Notation isn’t just about using arbitrary symbols to represent quantities. Consistent use of notation can help reveal the structure and relationships present in a collection of ideas, such as statistical inference, and can help clarify the roles of the various quantities used in data analysis. To emphasise the structure in the notation we include a brief overview here of the different types of notation and where they have been used.

Greek Letters

Greek letters are frequently used in mathematics for a range of purposes. You will have seen the Greek letter ‘p’, $\pi$, used for the area of the unit circle.
The most important role of Greek letters for us has been to signify a population parameter. The table below shows the ones we have used in this role and others, listed alphabetically.

Greek symbols

The whole Greek alphabet, showing the names and English equivalents of these letters, is given for reference in the below.

The Greek alphabet

Capital Letters

We have generally used capital letters to denote random variables, with lowercase letters used for particular outcomes of these. For example, $\bar{x}$ denotes a particular number, the mean from a sample, whereas $\bar{X}$ denotes the random process of taking a random sample and returning the mean.

We have had two main uses for random variables. Firstly we have thought of them as models for sampling from populations. The random variable $X$ might be the height of a randomly chosen female, for instance.
The second use has been to discuss the sampling distribution of statistics. In Chapter 5 we used the sample mean $\bar{x}$ to summarise the location of an observed distribution, while in Chapter 13 we used the random variable $\bar{X}$ to think about how $\bar{x}$ would change from sample to sample.

Other Symbols

The table below shows a list of some of the other symbols used in this book, together with the first section that discusses their use and meaning.

Other symbols