Data representation, distributions, and statistical variability using sampling and inference techniques. Integrates probability models, compound events, bivariate patterns, and linear models to guide data-driven decision making.
A 45-minute investigation into the world of data manipulation, covering misleading graphs, correlation vs. causation, and source credibility.
A quick, functional introduction to interpreting bar and pie charts using real-world life skills scenarios like budgeting and time management.
A collection of 10 distinct data analysis work samples featuring bar and circle graphs, designed for MCAS Alt portfolio evidence. Each sample focuses on identifying key information, making comparisons, and calculating totals.
A high school statistics and math lesson that uses data from the War on Drugs to explore disproportionate impact, ratio disparities, and data visualization. Students calculate and visualize significant statistical gaps in drug-related arrests, sentencing, and global incarceration rates.
Students apply ratios and percentages to analyze electoral fairness. They will learn to identify 'packing' and 'cracking' strategies and calculate a simplified efficiency gap to mathematically prove gerrymandering in a hypothetical state.
A math and statistics lesson where students interpret campaign spending data from a Crash Course video, visualize the scale of billions, and create comparative graphs against consumer spending habits.
A 6th-grade integrated math and science lesson where students analyze environmental data about the Great Lakes and Lake Baikal. Students practice interpreting and creating double bar graphs to explore the relationship between lake surface area and depth.
A data-focused lesson where students analyze the population decline of endangered species through statistics, percentage calculations, and visual graphing. Students use real-world data from a documentary to understand the severity of the biodiversity crisis.
A hands-on exploration of rarity and simple probability through the lens of pearl formation in oysters. Students simulate a pearl hunt and use data to understand why rare items are valued.
Students will interpret and analyze pie graphs in a financial context, calculating actual dollar amounts from percentages to compare different family budgets. The lesson features a video-guided quiz and a hands-on 'Budget Analyst' activity.
A math intervention lesson focused on converting data into pie graph components through fractions, decimals, percentages, and degrees. Students follow a structured workflow modeled after a financial budget scenario to master circle graph construction.
A Kindergarten to 1st Grade introduction to tally marks, focusing on the concept of bundling groups of five to count data efficiently. The lesson includes a video-guided observation activity, hands-on stick bundling, and a dice-rolling tally game.
Students learn to convert fractions to percentages by finding equivalent fractions with a denominator of 100, starting with a bakery-themed scenario and concluding with a classroom data analysis project.
Students become data detectives as they analyze real-world scenarios to determine which graphical representation—Stem-and-Leaf, Scatter Plot, Histogram, or Box-and-Whisker—best reveals the secrets hidden within the numbers.
Students will master the art of organizing numerical data using stem-and-leaf plots, identifying the mode and median to uncover trends within a dataset. This lesson uses a detective theme to solve a 'Family Reunion Mystery' using age data.
A math lesson where students learn to read analog electric and water meters, calculate monthly consumption, and determine the total cost based on unit rates. Includes a video-based instruction segment and a mock utility bill audit activity.
This lesson helps students transition from a concrete list of numbers to an organized stem and leaf plot using a physical sorting strategy. It includes a video warm-up, a hands-on 'Number Tile' sorting game, and a guided template for creating the final plot.
A lesson focused on creating stem and leaf plots for large numbers (over 100) and the critical importance of including a 'Key' to eliminate ambiguity. Students analyze bowling scores and practice identifying median, mode, and range.
A comprehensive 8th-grade math lesson focused on creating and interpreting stem and leaf plots using decimal data, featuring an Olympic sprinting theme and real-world data analysis.
A detective-themed lesson where students investigate 'crime scenes' (incorrect stem and leaf plots) to identify, explain, and correct common errors in data visualization.
Introduction à la distribution normale, au calcul des scores Z et à l'utilisation de la table de probabilités pour l'inférence.
Apprendre à choisir le bon graphique pour le bon type de données : histogrammes, boîtes à moustaches et diagrammes de dispersion.
Calculer et interpréter la moyenne, la médiane et le mode, ainsi que la variance et l'écart-type pour décrire la forme d'une distribution.
Comprendre la nature des données : variables qualitatives vs quantitatives, échelles de mesure (nominale, ordinale, intervalle, rapport) et introduction à l'échantillonnage.
A comprehensive ACT Math preparation module focusing on core concepts, time management strategies, and targeted practice across all test categories.
