- Descriptive Statistics
- Probability Theory
- Discrete Data Analysis
- Linear Regression Models
- Experimental Design
- Generalized Linear Models
- Non-parametric Tests
- Multivariate Analysis
- Data Mining and Machine Learning
- Sampling Theory and Methods
- Open Source Textbooks

## Descriptive Statistics

Numerical summaries, statistical graphics

- How to visualize data
- An introduction to descriptive statistics
- Slides on Descriptive Statistics and Exploratory Data Analysis
- A series of Videos on Descriptive Statistics

SAS

R

- Basic Graphics and Descriptive Statistics in R
- Exploring Data and Descriptive Statistics using R
- Descriptive statistics with R

SPSS

## Probability Theory

- Probabilities and random variables
- Conditional probability
- Distributions and densities
- Expected value and variance
- Law of Large Numbers
- Central Limit Theorem

Online Courses:

- Probability Theory and Mathematical Statistics, Penn State Online Course

Books available online:

*Introduction to Probability*by Charles M. Grinstead and J. Laurie Snell*Basic ProbabilityTheory*by Robert B. Ash*Probability: Theory and Examples*by Rick Durrett

## Discrete Data Analysis

- One-way Table: Chi-square Test of Goodness-of-Fit
- One-way Table: G Test of Goodness-of-Fit
- Two-way Table: Chi-square Test of Independence
- Two-way Table: G Test of Independence
- Two-way Table: Fisher’s Exact Test
- Two-way Table Dependent Samples: McNemar’s Test

Online Courses:

- Analysis of Discrete Data, Penn State Online Course

## Linear Regression Models

Linear regression and correlation

- An Introduction to Regression Analysis
- Introduction to Linear Regression and Correlation Analysis
- Interpret Regression Analysis Results: P-values and Coefficients
- Regression Analysis: How to Interpret the Constant
- Interpreting Regression Coefficients

Diagnostics and Transformations

Multiple linear regression

- Notes on multiple linear regression
- Multiple linear regression with R examples
- Lecture slides on multiple linear regression (1) (2)

Statistical forecasting:

Online Courses:

- Linear regression, an Penn State University online course

Books:

- Introduction to Linear Regression Analysis by D. Montgomery, E. Peck

## Experimental Design

A field guild to experimental designs – including complete randomized design, randomized complete block design, factorial design, split plot design, etc.

ANOVA

ANCOVA

- Analysis of Covariance from online text book: Experimental Design for Behavioral and Social Sciences
- Understanding Analysis of Covariance

Linear Mixed model

- Linear Mixed model, appendix to An R and S-PLUS Companion to Applied Regression
- Linear Mixed Effects Modeling using R

Repeated Measures

Sample size determination

Teaching materials

- Lecture notes for Introduction to Regression Models and Analysis of Variance
- Lecture notes and R codes for Experimental Design and Data Analysis for Biologists

Online Courses

- Analysis of Variance and Design of Experiments, Penn State Online Course

Books available online:

- Experimental Design for Behavioral and Social Sciences, by Howard J. Seltman
- A First Course in Design and Analysis of Experiments, by Gary W. Oehlert

## Generalized Linear Models

Generalized Linear Model

Logistic Regression

- Logit Models for Binary
- General Linear Models for Binary Data R codes for exercise
- Multinomial Response Models

Poisson Regression

## Non-parametric Tests

### Non-Parametric Alternatives to Parametric Tests

Type of Design |
Parametric Test |
Non-parametric Test |

Two Independent Samples | Independent –samples t-test | Mann-Whitney U or Wilcoxon Rank Sums Test |

Two Dependent Samples | Dependent-samples t-test | Wilcoxon T-test |

Three or more Independent Samples | Between-subjects ANOVA | Kruskal-Wallis H Test |

Three or more Dependent Samples | Within-subjects ANOVA | Friedman x2 Test |

### Mann-Whitney U* (*Wilcoxen-Rank Sums Test)* and *Kurskal-Wallis* *(independent samples)

#### Background information and tutorial

### Wilcoxen T-test and Friedman x2 Test (dependent samples)

#### Basic information and tutorials

### Basic R code for basic Non-parametric Testing

### Non-parametric regression

### Generalized Additive Modeling (a specific type of non-parametric regression)

- Journal on what additive models are
- Background and basic information on additive modeling (1)
- Background and basic information on additive modeling (2)
- R code for additive modeling in R
- R package information
- Great Textbook on additive modeling in R

### Online Courses

- Applied Nonparametric Statistics, Penn State Online Course

## Multivariate Analysis

A guild to choose different statistical techniques of multivariate analysis

MANOVA

Principle Component Analysis

Factor Analysis

Online Courses

- Applied Multivariate Statistical Analysis, Penn State Online Course

## Data Mining and Machine Learning

- Introduction on Statistical Learning with Applications in R
- Videos on Machine Learning Course in Caltech
- Classification and Regression Trees
- Cluster Analysis
- An Overview of Data Mining Techniques

Online Courses

- Applied Data Mining and Statistical Learning, Penn State Online Course

## Sampling Theory and Methods

Online Courses

- Sampling Theory and Methods, Penn State Online Course

## Open Source Textbooks

- General Statistics Textbook
*Introduction to Probability*by Charles M. Grinstead and J. Laurie Snell*Basic ProbabilityTheory*by Robert B. Ash*Probability: Theory and Examples*by Rick Durrett- Experimental Design for Behavioral and Social Sciences
- A First Course in Design and Analysis of Experiments