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Statistics and probability
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Analyzing categorical data
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Two-way tables
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Trends in categorical data
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Displaying and comparing quantitative data
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Summarizing quantitative data
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Variance and standard deviation
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Modeling data distributions
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z-scores
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Normal distributions and the empirical rule
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Exploring bivariate numerical data
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Making residual plots
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Study design
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Collecting data
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Difference between correlation and causation
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Misleading statistics
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Survivorship bias
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Simpson's paradox
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Probability
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Probability vs odds
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Probability trees
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Addition rule
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Paradox: Bertrand's box paradox
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Paradox: Birthday problem
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Non-transitive games
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Expected value
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Infinite consecutive independent events
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Challenge: Surviving The Deadliest Game
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Conditional probability
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Bayes's theorem and false positives
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Complementary events
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Challenge
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How To Solve Amazon's Pair Of Socks Interview Puzzle (MindYourDecisions)
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Multi-stage events
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Binomial probability
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Mutually exclusive events
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NRICH activities (probability theory for high schoolers)
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Newton–Pepys problem
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Probability with geometry
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Sets
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Set equality and subsets
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Introduction to sets
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Set operations
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Two envelopes problem
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Addition rule of probability
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Counting, permutations, and combinations
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Venn diagrams (combinatorics)
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Factorials, permutations, and combinations
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Permutations and factorials
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Combinations
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Solving factorial equations
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Multiplication principle
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Arranging in a circle
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Basic combinatorics proofs
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Combination and permutation word problems
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Euler squares
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Latin squares
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Lattice paths
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NRICH activities (combinatorics for high schoolers)
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Pascal's identity
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Connection between Pascal's identity and Pascal's triangle
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Pascal's rule
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Random variables
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Binomial distribution
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Expected value
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Random
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Hypothesis testing in experiments
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Simple hypothesis testing
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Sampling distributions
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Confidence intervals
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Significance tests (hypothesis testing)
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Simple hypothesis testing
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Hypothesis testing and p-values
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Two-sample inference for the difference between groups
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Inference for categorical data (chi-square tests)
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Advanced regression (inference and transforming)
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Analysis of variance (ANOVA)
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Statistics and probability
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Counting, permutations, and combinations
Euler squares