A comprehensive look at how 5th-grade mathematics is applied in various professional fields, featuring real-world problem-solving and career research.
A comprehensive 20-question practice test and answer key designed to prepare students for the TSIA2 Mathematics assessment, focusing on algebraic, geometric, and statistical reasoning.
A math-integrated lesson exploring the magnitude of the Amazon rainforest and the statistical impact of deforestation using large numbers and percentages.
A high school math lesson exploring the gap between theoretical and experimental probability through a die-roll simulation. Students investigate the Law of Large Numbers and analyze why variability decreases as sample sizes increase, concluding with a real-world look at casino economics.
Students will apply arithmetic operations like multiplication, addition, and division to calculate Grade Point Averages (GPA), exploring the concept of weighted averages through a real-world academic lens.
A foundational lesson for 8th-grade students to master the midpoint formula using the concept of averages, focusing on positive integers and physical movement.
Students will investigate how changing bin sizes in a histogram can drastically alter the interpretation of a single data set of 50 temperatures. They will practice the 'inclusive lower limit' rule, watch a video demonstration, and engage in a 'Bin Size Battle' to determine which interval size provides the most honest representation of the data.
A hands-on math lesson where 6th grade students become the data points, physically constructing a box-and-whisker plot using their own heights to understand the five-number summary.
A high-school level lesson for AP Calculus and Statistics students focusing on using Desmos for complex integrals and statistical calculations, emphasizing the balance between manual understanding and technological efficiency.
A hands-on lesson where students physically represent data points to understand the five-number summary and construct box and whisker plots.
Students will investigate how extreme values (outliers) affect the mean and median using a corporate salary dataset. They will practice calculating the 5-number summary, identifying outliers using the 1.5xIQR rule, and constructing box plots.
A mathematics lesson where students learn to identify outliers using the 1.5xIQR rule and graph them accurately on box and whisker plots.
A hands-on lesson where 7th-grade students collect class shoe size data, calculate the 5-number summary, and construct precise box and whisker plots to analyze data spread and symmetry.
A lesson where students compare two battery brands using double box plots to determine which is 'better' based on median performance, consistency (IQR), and maximum range. Students will learn to calculate five-number summaries and construct stacked box plots on a single number line.
A data analysis lesson where students compare rainfall line plots to draw evidence-based conclusions. Includes a video-guided tutorial on constructing line plots with fractions and a collaborative analysis activity.
A lesson focusing on the real-world application of absolute value through the lens of scientific error and a hands-on beanbag tossing activity.
Students will learn to calculate and interpret standard deviation as a measure of consistency. This lesson uses a sports-themed scenario to compare data sets with identical means but different spreads.
Students step into the role of an investment advisor to evaluate the risk and consistency of three stocks using measures of dispersion (Range, IQR, and Standard Deviation). They will use their calculations to make a data-driven recommendation for a risk-averse client.
In this lesson, 9th-10th grade students analyze data spread using Box and Whisker plots and Interquartile Range (IQR). Students compare the consistency of professional basketball players by calculating quartiles and visualizing distributions.
A high school math lesson exploring why central tendency (mean) can be misleading and how measures of dispersion (range, IQR, standard deviation) provide necessary context for decision-making.
An AP Statistics lesson exploring how outliers impact measures of dispersion (Range, IQR, and Standard Deviation), featuring a video-based case study and a spreadsheet simulation to determine which statistics are 'resistant'.
A comprehensive introduction to calculating sample standard deviation by hand, focusing on the concept of variability and consistency using quiz score comparisons.
This lesson explores the conceptual and mathematical differences between population and sample standard deviation, focusing on the derivation and application of Bessel's correction (n-1) to ensure unbiased estimation. Students will analyze video demonstrations, perform comparative calculations, and conduct a sampling simulation to witness bias in action.
Students will learn to distinguish between permutations (order matters) and combinations (order doesn't matter) through a video-based discussion and a card-sorting activity.
Students will master the distinction between permutations and combinations by identifying keywords in complex word problems. This lesson uses a 'Keyword Detective' theme to help students analyze scenarios for order-dependence versus group-membership.
Students explore the deep connection between the recursive nature of Pascal's Triangle and the combinatorial formula C(n,k), moving from basic addition to algebraic derivation.
A 12th-grade Pre-Calculus lesson that bridges the gap between combinatorics and algebra by introducing the Binomial Theorem through the lens of combination notation. Students will discover how combinations determine the coefficients of expanded binomials.
