# Standard Error in R: What is it and How to Calculate it

The standard error in R is a measure of the variability of a sample. It is calculated as the standard deviation of the sampling distribution of a statistic, such as the mean. The standard error is the standard deviation divided by the square root of the sample size.

R does not come with a standard error function. You need to create a standard error function or use a package like plotrix to calculate.

The sampling distribution is the variance of the data divided by N, and the SE is the square root.

The formula for finding standard error in R is the following.

``se <- function(x) sqrt(var(x) / length(x))``

The standard error can be calculated by dividing the standard deviation of our input by the square root of the length of our input. Let’s take an example.

``````std <- function(a) sd(a) / sqrt(length(a))

op <- std(c(11, 21, 19, 46))

print(op)``````

Output

``[1] 7.564996``

And we get the Standard Error of the vector.

If you want to remove NA values, you can use the following function.

``````std <- function(x, na.rm = FALSE) {
if (na.rm) x <- na.omit(x)
sqrt(var(x) / length(x))
}

op <- std(c(11, 21, 19, 46))

print(op)``````

Output

``[1] 7.564996``

Let’s take another example in which we will use the set.seed() function and then use the rnorm() function to generate 10 random numbers.

``````set.seed(1)

data <- rnorm(10)

print(data)

se <- sd(data) / sqrt(10)

cat("The Standard Error is: ", se)``````

Output

``````[1] -0.6264538 0.1836433 -0.8356286 1.5952808 0.3295078 -0.8204684
[7] 0.4874291 0.7383247 0.5757814 -0.3053884

The Standard Error is: 0.246843``````

## How to Calculate Standard Error in R

To calculate the standard error in R, use the std.error() function, which takes a numeric vector of values as input and returns the standard error of the mean for those values.

To use the std.error() function in R, install the plotrix package. The plotrix add-on package includes the std.error() function, which can also calculate the standard error of the mean.

The std.error() function calculates the standard error of the mean. The std.error() function will accept a numeric vector.

### Syntax

``std.error(x,na.rm)``

### Arguments

x: It is a vector of numerical observations.
na.rm: It is a dummy argument to match other functions.

### Example

``````library("plotrix")

op <- std.error(c(11, 21, 19, 46))

print(op)``````

#### Output

``[1] 7.564996``

## Conclusion

The the standard error (SE) in R is a valuable measure of the precision of sample statistics, such as the mean or regression coefficient. It represents the variability of sample means or coefficients across multiple random samples from the same population.

Understanding and calculating the SE can help researchers and analysts make inferences about the population based on the sample data and assess the reliability of their estimates.