AP Statistics ✏ In a Nutshell

1. Exploring One-Variable Data

A summary of Exploring One-Variable Data: Categorical and Quantitative Variables, Displaying Categorical Data, Displaying Quantitative Data, Discrete vs Continuous Quantitative Variables, Describing Distributions: SOCS (Shape, Outliers, Center, Spread), Key Terms for Descriptions, Measures of Center, Measures of Variability (Spread), Choosing Appropriate Measures, Identifying Outliers, Comparing Distributions, Measures of Position: Percentiles and Z-Scores, Interpreting Z-Scores, Transforming Data (Adding/Subtracting and Multiplying/Dividing)

2. Exploring Two-Variable Data

A summary of Exploring Two-Variable Data: Relationships Between Two Categorical Variables, Graphical Displays for Two Categorical Variables, Simpson’s Paradox, Relationships Between Two Quantitative Variables, Form Direction Strength and Outliers, Correlation (r), Least Squares Regression (LSR) Line, Interpreting the Slope and Y-Intercept, Making Predictions, Residuals and Residual Plots, Interpreting Residual Plots, Standard Deviation of the Residuals (s), Coefficient of Determination (r²), Transforming Data to Achieve Linearity, Beware of Influential Points and Outliers, Cautions About Correlation and Regression, Association vs. Causation, Summary of Regression Analysis

3. Collecting Data

A summary of Collecting Data: Population vs. Sample, Observational Studies: Retrospective vs. Prospective, Experimental Studies, Key Principles of Sampling, Random Sampling vs. Random Assignment, Confounding Variables, Bias in Data Collection, Sampling Methods, Choosing Sampling Methods Wisely, Designing Experiments, Key Principles of Experimental Design, Completely Randomized Design, Blocking, Matched Pairs Design, Blinding and Placebos, Common Pitfalls in Experimentation, Scope of Inference

4. Probability, Random Variables, and Probability Distributions

A summary of Probability, Random Variables, and Probability Distributions: Introduction to Probability, Basic Probability Rules, Understanding Independence and Mutual Exclusivity, Multistage Probability and Conditional Probability, Random Variables, Combining Random Variables, Transforming Random Variables, Binomial Distributions, Binomial Probability Formula, Mean and Standard Deviation of a Binomial Distribution, Geometric Distributions, Geometric Probability Formula, Mean and Standard Deviation of a Geometric Distribution, Interpreting Binomial and Geometric Distributions, Calculating Cumulative Probabilities, When to Use Normal Approximation, Important Warnings

5. Sampling Distributions

A summary of Sampling Distributions: Understanding Sampling Distributions, Normal Distribution Calculations, Sampling Distribution of a Sample Proportion, Sampling Distribution of a Sample Mean, Central Limit Theorem (CLT), Bias and Variability in Estimators, Sampling Distribution of the Difference of Sample Proportions, Sampling Distribution of the Difference of Sample Means, Simulation to Estimate Sampling Distributions, Why Larger Samples Are Better, Sample Size vs Population Size

6. Inference for Categorical Data: Proportions

A summary of Inference for Categorical Data: Basics of Statistical Inference, Margin of Error vs. Standard Error, Conditions for Inference on Proportions, Constructing Confidence Intervals for a Population Proportion, Determining Sample Size for Desired Margin of Error, Significance Testing for a Population Proportion, Interpreting P-values and Significance, Errors in Significance Testing, Inference for the Difference of Two Proportions, Constructing a Confidence Interval for p₁ − p₂, Hypothesis Test for p₁ − p₂, Steps in Two-Proportion Z-Test, Interpreting Confidence Intervals vs. Significance Tests, Choosing Between One-Proportion and Two-Proportion Procedures, When Procedures Are Robust

7. Inference for Quantitative Data: Means

A summary of Inference for Categorical Data: Chi-Square: Chi-Square Test for Goodness-of-Fit, Conditions for Chi-Square Goodness-of-Fit Test, Properties of the Chi-Square Distribution, Calculating Expected Counts, Example Interpretation (Goodness-of-Fit), Chi-Square Test for Independence, Chi-Square Test for Homogeneity, Common Steps for Chi-Square Tests (Independence and Homogeneity), Interpreting the Results, Comparing Chi-Square Tests, Important Notes About Chi-Square Tests

8. Inference for Categorical Data: Chi-Square

A summary of Inference for Categorical Data: Chi-Square Test for Goodness-of-Fit, Conditions for Chi-Square Goodness-of-Fit Test, Properties of the Chi-Square Distribution, Calculating Expected Counts, Example Interpretation (Goodness-of-Fit), Chi-Square Test for Independence, Chi-Square Test for Homogeneity, Common Steps for Chi-Square Tests (Independence and Homogeneity), Interpreting the Results, Comparing Chi-Square Tests, Important Notes About Chi-Square Tests

9. Inference for Quantitative Data: Slopes

A summary of Inference for Quantitative Data: Sampling Distribution for the Slope, Conditions for Inference on the Slope, Understanding Standard Error of the Slope, Generic Computer Output for Regression, Reading Regression Output, Constructing a Confidence Interval for the Slope, Performing a Hypothesis Test for the Slope, Steps for Inference About the Slope, Important Interpretation Tips, Common Pitfalls to Avoid