A 10th-grade statistics lesson where students derive and apply the combination formula by investigating how 'sharing' or grouping items removes the importance of order, culminating in a probability analysis of a class lottery.
Students will construct Pascal's Triangle and explore the mathematical logic of the symmetry of combinations ($nCr = nC(n-r)$) through visual patterns and algebraic reasoning.
A collaborative high school math lesson where students use Pascal's Triangle to solve complex combination and probability scenarios in a high-stakes 'Casino Roy-Al' theme.
A lesson connecting Pascal's Triangle to probability outcomes and path-finding permutations for high school statistics students.
This lesson guides students through the discovery of advanced patterns within Pascal's Triangle, moving from basic combinations to complex identities like the Hockey Stick and Fibonacci sums. Students transition from procedural calculation to visual mathematical investigation.
This lesson introduces 5th-grade students to the concept of probability using a 0 to 1 number line. Students explore likelihood vocabulary, analyze a dice-rolling experiment through video, and apply their learning by placing real-world and mathematical events on a probability spectrum.
A hands-on introduction to simple probability where 6th grade students use their own classroom population as a sample space to calculate and simplify probabilities.
Students explore simple probability and sample space through a station-based lab, using dice, marbles, and spinners to calculate P(event) while addressing common misconceptions.
A 7th-grade math lesson where students apply simple and complementary probability concepts to design their own closet inventory and challenge peers with probability questions.
Students investigate and debunk the common 'Category Trap' in simple probability. They will learn to distinguish between the number of categories and the total number of individual outcomes to accurately define sample spaces.
A lesson on calculating permutations with indistinguishable objects, specifically focusing on repeating letters in words. Students will analyze the 'DAD' scramble, watch a tutorial on 'ALABAMA' and 'MISSISSIPPI', and calculate the permutations of their own names.
A high school math lesson focused on using the Fundamental Counting Principle (the 'Slot Method') as a flexible alternative to the permutation formula for solving arrangement problems. Students transition from tree diagrams to multiplying possibilities for seating, passwords, and license plates.
A high school math lesson focused on distinguishing between and calculating permutations and combinations using nPr and nCr formulas. Includes a video-based instruction phase, a collaborative sorting activity, and a creative exit ticket assessment.
A high-school level math lesson that applies the concept of combinations to real-world scenarios like lottery draws and poker hands. Students explore why order doesn't matter in these contexts and calculate the astronomical odds of winning.
Students learn to construct and interpret probability tree diagrams using percentages and counts, grounded in a real-world census-themed activity. The lesson utilizes a detailed math tutorial video for direct instruction followed by a hands-on data interpretation task.
A 10th-grade statistics lesson focused on distinguishing between permutations (where order matters) and combinations (where order doesn't matter) using tree diagrams and compound probability. Students will analyze the impact of order on whether to add multiple branches of a probability tree or focus on a single path.
A comprehensive lesson on probability tree diagrams and compound events for 7th-grade students, featuring a video-based exploration of independent events and a hands-on creative activity.
Students will learn to distinguish between independent and dependent events by exploring how probabilities change when items are not replaced, using tree diagrams to visualize outcomes.
A high-school level lesson focused on the efficiency of the probability complement rule (\(1 - P(\text{not } E)\)) for solving 'at least one' problems in multi-stage experiments.
A middle school math lesson focused on identifying the linguistic cues that distinguish independent from dependent compound events in word problems. Students analyze scenarios to see how the sample space changes (or doesn't) based on specific keywords.
A comprehensive lesson on compound probability where students use the multiplication rule to solve problems involving independent and dependent events, themed around a bagel shop.
A high-level honors probability lesson where students explore compound events through card challenges, a structured video review, and a hands-on 'Mystery Bag' experiment comparing theoretical models to experimental data.
A visual exploration of compound probability, focusing on how 'without replacement' scenarios change the sample space. Students use a marble jar motif to track denominator shifts during a guided video viewing and collaborative practice.
A high school statistics lesson focused on identifying and creating biased polls to understand sampling error and selection bias in political contexts.
A hands-on exploration of theoretical versus experimental probability using a dice rolling lab and video analysis. Students compare mathematical expectations with real-world data to discover how sample size affects results.
Students investigate the fairness of dice by conducting 50 trials and comparing experimental outcomes to theoretical probability. Using a provided video and data collection sheets, they learn to distinguish between normal statistical variation and evidence of a rigged game.
