a <- 1:5
mean(a)[1] 3Function Basics
How Functions are Named
You will almost always be able to quickly identify the functions in R code by the fixed pattern: FUNCTION_NAME(). That is, an R function is called by writing the function name followed immediately by an opening parenthesis The following list shows some commonly encountered R functions.
c()list()ls()summary()mean()lm()
So, anytime you see a word followed by parenthesis in some R code, you know you’ve found a function call.
How Functions Work
In most cases, R functions work in the same way as mathematical functions:
- Accept some input
- Perform some operation on the input
- Return the results of the operation
For example, the following equation represents a linear function of \(x\).
\[ f(x) = 1.5 + 2x \]
For any value of \(x\) that we provide as input, \(f(x)\) will first multiply that value by 3 and then add 1.5 to the resulting product. So, if we let \(x = 3\), we get \(f(3) = 7.5\).
\[ \begin{align*} f(3) &= 1.5 + 2 \times 3\\ &= 7.5 \end{align*} \]
The mean() function that we used to motivate these ideas operates through the same conceptual process. In terms of a mathematical function, you can think of the R function call mean(1:5) as supplying the input \(x = [1, 2, 3, 4, 5]\) to a function, \(f(x)\), that computes the arithmetic mean of the values in \(x\).
If we let \(n\) represent the number of values in \(x\), we could notate the mathematical representation of the mean() function as follows.
\[ \begin{align} f(x) = \frac{1}{n}\sum_{i = 1}^{n} x_i \end{align} \tag{1}\]
In programming jargon, we would call Equation 1 the definition of the mean function. That is, we’ve defined a tool that we can use to compute the mean of any given set of values, but we haven’t yet used that tool to compute an actual mean.
To use our defined function to compute a mean, we need to apply \(f(x)\) to some input, say, \(a = [1, \ldots, 5]\). After replacing the variable \(x\) on the right hand side of Equation 1 with the input data \(a\), we can compute the mean, \(f(a)\).
\[ \begin{align*} f(a) &= \frac{1 + 2 + 3 + 4 + 5}{5}\\ &= 3 \end{align*} \]
Doing the analogous calculation in R would look like the following.
In most of your R analyses, you won’t need to worry about defining the functions you use: that work has already been done by the developers who wrote the packages you’re using. You will usually only have to worry about preparing the inputs, calling an appropriate function, and processing the function’s output.
Calling Functions
Reading
When you call an R function, you will specify the function inputs by defining values for the function’s arguments. R function arguments are named, and most R functions have multiple arguments. You specify the argument values by writing a comma-separated list of name-value pairs between the parentheses of the function call. For example, the following code creates a vector of 100 random normal deviates, dat, and computes the trimmed mean of dat excluding the most extreme 10% of the values.
dat <- rnorm(n = 100)
mean(x = dat, trim = 0.05)[1] 0.01313535There are some nuances to how we specify the arguments when we call an R function. Most importantly, we don’t always need to explicitly write out the argument’s name, and we don’t necessarily need to provide a value for all arguments. Before we can make much headway on these finer points, however, we need to answer a couple unresolved questions:
- Where are all these mysterious R functions defined, and how do I access new functions?
- How do I know a function’s arguments and what values to specify for those arguments?
In the next two tutorials, you will learn about R packages (the source of most R functions) and R’s documentation system (the means by which you will learn how to use new functions). We will revisit the finer points of calling R functions when we discuss documentation.