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This post originally appeared on my WordPress blog on May 23, 2010. I present it here in its original form.

The R Function of the Day series will focus on describing in plain language how certain R functions work, focusing on simple examples that you can apply to gain insight into your own data.

Today, I will discuss the sample function.

### Random Permutations

In its simplest form, the sample function can be used to return a random permutation of a vector. To illustrate this, let’s create a vector of the integers from 1 to 10 and assign it to a variable x.

```x <- 1:10
```

Now, use sample to create a random permutation of the vector x.

```sample(x)

  3  2  1 10  7  9  4  8  6  5
```

Note that if you give sample a vector of length 1 (e.g., just the number 10) that it will do the exact same thing as above, that is, create a random permutation of the integers from 1 to 10.

```sample(10)

 10  7  4  8  2  6  1  9  5  3
```

#### Warning!

This can be a source of confusion if you're not careful. Consider the following example from the sample help file.

```sample(x[x > 8])
sample(x[x > 9])

 10  9
  9  3  4  8  1 10  7  5  2  6
```

Notice how the first output is of length 2, since only two numbers are greater than eight in our vector. But, because of the fact that only one number (that is, 10) is greater than nine in our vector, sample thinks we want a sample of the numbers from 1 to 10, and therefore returns a vector of length 10.

### The replace argument

Often, it is useful to not simply take a random permutation of a vector, but rather sample independent draws of the same vector. For instance, we can simulate a Bernoulli trial, the result of the flip of a fair coin. First, using our previous vector, note that we can tell sample the size of the sample we want, using the size argument.

```sample(x, size = 5)

  2 10  5  1  6
```

Now, let's perform our coin-flipping experiment just once.

```coin <- c("Heads", "Tails")
sample(coin, size = 1)

 "Tails"
```

And now, let's try it 100 times.

```sample(coin, size = 100)

Error in sample(coin, size = 100) :
cannot take a sample larger than the population when 'replace = FALSE'
```

Oops, we can't take a sample of size 100 from a vector of size 2, unless we set the replace argument to TRUE.

```table(sample(coin, size = 100, replace = TRUE))

53    47
```

### Simple bootstrap example

The sample function can be used to perform a simple bootstrap. Let's use it to estimate the 95% confidence interval for the mean of a population. First, generate a random sample from a normal distribution.

```rn <- rnorm(1000, 10)
```

Then, use sample multiple times using the replicate function to get our bootstrap resamples. The defining feature of this technique is that replace = TRUE. We then take the mean of each new sample, gather them, and finally compute the relevant quantiles.

```quantile(replicate(1000, mean(sample(rn, replace = TRUE))),
probs = c(0.025, 0.975))

2.5%     97.5%
9.936387 10.062525
```

Compare this to the standard parametric technique.

```t.test(rn)\$conf.int

  9.938805 10.061325
attr(,"conf.level")
 0.95
```