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