- Introductory Statistics
- Descriptive Statistics
- Probability Theory
- Discrete Data Analysis
- Linear Regression Models
- Experimental Design
- Generalized Linear Models
- Non-parametric Tests
- Multivariate Analysis
- Bayesian Statistics
- Omics Data
- Structural Equation Modeling
- Longitudinal Data Analysis
- Data Mining and Machine Learning
- Sampling Theory and Methods
- Open Source Textbooks
- Miscellaneous Resources

## Introductory Statistics

- Intro to Statistics – Udacity free online course
- Intro to Statistics – Saylor free online course
- Introductory Statistics – textbook
- Elementary Statistics and Probability Tutorials

## 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 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 Probability Theory*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 (LRT) 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

- 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

- Slides on Multiple Linear Regression
- Notes on multiple linear regression
- Multiple linear regression with R examples
- Lecture slides on multiple linear regression

Statistical forecasting:

Online Courses:

- Linear regression, an Penn State University online course

## Experimental Design

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

ANOVA & ANCOVA

- One-way ANOVA and Two-way ANOVA
- Online Statbook: Analysis of Variance
- ANOVA
- Analysis of Covariance from online text book: Experimental Design for Behavioral and Social Sciences
- Understanding Analysis of Covariance

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

Resources on Causal Inference

- Course on Causal Inference
- Regression Discontinuity
- Introduction to Mediation Analysis
- Statistics and Causal Inference

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 (GLMs)

Generalized Linear Model

Linear Mixed model

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

Logistic Regression

- Logit Models for Binary
- General Linear Models for Binary Data R codes for exercise
- Multinomial Response Models
- Fitting and Interpreting a Proportional Odds Model

Count Regression

- Poisson Models for Count
- General Linear Models for Count Data R codes for exercise
- Negative Binomial Regression
- Zero-Inflated Poisson Models
- Getting Started with Hurdle Models
- Do We Really Need Zero-Inflated Models?

## 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* (*Wilcoxon-Rank Sums Test)* and *Kruskal-Wallis* *(independent samples)

#### Background information and tutorial

- Mann-Whitney U and Kurskal-Wallis
- Wilcoxon-Rank Sums only
- Kruskal-Wallis Tutorial in R
- Excel calculator (downloads Excel file)

### Wilcoxen Signed-Rank 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 (nonparametric analog to GLMs)

- Journal article 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

### Online Courses

- Applied Nonparametric Statistics, Penn State Online Course

## Multivariate Analysis

A guide to choose different statistical techniques of multivariate analysis

MANOVA

Principle Component Analysis

- A Tutorial on Principal Component Analysis
- The Difference Between Principal Component Analysis and Factor Analysis
- Linear Discriminant Analysis

Factor Analysis

- Lecture slides on factor analysis
- What is Rotating in Exploratory Factor Analysis?
- Exploratory and Confirmatory Factor Analysis
- How Many Factors?

Online Courses

- Applied Multivariate Statistical Analysis, Penn State Online Course

## Bayesian Statistics

- “Plain English” Bayesian Statistics
*Introduction to Bayesian Statistics*by Brendon Brewer (open source textbook)- Bayesian Statistics – course notes

## Omics Data

- MetaboAnalyst – interfaces with R to analyze and display metabolomics data
- MicobiomeAnalyst – analyze and display microbiome data
- OmicsNet – create and explore relationships among genes, proteins, metabolites, etc. in 3-D space

## Structural Equation Modeling

- What is a Latent Variable?
- Overview of Structural Equation Modeling
- Structural Equation Models with Latent Variables
- Confirmatory Factor Analysis
- SEM Fit Guidelines
- Item Response Theory
- Latent Class Analysis Mathematical Model
- Latent Class Analysis Applied Example
- Mixture Models
- Multilevel Structural Equation Modeling

## Longitudinal Data Analysis

- Repeated Measures ANOVA
- Longitudinal Data Analysis (SPSS)
- Sphericity
- Latent Growth Curve Models Lecture
- Latent Growth Curve Modeling
- Multilevel Growth Models
- Generalized Estimating Equations
- Nonlinear Trajectories
- Introduction to Survival Analysis
- Models for Survival Analysis with Covariates
- Patterns In Time Series Analysis
- Autoregressive Models
- Moving Average Models
- Introduction to ARIMA models
- Seasonal ARIMA models
- Growth Mixture Models (downloads PowerPoint file)
- Latent Transition Analysis (downloads PowerPoint file)

## Data Mining and Machine Learning

- What is Machine Learning?
- Introduction on Statistical Learning with Applications in R
- Videos on Machine Learning Course in Caltech
- Classification and Regression Trees
- Cluster Analysis
- Support Vector Machines
- Multivariate Adaptive Regression Splines
- Bagging and Ensemble Methods
- First Steps with TensorFlow
- Introduction to Deep Neural Networks
- Convolutional Neural Networks
- Performance Measures for Machine Learning
- Improving Machine Learning

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 Probability Theory*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
- Introduction on Statistical Learning with Applications in R