Random variables

Chapter 1 introduced the data frame as the data structure for storing vectors of numbers as well as factors. Numerical vectors and factors represent in R what statisticians call random variables. A random variable is the outcome of an experiment. Here are some examples of experiments and their associated random variables:

• tossing a coin Tossing a coin will result in either “head” or “tail.” Hence, the toss of a coin is a random variable with two outcomes.

• throwing a dice In this case, we are dealing with a random variable with six possible outcomes, 1, 2, …, 6.

• counting words We can count the frequencies with which words occur in a given corpus or text. Word frequency is a random variable with, as possible values, 1,2,3, …, N, with N the size of the corpus.

• familiarity rating Participants are asked to indicate on a seven-point scale how frequently they think words are used. The ratings elicited for a given word will vary from participant to participant, and constitute a random variable.

• lexical decision Participants are asked to indicate, by means of button presses, whether a word presented visually or auditorily is an existing word of the language. There are two outcomes, and hence two random variables, for this type of experiment: the accuracy of a response (with levels “correct” and “incorrect”) and the latency of the response (in milliseconds).