A review lesson where students are presented with mixed scenarios (proportions vs. means, paired vs. independent). They must select the appropriate test and justify their choice, reinforcing the decision-making skills required for the AP exam or real-world analysis.
Students participate in a live sensory experiment to generate paired data, performing the complete inference procedure to determine if a preference exists between two products.
Students perform hypothesis tests and calculate confidence intervals for the mean difference. The lesson emphasizes treating the differences as a single sample for a one-sample t-procedure.
Students focus on the mechanics of calculating differences for matched pairs and visualizing these differences to check for normality before inference.
The project concludes with students synthesizing their findings into a final presentation, focusing on clear communication of complex statistical results to a general audience.
Teams select and perform appropriate hypothesis tests and confidence intervals, verifying conditions and interpreting p-values in the context of their specific research questions.
Students use graphical displays and summary statistics to explore their collected data, cleaning datasets and identifying preliminary trends before formal inference.
Focusing on the practical and ethical aspects of research, students execute their sampling plans while addressing challenges like non-response bias and ensuring participant anonymity.
Students formulate a research question comparing two populations and design a sampling methodology that minimizes bias. They submit a formal research proposal for approval before beginning data collection.
Students distinguish between independent and paired designs, understanding how matching reduces nuisance variation and when each design is appropriate.
Focus on articulating conclusions in non-technical language and discussing Type I and Type II errors. Students differentiate between statistical and practical significance.
An 11th-grade statistics lesson exploring the Gambler's Fallacy through conditional probability and hands-on experimentation. Students investigate whether past coin flips influence future outcomes using data tracking and the P(A|B) formula.
Computational estimation of expected payoffs for path-dependent derivatives using Geometric Brownian Motion and Monte Carlo simulations.
Analysis of tail risk through Value at Risk (VaR) and Expected Shortfall, focusing on the limitations of normal distributions.
Introduction to risk-neutral measures and binomial pricing models, using expected values to price options without arbitrage.
Application of expected value to asset returns using matrix algebra to derive the Efficient Frontier and optimize portfolios.
Students contrast mathematical expected value with expected utility to explain decision-making under uncertainty, analyzing different utility functions to model risk-averse behavior.
Part 2 of the simulation focusing on analysis, interpretation, and presenting findings to a simulated 'board of directors'.
Part 1 of a simulation where students act as consultants to clean, organize, and select the correct test for a messy real-world dataset.
A conceptual exploration of statistical power, investigating how sample size and effect size influence the ability to detect differences.
Explores the real-world impact and definitions of Type I and Type II errors within the context of comparative studies.
Students master the logic of selecting between 2-sample t, paired t, and 2-prop z tests based on data structure and study design.
A culminating simulation where students act as a review board, synthesizing p-values, errors, and effect sizes to make evidence-based funding recommendations.
An introduction to quantifying the magnitude of differences using Cohen's d and other effect size measures to provide context to statistical findings.
Students distinguish between statistical results and real-world impact by analyzing how massive sample sizes can produce significant results for negligible differences.
An exploration of Type I and Type II errors, their consequences in fields like medicine and technology, and the use of truth tables to visualize statistical outcomes.
Students explore the conceptual meaning of P-values as conditional probabilities and debate the selection of significance levels (alpha) in different contexts.
A tiered assignment covering TEKS A.4(A-C) focusing on correlation, causation, and linear regression. Students progress through three levels of complexity to master data analysis skills.
A lesson where students use point-slope form to model real-world statistics, research their own data points, and forecast future trends.
Students explore the practical application of linear equations by analyzing data trends, specifically focusing on negative correlations and calculating x-intercepts to predict when values hit zero. The lesson uses a real-world tech-transition video as a springboard for extrapolation.
Students explore bivariate data by measuring their own physical proportions, creating a class-wide scatter plot, and identifying correlations and outliers. The lesson includes a video hook, hands-on data collection, and collaborative graphing.
An 11th Grade Advanced Algebra lesson exploring the boundaries of mathematical modeling. Students distinguish between interpolation and extrapolation while analyzing when exponential models fail due to real-world constraints like carrying capacity.
Students will learn to use the R-squared value in GeoGebra to mathematically justify the choice between linear and exponential regression models through a competitive 'Regression Battle' activity.
