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

The sampling distribution

So, we have estimated that the true population mean is about 65.2; we know the population mean isn't exactly `65.19704`—but by just how much might our estimate be off?

To answer this question, let's take repeated samples from the population again. This time, we're going to take samples of size 40 from the population 10,000 times and plot a frequency distribution of the means:

``` > means.of.our.samples <- numeric(10000)
> for(i in 1:10000){
+   a.sample <- sample(all.us.women, 40)
+   means.of.our.samples[i] <- mean(a.sample)
+ } ```

We get the distribution as follows:

Figure 5.3: The sampling distribution of sample means

This frequency distribution is called a sampling distribution. In particular, as we used sample means as the value of interest, this is called the sampling distribution of the sample means (whew!). You can create a sampling distribution of any statistic (median, variance, and so on), but when we refer to sampling distributions throughout...