Week 4 Tutorial: Functions in R

POP77001 Computer Programming for Social Scientists

Naming Functions

Use lower_case_with_underscores style for R objects.
Give short, but descriptive names.
Try to use verbs in function names:

summarise()
get_coefs()

rather than:

summary()
coefs()

An added benefit is in distinguishing user-defined functions from built-it (e.g. summary(), coef())

Code Layout

Limit all lines to a maximum of 79 characters.
If the function name and definition are too long, break it up:
- across function-indented lines:

long_function_name <- function(a = "a long argument",
                               b = "another argument",
                               c = "another long argument") {
  # As usual code is indented by two spaces.
}

across double-indented lines:

long_function_name <- function(
    a = "a long argument",
    b = "another argument",
    c = "another long argument") {
  # As usual code is indented by two spaces.
}

When it fits, function-indented style should be preferred to double-indented.

Exercise: Function Definition

Study the code for calculating a t-test below:

t_test <- function(x, y) {
  # Calculate the means of the two samples
  mean_x <- mean(x)
  mean_y <- mean(y)
  
  # Calculate the variances of the two samples
  var_x <- var(x)
  var_y <- var(y)
  
  # Calculate the sample sizes
  n_x <- length(x)
  n_y <- length(y)
  
  # Calculate the sample standard errors
  se_x <- sqrt(var_x/n_x)
  se_y <- sqrt(var_y/n_y)
  se <- sqrt(se_x^2 + se_y^2)
  
  # Calculate the t-statistic
  t_stat <- (mean_x - mean_y) / se
  
  # Calculate the degrees of freedom
  df <- se^4/(se_x^4/(n_x - 1) + se_y^4/(n_y - 1))
  
  # Calculate the p-value
  p_val <- 2 * (1 - pt(abs(t_stat), df))
  
  # Create a result list
  res <- list(
    t_statistic = t_stat,
    degrees_of_freedom = df,
    p_value = p_val
  )
  
  return(res)
}

Exercise: Function Components

What are the components of the function t_test()?
Check each component using access functions.

Exercise: Function Call

Call the function on 2 random samples from the standard normal distribution (rnorm()).
What is the return object of this function?
Compare the return object of the t_test() with that of the built-in t.test().
Modify the function code to use implicit return.
Modify the function to return a named vector instead of a list.

Exercise: Built-in Source Code

As R is an open source language, you can check the inner workings of all the built-in functions.
Run getS3method("t.test", "default") to study the source code of the built-in t.test() function.

Exercise: Functionals

As R is a functional language, many of iteration routines can be avoided.
E.g. instead of creating a loop for calculating standard deviations, we can use apply() function.
apply(<object_name>, 2, <function_name>) allows to calculate the desired summary statistic for each of the variables.
Apply this function to the matrix from the exercise above
Now, change 2 in the function call to 1
What do you see? What do the current numbers show? Does this summary make sense and why?

# When dealing with random number generation it's always a good idea to make your code replicable
# by setting the seed with set.seed(function)
set.seed(2025)
# Here we create a matrix of 30 observations of 5 variables
# where each variable is a random draw from a normal distribution with mean 0
# and standard deviation drawn from a uniform distribution between 0 and 10
mat <- mapply(
  function(x) cbind(rnorm(n = 30, mean = 0, sd = x)),
  runif(n = 5, min = 0, max = 10)
)

mat

             [,1]        [,2]        [,3]        [,4]         [,5]
 [1,]   0.0780885  3.48089343   2.9553545   3.2248615  -4.66712911
 [2,]  -8.3269637 -2.05680059   6.5670977   8.3727181 -13.86628154
 [3,]   1.2834069 -4.25078791   3.0311714  -3.6736945   2.20685092
 [4,]  12.2189488 12.51048821   2.2500211   5.8992348  12.81071523
 [5,] -14.5079803 -0.83591818  -0.8329266   1.0321989   5.73323413
 [6,]   7.8277431 -0.04931062   1.4101378   6.7058639   2.63359979
 [7,]  -2.5172557  1.27351635  -5.6927903 -12.9850971  -8.19349948
 [8,]  -9.0808601  1.07779111   3.0050245  -4.1673004   0.51438396
 [9,]   6.5582896 -3.70133731   7.1498934  -8.8572673   0.05485376
[10,]   4.1685004 -6.50775660   9.0180872  -4.5555447  -4.32601307
[11,]  10.2156894 -1.84773737   2.4000462   6.2044559  -6.12311135
[12,]  -6.1880010 -4.12393197  -2.1740754  -0.4008144   3.40181041
[13,]  -4.7220233  0.21939243   3.2602544   1.7233189  -1.59565895
[14,]  -7.7975071  7.67400612   5.9990204   7.2296638  -0.54940831
[15,]   0.8389551  6.27673537   5.4250108   4.9929334  -4.11237985
[16,]  -8.8303620  2.01744395  -1.2485669   7.0326504   7.41427192
[17,]  -6.7987871  3.87487181 -11.5966579  -4.1382655  12.93379615
[18,]   9.6151288 -2.91265614   5.0533075   2.0702789  -1.76367895
[19,]  10.8374659  8.50027774  -2.1024975  -2.2128037   9.27726204
[20,]   6.5590893  4.15403829  -3.4412653   0.2689806  -1.02485010
[21,]   6.5197367  4.07635880   6.7820067  -3.9887753   5.01717503
[22,]  -8.2150378 -0.79340248  -5.5809099   0.7797501   1.38873142
[23,]   0.7504032  7.01848922   0.4065937 -10.0721259  -4.42487986
[24,]   4.6233436 -5.21899205   0.6368000  -8.9976512   9.75800935
[25,]  -8.1970619  4.13052036   3.6410426  13.1384188  -0.18438540
[26,]  -2.6565373 -5.58620440   1.8889740   8.9695624  12.56154387
[27,]   1.6696565  2.71295623  -6.5482715 -10.2190913   0.64368393
[28,]   1.8708354 -4.61167206  -1.1712393   0.6024034   4.14227228
[29,]   4.7594528  2.03420819   6.3618553  -2.6569757  -3.66269350
[30,]  -5.7215014  0.63822093   6.7654597   5.9124287  -8.75833965

Week 4 Exercise (unassessed)

Re-visit the code for converting grades into marks:

convert_mark_to_grade <- function(mark) {
  if (mark >= 70) {
    grade <- "I"
  } else if (mark >= 60) {
    grade <- "II.1"
  } else if (mark >= 50) {
    grade <- "II.2"
  } else {
    grade <- "F"
  }
  grade
}

As discussed in the lecture, this function only takes a single mark as an input.
Modify this function such that if takes a vector of marks (longer than 1) as an input and returns a vector of grades.