Book Image

Data Analysis with R, Second Edition - Second Edition

Book Image

Data Analysis with R, Second Edition - Second Edition

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.
Table of Contents (24 chapters)
Title Page
Copyright and Credits
Packt Upsell
Contributors
Preface
Index

The Bayesian independent samples t-test


For our last example in the chapter, we will be performing a sort-of Bayesian analogue to the two-sample t-test using the same data and problem from the corresponding example in the previous chapter-testing whether the means of the gas mileage for automatic and manual cars are significantly different.

Note

There is another popular Bayesian alternative to NHST, which uses something called Bayes factors to compare the likelihood of the null and alternative hypotheses.

As before, let's specify the model using non-informative flat priors, as shown in the following code:

the.model <- " 
model { 
  # each group will have a separate mu 
  # and standard deviation 
  for(j in 1:2){ 
    mu[j] ~ dunif(0, 60)       # prior 
    stddev[j] ~ dunif(0, 20)   # prior 
    tau[j] <- pow(stddev[j], -2) 
  } 
  for(i in 1:theLength){ 
    # likelihood function 
    y[i] ~ dnorm(mu[x[i]], tau[x[i]])    
  } 
}" 

Notice that the construct that describes the likelihood...