This article will introduce to you how to calculate standard error in R is progressed. Let’s jump right in!

Standard Error In R

What is standard error in R, anyway? 

The standard error of mean is a highly significant and helpful concept in the field of statistics. In contrast to standard deviation, which measures the degree of data dispersion, it reveals how the sample deviates from the real mean.

Simply dividing the standard deviation by the square root of the sample size will yield this kind of fluctuation. Besides, the SE is equal to the square root of the variance of the sampling distribution, which is equal to the variance of the data divided by N.

How To Calculate Standard Error In R?

There are 2 methods that can be of great use in standard error calculation using R programming language.

Method #1: Employing sd() Function With Length Function

In this case, the sd() function will be used to get the standard deviation, and the length() function will be used to determine the observations’ sum.

Syntax: 

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

Let’s say you wish to measure a standard error from a 10-value set in a vector using the R program. Here is what the scene may look like:

Running the code:

# consider a vector with 10 elements
a < - c(179, 160, 136, 227, 123, 23,
        45, 67, 1, 234)

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

Output:

26.20274

Method #2: Employing The std.error() Function

The std.error() function directly returns the value’s Standard Error. Yet first, you need to install the plotrix package in R so you can utilize this method. That way, the std.error() method is a part of the plotrix add-on package.

Have a look at the example below.

Syntax:

std.error(x,na.rm)

As such, x is a numerical observations’ vector and na.rm is a dummy argument to fit in demand with other features.

Running the code:

# import plotrix package
library("plotrix")

# consider a vector with 4 elements
op <- std.error(c(11, 21, 19, 46))

# calculate standard error using in built
# function
print(op)

Output:

[1] 7.564996

Method #3: Employing Standard Error Formula

Another approach is to utilize the formula for standard error to manually compute the standard error as illustrated below.

Syntax: 

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

Argument:

• sqrt function is to address the square root
• data is the input you wish to calculate
• sum is of usage to determine the elements’ sum in the data
• length is the feature returning the length of the data
• mean is the feature finding the mean of the data

Running the code:

# consider a vector with 10 elements
a <- c(1,2,3,4)

# calculate standard error
print(sqrt(sum((a - mean(a)) ^ 2/(length(a) - 1)))
      /sqrt(length(a)))

Output:

[1] 0.6454972

The Bottom Line

Above is our in depth instruction regarding how to calculate standard error in R. Hopefully, this article can be of great help to you. See then!