The continuing revolution in computing is having a dramatic influence on statistics. Not only is the exploratory analysis of data becoming easier, with more and more automated graphs and calculations, but also the statistical study of very large and very complex data sets (e.g., big data) is now feasible. Companies that have long collected information on customers are now using business analytics to discover meaningful patterns in these data, which in turn drive decision making.

This fast and inexpensive computing has also led to the development of new analysis methods—methods that apply previously unthinkable amounts of computation. In this chapter, we focus on bootstrap confidence intervals and permutation tests. These methods apply the power of the computer to relax some of the conditions needed for traditional inference and to do inference in new settings. They can be used to answer questions such as:

• Do all daily numbers in a lottery have the same payoff? In other words, are all daily numbers equally likely to be chosen by the players?
• What is the 95% confidence interval for the correlation between price and rating for the population of laundry detergents?
• Does the daily number of aggressive behaviors of nursing-home patients with dementia increase when there is a full moon?

As with all the other methods discussed in this textbook, the most important requirement for trustworthy conclusions about a population is still that our data can be regarded as random samples from a population or populations; not even the computer can rescue voluntary response samples or confounded experiments. But these new methods set us free from the need for Normal data or samples large enough to rely on the central limit theorem. They also work the same way for many different statistics in many different settings. They can, with sufficient computing power, give results that are more accurate than those from traditional methods.

Bootstrap confidence intervals (Sections 16.2 and 16.4) and permutation tests (Section 16.5) are conceptually simple because they appeal directly to the basis of all inference: the sampling distribution, which shows what would happen if we took very many samples under the same conditions. Although the new methods do have limitations, some of which we will illustrate, their effectiveness and range of use are so great that they are now widely used in a variety of settings.