment Intro ML; Statistical Learning “Train/evaluate models; communicate model limits.” 16 ABET DS topic Typical course(s) that satisfy it Example program-level outcome you can assess Visualization & communication Data Viz; Technical Writing “Create audience-appropriate displays with uncertainty.” Ethics (legitimate use, algorithmic fairness) DS Ethics; Responsible AI “Identify risks; apply fairness checks; document decisions.” Governance (privacy, security, stewardship) Privacy/Security for DS “Apply privacy-aware workflows; manage sensitive data.” Math/Stats: inference, modeling, linear algebra, probability, optimization Calc/Linear Algebra; Probability & Statistics; Optimization for DS “Derive/justify estimators; analyze convex objectives.” Computing: data structures & algorithms Programming II; Data Structures & Algorithms “Analyze algorithmic complexity; choose appropriate ADTs.” Advanced DS depth Electives (e.g., NLP, causal inference, time series) “Synthesize methods to a new domain problem.” Application area Domain minor or track “Integrate domain constraints into DS design.” Major project Capstone “Deliver a full protocol-to-report artifact.” The one-week DAG module addresses data-science lifecycle framing (fair comparison, not just prediction), ethics and governance (honest causal claims), and communication (articulating assumptions in plain language). Regression/ANOVA with DAG-based identification explicitly meets the applied statistical topics requirement. A causal inference elective contributes to advanced DS depth and yields capstone-ready protocols. Programs can cite this sequence as evidence for the inference/modeling requirement, the advanced-depth requirement, and the major-project requirement in accreditation reviews. 9. Recommended Resources For instructors and students wanting to deepen their understanding of causal inference, I recommend the following resources organized by purpose: Books and Courses For concise examples with R: (Brumback 2022) provides Fundamentals of Causal Inference: With R, offering accessible examples for computational implementation. For a calculus-free approach: (McElreath 2023) Statistical Rethinking course materials (freely available on GitHub) present Bayesian methods and causal thinking without requiring calculus prerequisites. For detailed guidance on drawing DAGs: (Huntington-Klein 2021) Chapter 6 in The Effect offers excellent instruction on constructing and interpreting causal diagrams, with many worked examples available at theeffectbook.net. 17 For exercises with solutions: (Pearl, Glymour, and Jewell 2016) Causal Inference in Statistics: A Primer provides structured exercises that build intuition for graphical models and identification strategies. For introducing potential outcomes: (Imai 2022) Quantitative Social Science: An Introduction by Kosuke Imai offers a gentle entry point to the potential outcomes framework with real social science applications. For comprehensive coverage: (Hernán and Robins 2020) Causal Inference: What If by Hernán & Robins is a free textbook, covering both graphical and potential outcomes approaches with epidemiological examples. Software and Online Tools DAGitty: Interactive web-based tool for drawing and analyzing causal diagrams (DAGs), available at dagitty.net. Includes built-in algorithms for identifying adjustment sets and testable implications. DoWhy (Python): Microsoft’s Python library for causal inference that integrates with common data science workflows. Full documentation at https://www.pyvwhy.org/dowhy/. causaldiagrams.org: Curated tutorials and research article database providing examples and pedagogical resources for teaching with DAGs. R package causaldata: Collection of datasets specifically designed for teaching causal inference, available on CRAN. Exemplar Classroom Implementation (Cummiskey et al. 2020) describe an excellent implementation of causal inference in introductory statistics courses, demonstrating how DAG-based reasoning can be integrated into existing curricula with minimal disruption. Their paper in the Journal of Statistics Education provides practical classroom examples and assessment strategies. 10. Conclusion In an era where AutoML and AI assistants can generate code and fit sophisticated predictive models, undergraduate statistics education should prioritize causal reasoning, the analytical skill that remains irreducibly human and professionally consequential. This paper presents a complete, classroom-tested module that introduces directed acyclic graphs, the backdoor criterion, and causal assumptions in an introductory statistics or data science course, addressing a critical gap in undergraduate data literacy education. By teaching students to identify confounders early, before they master hypothesis testing or regression, we equip them to critique descriptive summaries, visualizations, and automated analyses with the same rigor they bring to formal inference. Additionally, students will develop the critical thinking skills necessary to evaluate causal claims in news, health information, and policy discussions. 18 11. 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