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If you know how to program, you have the skills to turn data into knowledge, using tools of probability and statistics. This concise introduction shows you how to perform statistical analysis computationally, rather than mathematically, with programs written in Python. By working with a single case study throughout this thoroughly revised book, you’ll learn the entire process of exploratory data analysis—from collecting data and generating statistics to identifying patterns and testing hypotheses. You’ll explore distributions, rules of probability, visualization, and many other tools and concepts. New chapters on regression, time series analysis, survival analysis, and analytic methods will enrich your discoveries. Develop an understanding of probability and statistics by writing and testing code Run experiments to test statistical behaviour, such as generating samples from several distributions Use simulations to understand concepts that are hard to grasp mathematically Import data from most sources with Python, rather than rely on data that is cleaned and formatted for statistics tools Use statistical inference to answer questions about real-world data. Copyright Table of Contents Preface How I Wrote This Book Using the Code Contributor List Safari® Books Online How to Contact Us Chapter 1. Exploratory Data Analysis A Statistical Approach The National Survey of Family Growth Importing the Data DataFrames Variables Transformation Validation Interpretation Exercises Glossary Chapter 2. Distributions Representing Histograms Plotting Histograms NSFG Variables Outliers First Babies Summarizing Distributions Variance Effect Size Reporting Results Exercises Glossary Chapter 3. Probability Mass Functions Pmfs Plotting PMFs Other Visualizations The Class Size Paradox DataFrame Indexing Exercises Glossary Chapter 4. Cumulative Distribution Functions The Limits of PMFs Percentiles CDFs Representing CDFs Comparing CDFs Percentile-Based Statistics Random Numbers Comparing Percentile Ranks Exercises Glossary Chapter 5. Modeling Distributions The Exponential Distribution The Normal Distribution Normal Probability Plot The lognormal Distribution The Pareto Distribution Generating Random Numbers Why Model? Exercises Glossary Chapter 6. Probability Density Functions PDFs Kernel Density Estimation The Distribution Framework Hist Implementation Pmf Implementation Cdf Implementation Moments Skewness Exercises Glossary Chapter 7. Relationships Between Variables Scatter Plots Characterizing Relationships Correlation Covariance Pearson’s Correlation Nonlinear Relationships Spearman’s Rank Correlation Correlation and Causation Exercises Glossary Chapter 8. Estimation The Estimation Game Guess the Variance Sampling Distributions Sampling Bias Exponential Distributions Exercises Glossary Chapter 9. Hypothesis Testing Classical Hypothesis Testing HypothesisTest Testing a Difference in Means Other Test Statistics Testing a Correlation Testing Proportions Chi-Squared Tests First Babies Again Errors Power Replication Exercises Glossary Chapter 10. Linear Least Squares Least Squares Fit Implementation Residuals Estimation Goodness of Fit Testing a Linear Model Weighted Resampling Exercises Glossary Chapter 11. Regression StatsModels Multiple Regression Nonlinear Relationships Data Mining Prediction Logistic Regression Estimating Parameters Implementation Accuracy Exercises Glossary Chapter 12. Time Series Analysis Importing and Cleaning Plotting Linear Regression Moving Averages Missing Values Serial Correlation Autocorrelation Prediction Further Reading Exercises Glossary Chapter 13. Survival Analysis Survival Curves Hazard Function Estimating Survival Curves Kaplan-Meier Estimation The Marriage Curve Estimating the Survival Function Confidence Intervals Cohort Effects Extrapolation Expected Remaining Lifetime Exercises Glossary Chapter 14. Analytic Methods Normal Distributions Sampling Distributions Representing Normal Distributions Central Limit Theorem Testing the CLT Applying the CLT Correlation Test Chi-Squared Test Discussion Exercises Index About the Author