Statistical analysis is at work in nearly every human endeavor. Generally, we use it to forecast the future, test our theories, control variation in processes, make decisions, optimize, and estimate. Specifically, we apply it to economic problems, scientific experiments, quality control, artificial intelligence, data mining, and many other arenas.
Here, I will attempt to summarize some important ideas in statistical analysis and some important applications (my toolbox, if you will):
- Foundations
- Axioms of Probability
- Central Limit Theorem
- Basics
- Descriptive Statistics
- Conditional Probability
- Statistical Tests (See A Review of Basic Statistical Tests for an excellent single-page reference or UCLS Statistical Computing Department’s What statistical analysis should I use?)
- Parametric Tests
- Nonparametric Tests
- Design of Experiments
- Decision Theory
- Choice Theory
- Utility Theory
- Game Theory
- Decision Aggregation
- Multi-Criterion Decision Analysis
- Statistical Process Control
- Control Charts
- Process Capability
- Taguchi Methods
- Forecasting Methods
- Moving Averages
- Exponential Smoothing
- Regression Analysis
- Autoregressive Moving Averages (ARMA)
- Autoregressive Integrated Moving Averages (ARIMA)
- Simulation and Modeling Methods
- Monte Carlo Simulation
- Markov Chain Monte Carlo (MCMC)
- Simulated Annealing
- Machine Learning/Data Mining/Exploratory Data Analysis Methods