A lesson introducing students to regression and the 'line of best fit' by moving from manual estimation to computer-aided modeling using real-world messy data.
Students transition from textbook-perfect functions to real-world data analysis using GeoGebra. They will learn to perform linear and exponential regressions, interpret the R-squared value to determine the best fit, and apply these skills to distinguish between population growth and linear accumulation.
A technical, hands-on lesson teaching 11th-grade students how to perform linear and exponential regressions using GeoGebra, transitioning from textbook examples to messy real-world data analysis.
A high school interdisciplinary lesson connecting physics and algebra. Students analyze real-world lab data using linear and exponential regression in GeoGebra, exploring why experimental data rarely fits perfect mathematical models and how R-squared measures the quality of a fit.
Students analyze complex graphs from news media (infographics), identifying how visual choices influence interpretation. They conclude by creating their own accurate graph to represent a dataset, ensuring visual honesty.
Students take raw data tables and practice plotting points to visualize non-linear trends (quadratic or exponential). They learn to sketch smooth curves to predict future data points, visualizing growth and decay.
Focusing on systems of linear inequalities and equations, students explore what it means visually when lines cross or regions overlap. They use shading techniques to represent solution sets for real-world constraints.
Students investigate slope using staircases and ramps to physically and visually understand 'rise over run', transitioning to coordinate planes and gradient calculations.
Students explore qualitative graphing by matching narrative stories to the shapes of lines on a graph without numerical values, focusing on the concepts of rate of change and direction.
Students use their constructed models to extrapolate and answer questions about future events, solving trigonometric inequalities graphically.
Students use graphing calculators or regression software to fit trigonometric equations to data sets. They compare their hand-calculated models to the regression models.
Focusing on the x-axis, students determine the period of real-world cycles. They calculate the horizontal scaling factor and determine appropriate horizontal shifts.
Students learn the algebraic techniques to extract the midline and amplitude from a data table. They practice these calculations on various environmental data sets.
Students plot given data sets and identify the periodic nature of the data. They sketch a 'best fit' curve by hand to estimate the maximums, minimums, and cycle length.
The sequence concludes with an introduction to stochastic sequences, simulating random walks to model stock price movements.
Students analyze bonds as series of cash flows, using differentiation to calculate Duration and assess interest rate risk.
This lesson explores the valuation of infinite horizons, applying geometric series convergence to price perpetuities and the Dividend Discount Model.
Learners model loan payments and savings plans using finite geometric series, deriving amortization formulas for mortgages and annuities.
Students derive the compound interest formulas as geometric sequences, exploring the impact of compounding frequency and the limit as it approaches infinity (continuous compounding).
Introduction to Martingales and the Optional Stopping Theorem, applying these concepts to fair games and boundary crossing probabilities.
Defines conditional expectation as a random variable measurable with respect to a sub-sigma-algebra, utilizing the Radon-Nikodym theorem.
Analysis of Monotone Convergence, Fatou's Lemma, and Dominated Convergence Theorems to determine when limits and expectations commute.
Focuses on the derivation and application of Markov, Chebyshev, Jensen, Hölder, and Minkowski inequalities to bound expected values.
Students define expectation using the Lebesgue integral, moving from simple functions to non-negative random variables and addressing the limitations of Riemann integration.
Exploring Stochastic Gradient Descent (SGD) and its role in navigating high-dimensional, non-convex landscapes in machine learning.
Solving optimization problems under constraints using the method of Lagrange multipliers, focusing on the alignment of gradient vectors.
Implementation of iterative numerical methods, focusing on the geometry of convergence, learning rates, and momentum in gradient descent.
An examination of second-order derivatives via the Hessian matrix to understand surface curvature and classify critical points using eigenvalues.
Students analyze the gradient vector as a directional quantity, establishing its geometric relationship with level sets and proving it indicates the steepest ascent.
Application of stochastic modeling to queueing systems, using Little's Law and steady-state analysis to optimize performance in complex environments.
Transitioning to continuous-time Markov chains using generator matrices and solving Kolmogorov's differential equations for birth-death processes.
Investigation of the Poisson process, its relationship to the exponential distribution, and the implications of the memoryless property in continuous-time modeling.
Analysis of the long-term behavior of Markov chains, focusing on state classification (recurrence, transience) and the computation of stationary distributions.
Foundational concepts of Markov processes, the Markov property, and the mathematical framework of transition matrices and Chapman-Kolmogorov equations.
