# How to Use the all.equal() Function in R

Often you may want to check if all corresponding elements in two vectors are equal or roughly equal in R.

The easiest way to do so is by using the all.equal() function from base R, which is designed to perform this exact task.

The all.equal() function uses the following basic syntax:

all.equal(target, current, tolerance=1.5e=8, …)

where:

• target: Name of one vector
• current: Name of another vector to compare
• tolerance: Differences smaller than this number are not reported.

Note that you do not have to provide a value for the tolerance argument. The default value used is 1.5e-8.

This function will return one of the following values:

• TRUE if all corresponding elements in each vector are equal (or less than the tolerance value)
• The mean relative difference if all corresponding elements in each vector are not equal

The following example shows how to use the all.equal() function in practice in several different scenarios.

Note: The all.equal() function comes built-in with base R so you do not need to install or load any external packages to use this function.

## Example: How to Use the all.equal() Function in R

Suppose we create the following two vectors named vector1 and vector2:

```#create two vectors
vector1 <- c(1, 2, 3, 4, 5, 6, 7, 8)
vector2 <- c(1, 2, 3, 4, 5, 6, 7, 8)
```

We can use the all.equal() function to check if each of the corresponding elements from each of these vectors is equal:

```#check if vectors are equal
all.equal(vector1, vector2)

[1] TRUE```

Since each of the corresponding elements from each of these vectors are equal, the all.equal() function simply returns a value of TRUE.

Now suppose we create the following two vectors named vector1 and vector2 that do not have all of the same elements:

```#create two vectors
vector1 <- c(1, 2, 3, 4, 5)
vector2 <- c(1, 2, 3, 4, 12)
```

We can use the all.equal() function to check if each of the corresponding elements from each of these vectors is equal:

```#check if vectors are equal
all.equal(vector1, vector2)

[1] "Mean relative difference: 1.4"
```

Since each of the corresponding elements from each of these vectors are not equal, the all.equal() function returns the mean relative difference between the two vectors, which turns out to be 1.4.

Note that the mean relative difference simply represents the difference between the mean of vector2 and vector1.

In this particular example, the mean of vector2 is 4.4 while the mean of vector1 is 3.

Thus, the mean relative difference is calculated as 4.4 – 3 = 1.4.

Note that we could specify a value for the tolerance argument if we’d like to specify an upper difference value that should be considered “equal” between the values.

For example, we can use the following syntax with the all.equal() function to check if all elements between two vectors are equal in which the tolerance value is set to 2:

```#create two vectors
vector1 <- c(1, 2, 3, 4, 5)
vector2 <- c(1, 2, 3, 4, 7)

#check if vectors are equal
all.equal(vector1, vector2, tolerance=2)

[1] TRUE```

This returns TRUE because there are no corresponding elements that have a difference greater than 2.