R Cookbook, 2nd Edition

Chapter 9. General Statistics

Any significant application of R includes statistics or models or graphics. This chapter addresses the statistics. Some recipes simply describe how to calculate a statistic, such as relative frequency. Most recipes involve statistical tests or confidence intervals. The statistical tests let you choose between two competing hypotheses; that paradigm is described next. Confidence intervals reflect the likely range of a population parameter and are calculated based on your data sample.

Null Hypotheses, Alternative Hypotheses, and p-Values

Many of the statistical tests in this chapter use a time-tested paradigm of statistical inference. In the paradigm, we have one or two data samples. We also have two competing hypotheses, either of which could reasonably be true.

One hypothesis, called the null hypothesis, is that nothing happened: the mean was unchanged; the treatment had no effect; you got the expected answer; the model did not improve; and so forth.

The other hypothesis, called the alternative hypothesis, is that something happened: the mean rose; the treatment improved the patients’ health; you got an unexpected answer; the model fit better; and so forth.

We want to determine which hypothesis is more likely in light of the data. Here’s how we do this:

1. To begin, we assume that the null hypothesis is true.

2. We calculate a test statistic. It could be something simple, such as the mean of the sample, or it could be quite complex. The critical requirement ...