This lesson guides students through the application of the weighted mean formula to determine solution concentrations. It combines visual learning from video demonstrations with a paper-based lab simulation to reinforce the relationship between volume and concentration 'weight'.
Students synthesize their learning by creating a consumer guide that provides mathematically-backed advice on when to purchase insurance versus when to self-insure.
Students compare different decision-making strategies, such as Maximin and Expected Value, to evaluate complex financial scenarios like car and travel insurance.
A simulation-based lesson where students act as an insurance company to understand risk pooling, premiums, and the impact of deductibles on solvency.
Students use expected value to analyze the financial viability of extended warranties on consumer electronics, determining when protection plans are mathematically sound.
Students categorize risks by frequency and severity, analyzing data to understand the difference between high-probability/low-impact events and low-probability/high-impact catastrophes.
A cumulative project where students model and solve a complex event planning scenario involving risk and reward.
Students explore how changing probabilities impacts the final decision, identifying 'tipping points' in decision models.
Students learn the algorithm for solving decision trees by calculating weighted averages from outcomes back to the start.
A simulation where students evaluate peer-designed games and make data-driven decisions on where to 'bet' their tokens.
A hands-on 7th-grade math lesson where students use colored counters to discover the difference between independent and dependent compound events, supported by a video walkthrough and data collection.
An 8th-grade math lesson focusing on the distinction between independent and dependent events through the lens of replacement. Students explore how the presence or absence of replacement affects probability calculations through video analysis and a hands-on card activity.
Students analyze compound events with and without replacement, comparing the probability of specific sequences versus general outcomes using tree diagrams.
A Pre-Algebra lesson focusing on the addition (OR) and multiplication (AND) rules of probability, featuring a video-based instruction, a probability maze activity, and a reflective journal.
A high-school level lesson focused on designing and solving complex probability word problems using compound events, featuring a 'Stump the Teacher' activity.
Students will learn how to calculate conditional probability using frequency tables, using the metaphor of a 'funnel' to understand how conditions narrow the sample space. The lesson includes a video analysis, a two-way table activity on school lunch preferences, and a visual extension.
A comprehensive 9th-grade Algebra I lesson on conditional probability, focusing on how conditions narrow the sample space using the 'funnel' metaphor. Includes video-guided notes, a hands-on card-sorting activity, and conceptual checks on independent vs. dependent events.
A 10th-grade geometry lesson exploring conditional probability through the lens of 'zooming in' on sample spaces. Students use visual funnel models, video analysis, and real-world data collection to master the P(A|B) notation and distinguish between independent and dependent events.
A high school math intervention lesson focusing on visualizing conditional probability through the 'funnel' metaphor and hands-on manipulatives. Students explore how conditions narrow the sample space and distinguish between independent and dependent events.
A culminating presentation where students share a power function model derived from real-world data, justifying their choice of rational exponent.
Students learn the fundamentals of power regression and use data sets to fit functions of the form y = ax^b, where b is a rational number.
A high school statistics lesson focusing on the ethical implications of handling outliers in scientific data, featuring a historical case study on the Antarctic Ozone Hole.
This lesson focuses on the precision of financial modeling when using rational exponents to calculate interest for partial compound periods.
Applying rational exponents to orbital mechanics, students use Kepler's Third Law to calculate planetary distances and periods.
Students investigate the non-linear relationship between animal mass and metabolic rate, evaluating Kleiber's Law (B = M^(3/4)) to understand biological scaling.
A capstone workshop where students apply their knowledge to critique actual research abstracts, acting as peer reviewers to evaluate the validity of comparative claims.
An investigation into the replication crisis and unethical practices like p-hacking, emphasizing the ethical responsibility of statisticians in reporting findings.
A lesson on using Box-and-Whisker plots to compare two sets of basketball player data, focusing on consistency, range, and the Interquartile Range (IQR).
Students learn to calculate and interpret Cohen's d, distinguishing between statistical significance (is there an effect?) and practical importance (how big is the effect?).
A simulation-based lesson where students manipulate sample size, alpha levels, and effect size to see how they influence a test's ability to detect a true difference between populations.
Students explore the trade-offs between Type I and Type II errors through a courtroom analogy and medical scenarios, understanding the real-world consequences of statistical decision-making.
A culminating case study where students analyze clinical trial data to determine treatment efficacy and write a formal statistical report.
