How to Calculate Standard Error in R

Standard Error (SE) measures the variability or dispersion of the sample mean estimate of a population mean.

Here are three ways to calculate standard error in R:

1. Using sd() with length()
2. Using the standard error formula
3. Using std.error() from plotrix package

Here is the basic formula:

where:

1. σ = sample standard deviation

2. n = sample size

Method 1: Using sd() with length()

The easiest way to calculate the standard error is to divide the standard deviation by the square root of the sample size.

Syntax

sd(data)/sqrt(length((data)))

Example

# vector
rv <- c(11, 21, 19, 46)

# calculate standard error
print(sd(rv) / sqrt(length((rv))))

# Output: [1] 7.564996

Method 2: Using the standard error formula

This is a manual way of implementing the first method. You can use the formula above if you have the standard deviation and the sample size.

Syntax

sqrt(sum((vec-mean(vec))^2/(length(vec)-1)))/sqrt(length(vec))

Example

# vector
rv <- c(11, 21, 19, 46)

# calculate standard error
s_err <- sqrt(sum((rv - mean(rv))^2 / (length(rv) - 1))) / sqrt(length(rv))

# print the standard error
print(s_err)

# Output: [1] 7.564996

Method 3: Using std.error() from ‘plotrix’ package

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

Syntax

std.error(x,na.rm)

Parameters

library("plotrix")

rv <- c(11, 21, 19, 46)

op <- std.error(rv, na.rm = TRUE)

print(op)

# [1] 7.564996

That’s it!