# Statistics for life and health sciences EBook

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 Revision as of 23:33, 18 March 2013 (view source)IvoDinov (Talk | contribs)← Older edit Current revision as of 23:51, 18 March 2013 (view source)IvoDinov (Talk | contribs) (One intermediate revision not shown) Line 31: Line 31: ==Chapter II: Data and variability== ==Chapter II: Data and variability== * Data * Data + * Measures of center, dispersion/variation, skewness, flatness * Design of experiments * Design of experiments * R data management (Import and Export) * R data management (Import and Export) Line 42: Line 43: ==Chapter IV: Probability Models== ==Chapter IV: Probability Models== + * Fundamentals + * Rules for Computing Probabilities + * Probabilities Simulations + * Counting Principles - ==Chapter V: Statistical Models== + ==Chapter V: Statistical Parametric Models and Inference== - + - ==Chapter VI: Parametric Model-based Inference== + * Hypothesis testing foundations * Hypothesis testing foundations * Type I and II errors, Power, sensitivity, specificity * Type I and II errors, Power, sensitivity, specificity + * Parametric Assumptions ===One sample inference=== ===One sample inference=== Line 58: Line 62: * Paired samples * Paired samples - ==Chapter VII: Limiting Theorems== + ==Chapter VI: Limiting Theorems== * Law of Large Numbers (First Fundamental Law of Probability Theory) * Law of Large Numbers (First Fundamental Law of Probability Theory) * Central Limit Theorem (Second Fundamental Law of Probability Theory) * Central Limit Theorem (Second Fundamental Law of Probability Theory) + * Relations between Distributions (Distributome) - ==Chapter VIII: Multivariate Statistics== + ==Chapter VII: Multivariate Statistics== * Parametric (simple and multivatiate) regression * Parametric (simple and multivatiate) regression - * Parametric ANOVA + * Parametric ANOVA/ANCOVA/MANCOVA + * Logistic Regression * Parametric assumptions and model validation * Parametric assumptions and model validation * Non-parametric linear modeling * Non-parametric linear modeling Line 70: Line 76: * Genome-wide association studies (GWAS) * Genome-wide association studies (GWAS) - ==Chapter IX:== + ==Chapter VIII: Multinomial Experiments and Inference== + * Chi-square + + ==Chapter IX: Parameter Estimation== + * MOM + * MLE + + ==Chapter X: Bayesian Inference== + + ==Chapter XI: Dimensionality Reduction== + * PCA + * ICA + + ==Chapter XII: Classification Methods== + * Supervised classification methods (Support Vector Machines, SVM, ADABOOST) + * Unsupervised (K-means clustering, hierarchical clustering) - ==Chapter II:== + == Chapter XIII: Survival Analysis== - ==Chapter II:== + == Chapter XIV: Mixture modeling== - ==Chapter II:== + == Chapter XV: Causality== - ==Chapter II:== + ==Appendix==

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## Current revision as of 23:51, 18 March 2013

Welcome to the UCLA Statistics for the Biomedical and Health Sciences (Stats 13) electronic book (EBook).

## Preface

This is an Internet-based probability and statistics for biomedical and health sciences EBook. The materials, tools and demonstrations presented in this EBook would are used for the UCLA Statistics 13 course. The EBook is developed, updated and manages by the UCLA Statistics faculty teaching this course over the years. Many other instructors, researchers, students and educators have contributed to this EBook.

There are four novel features of this Statistics EBook. It is community-built and allows easy modifications and customizations, completely open-access (in terms of use and contributions), blends information technology, scientific techniques, heterogeneous data and modern pedagogical concepts, and is multilingual.

### Format

Each section in this EBook includes

• Motivation
• Concepts, definitions, formulations
• Examples
• Small (mock-up) and real (research-derived) data
• Webapp demonstration with real data (HTML5)
• R programming
• Problems

...

### Copyright

The Probability and Statistics EBook is a freely and openly accessible electronic book for the entire community under CC-BY license ...

## Chapter I: Introduction to Statistics

• Natural Biomedical and Health Research Studies
• Data-driven Statistics
• Uses and Abuses of Statistics
• Statistical Software Tools

## Chapter II: Data and variability

• Data
• Measures of center, dispersion/variation, skewness, flatness
• Design of experiments
• R data management (Import and Export)
• Histograms, densities and summary statistics

## Chapter III: Randomization-based statistical inference

• Samples, Populations, Repeated Samples, Resampling
• Bootstrapping
• Testing one, two or more samples
• Confidence intervals

## Chapter IV: Probability Models

• Fundamentals
• Rules for Computing Probabilities
• Probabilities Simulations
• Counting Principles

## Chapter V: Statistical Parametric Models and Inference

• Hypothesis testing foundations
• Type I and II errors, Power, sensitivity, specificity
• Parametric Assumptions

### One sample inference

• T-Test
• Normal Z-test
• Confidence intervals

### Two sample inference

• Independent samples
• Paired samples

## Chapter VI: Limiting Theorems

• Law of Large Numbers (First Fundamental Law of Probability Theory)
• Central Limit Theorem (Second Fundamental Law of Probability Theory)
• Relations between Distributions (Distributome)

## Chapter VII: Multivariate Statistics

• Parametric (simple and multivatiate) regression
• Parametric ANOVA/ANCOVA/MANCOVA
• Logistic Regression
• Parametric assumptions and model validation
• Non-parametric linear modeling
• Randomization and Resampling based multivariate inference
• Genome-wide association studies (GWAS)

• Chi-square

• MOM
• MLE

• PCA
• ICA

## Chapter XII: Classification Methods

• Supervised classification methods (Support Vector Machines, SVM, ADABOOST)
• Unsupervised (K-means clustering, hierarchical clustering)

## Appendix

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