I. Introduction
Statistics is the science of learning from data. It focuses on collecting good data, summarizing it clearly, and making sound conclusions under uncertainty.
II. Outline
- Statistics I - Data & Description
- Types of data and variables
- Visuals: histograms, boxplots, scatterplots
- Summary measures: mean/median, variance/standard deviation, percentiles/IQR
- Association vs causation
- Data ethics and “how graphs can lie”
- Statistics II - Sampling & Experimental Design
- Populations vs samples, sampling frames, bias
- Random sampling methods
- Experiments vs observational studies
- Randomization, control groups, blinding, placebo
- Power and sample size intuition
- Statistics III - Inference: Estimation & Confidence Intervals
- Sampling distributions
- Standard error, margin of error
- Confidence intervals for:
- Means and proportions
- Differences of means/proportions
- Robustness and assumptions
- Statistics IV - Inference: Tests & Models
- Hypothesis testing framework
- Type I/II errors, significance level, power
- Common tests:
- t-tests
- Chi-square tests
- ANOVA basics
- Regression:
- Simple linear regression, interpretation, residuals/diagnostics
- Multiple regression basics
- Bayesian basics
III. Free Books
- OpenStax — Introductory Statistics 2e OpenIntro — OpenIntro Statistics
- An Introduction to Statistical Learning Website
- Very high quality, free, digital resource.
- OpenIntro — Introduction to Modern Statistics (2e)
IV. Video Series
These are courses that includes lecture videos, notes, and problem sets.
- MIT OpenCourseWare — 18.05 Introduction to Probability and Statistics
- MIT OpenCourseWare — 18.650 Statistics for Applications
YouTube Playlists:
- Crash Course Statistics
- Intro to Statistics and Data Analysis - Steve Brunton
- Simple Learning Pro - Statistics 1
V. See Also
Probability, Discrete Math, Calculus, Linear Algebra
