Probability & StatisticsProbability & Statistics

Populations and samples, kinds of data, sampling methods and bias, frequency tables, and how experiments differ from observational studies.

1. 1Populations, Samples and Variables
2. 2Sampling Methods and Bias
3. 3Levels of Measurement and Frequency Tables
4. 4Experimental Design and Ethics

Graphing distributions, the mean and median, standard deviation and z-scores, and quartiles, box plots and outliers.

1. 5Graphs of Data
2. 6Measures of Center
3. 7Measures of Spread
4. 8Quartiles, Box Plots and Outliers

Sample spaces and events, the addition and multiplication rules, conditional probability with tables and trees, and Bayes' theorem.

1. 9Probability Basics
2. 10The Addition and Multiplication Rules
3. 11Contingency Tables and Tree Diagrams
4. 12Bayes' Theorem

Probability distributions for counts, expected value and standard deviation, and the binomial, geometric, hypergeometric and Poisson distributions.

1. 13Discrete Probability Distributions
2. 14Expected Value and Standard Deviation
3. 15The Binomial Distribution
4. 16Geometric and Hypergeometric Distributions
5. 17The Poisson Distribution

Probability as area under a density curve, the uniform and exponential distributions, and the normal distribution with z-scores and percentiles.

1. 18Continuous Random Variables
2. 19The Uniform Distribution
3. 20The Exponential Distribution
4. 21The Normal Distribution
5. 22Using the Normal Distribution

Why averages and totals of many random values are approximately normal, the standard error, and the normal approximation for proportions.

1. 23The Central Limit Theorem for Means
2. 24The CLT for Sums and Proportions

Estimating a mean or proportion with a margin of error: z intervals, the t distribution, intervals for proportions, and choosing a sample size.

1. 25Confidence Intervals for a Mean
2. 26The t Distribution and t Intervals
3. 27Confidence Intervals for a Proportion

Null and alternative hypotheses, Type I and II errors, p-values, and tests for a mean (z and t) and for a proportion.

1. 28Hypotheses and Errors
2. 29p-Values and the z-Test for a Mean
3. 30The t-Test for a Mean
4. 31Testing a Proportion

Tests for the difference of two means with independent samples, matched pairs, and the difference of two proportions.

1. 32Two Independent Means
2. 33Matched Pairs
3. 34Two Proportions

Testing whether counts fit a claimed distribution, and whether two categorical variables are independent.

1. 35Goodness of Fit
2. 36Tests of Independence

Scatter plots and the correlation coefficient, the least-squares line, residuals and r², and logistic regression for yes-or-no outcomes.

1. 37Scatter Plots and Correlation
2. 38The Least-Squares Regression Line
3. 39Residuals, r² and Outliers
4. 40Logistic Regression

Comparing several group means at once with the F statistic.

1. 41One-Way ANOVA