#### Overview of this book

Frequently the tool of choice for academics, R has spread deep into the private sector and can be found in the production pipelines at some of the most advanced and successful enterprises. The power and domain-specificity of R allows the user to express complex analytics easily, quickly, and succinctly. Starting with the basics of R and statistical reasoning, this book dives into advanced predictive analytics, showing how to apply those techniques to real-world data though with real-world examples. Packed with engaging problems and exercises, this book begins with a review of R and its syntax with packages like Rcpp, ggplot2, and dplyr. From there, get to grips with the fundamentals of applied statistics and build on this knowledge to perform sophisticated and powerful analytics. Solve the difficulties relating to performing data analysis in practice and find solutions to working with messy data, large data, communicating results, and facilitating reproducibility. This book is engineered to be an invaluable resource through many stages of anyone’s career as a data analyst.
Title Page
Packt Upsell
Contributors
Preface
Free Chapter
RefresheR
The Shape of Data
Describing Relationships
Probability
Using Data To Reason About The World
Testing Hypotheses
Bayesian Methods
The Bootstrap
Predicting Continuous Variables
Predicting Categorical Variables
Predicting Changes with Time
Sources of Data
Dealing with Missing Data
Dealing with Messy Data
Dealing with Large Data
Working with Popular R Packages
Reproducibility and Best Practices
Other Books You May Enjoy
Index

## Smaller samples

Remember when I said that the sampling distribution of sample means is approximately normal for a large enough sample size? This caveat means that for smaller sample sizes (usually considered to be below 30), the sampling distribution of the sample means is not well approximated by a normal distribution. It is, however, well approximated by another distribution: the t-distribution.

### Note

A bit of history... The t-distribution is also known as the Student's t-distribution. It gets its name from the 1908 paper that introduces it, by William Sealy Gosset writing under the pen name Student. Gosset worked as a statistician at the Guinness Brewery and used the t-distribution and the related t-test to study small samples of the quality of the beer's raw constituents. He is thought to have used a pen name at the request of Guinness so that competitors wouldn't know that they were using the t statistic to their advantage.

The t-distribution has two parameters, the mean and the degrees...