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Statistical methods are a key part of data science, yet few data scientists have formal statistical training. Courses and books on basic statistics rarely cover the topic from a data science perspective. The second edition of this popular guide adds comprehensive examples in Python, provides practical guidance on applying statistical methods to data science, tells you how to avoid their misuse, and gives you advice on what's important and what's not.

Many data science resources incorporate statistical methods but lack a deeper statistical perspective. If you're familiar with the R or Python programming languages and have some exposure to statistics, this quick reference bridges the gap in an accessible, readable format.

With this book, you'll learn:

Why exploratory data analysis is a key preliminary step in data science
How random sampling can reduce bias and yield a higher-quality dataset, even with big data
How the principles of experimental design yield definitive answers to questions
How to use regression to estimate outcomes and detect anomalies
Key classification techniques for predicting which categories a record belongs to
Statistical machine learning methods that ´learn´ from data
Unsupervised learning methods for extracting meaning from unlabeled data



Table of Contents

Preface
Conventions Used in This Book
Using Code Examples
O'Reilly Online Learning
How to Contact Us
Acknowledgments
1. Exploratory Data Analysis
Elements of Structured Data
Further Reading
Rectangular Data
Data Frames and Indexes
Nonrectangular Data Structures
Further Reading
Estimates of Location
Mean
Median and Robust Estimates
Example: Location Estimates of Population and Murder Rates
Further Reading
Estimates of Variability
Standard Deviation and Related Estimates
Estimates Based on Percentiles
Example: Variability Estimates of State Population
Further Reading
Exploring the Data Distribution
Percentiles and Boxplots
Frequency Tables and Histograms
Density Plots and Estimates
Further Reading
Exploring Binary and Categorical Data
Mode
Expected Value
Probability
Further Reading
Correlation
Scatterplots
Further Reading
Exploring Two or More Variables
Hexagonal Binning and Contours (Plotting Numeric Versus Numeric Data)
Two Categorical Variables
Categorical and Numeric Data
Visualizing Multiple Variables
Further Reading
Summary
2. Data and Sampling Distributions
Random Sampling and Sample Bias
Bias
Random Selection
Size Versus Quality: When Does Size Matter?
Sample Mean Versus Population Mean
Further Reading
Selection Bias
Regression to the Mean
Further Reading
Sampling Distribution of a Statistic
Central Limit Theorem
Standard Error
Further Reading
The Bootstrap
Resampling Versus Bootstrapping
Further Reading
Confidence Intervals
Further Reading
Normal Distribution
Standard Normal and QQ-Plots
Long-Tailed Distributions
Further Reading
Student's t-Distribution
Further Reading
Binomial Distribution
Further Reading
Chi-Square Distribution
Further Reading
F-Distribution
Further Reading
Poisson and Related Distributions
Poisson Distributions
Exponential Distribution
Estimating the Failure Rate
Weibull Distribution
Further Reading
Summary
3. Statistical Experiments and Significance Testing
A/B Testing
Why Have a Control Group?
Why Just A/B? Why Not C, D,.?
Further Reading
Hypothesis Tests
The Null Hypothesis
Alternative Hypothesis
One-Way Versus Two-Way Hypothesis Tests
Further Reading
Resampling
Permutation Test
Example: Web Stickiness
Exhaustive and Bootstrap Permutation Tests
Permutation Tests: The Bottom Line for Data Science
Further Reading
Statistical Significance and p-Values
p-Value
Alpha
Type 1 and Type 2 Errors
Data Science and p-Values
Further Reading
t-Tests
Further Reading
Multiple Testing
Further Reading
Degrees of Freedom
Further Reading
ANOVA
F-Statistic
Two-Way ANOVA
Further Reading
Chi-Square Test
Chi-Square Test: A Resampling Approach
Chi-Square Test: Statistical Theory
Fisher's Exact Test
Relevance for Data Science
Further Reading
Multi-Arm Bandit Algorithm
Further Reading
Power and Sample Size
Sample Size
Further Reading
Summary
4. Regression and Prediction
Simple Linear Regression
The Regression Equation
Fitted Values and Residuals
Least Squares
Prediction Versus Explanation (Profiling)
Further Reading
Multiple Linear Regression
Example: King County Housing Data
Assessing the Model
Cross-Validation
Model Selection and Stepwise Regression
Weighted Regression
Further Reading
Prediction Using Regression
The Dangers of Extrapolation
Confidence and Prediction Intervals
Factor Variables in Regression
Dummy Variables Representation
Factor Variables with Many Levels
Ordered Factor Variables
Interpreting the Regression Equation
Correlated Predictors
Multicollinearity
Confounding Variables
Interactions and Main Effects
Regression Diagnostics
Outliers
Influential Values
Heteroskedasticity, Non-Normality, and Correlated Errors
Partial Residual Plots and Nonlinearity
Polynomial and Spline Regression
Polynomial
Splines
Generalized Additive Models
Further Reading
Summary
5. Classification