How to Calculate Standard Error in R

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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

Figure of using sd() with length() function

Here is the basic formula:

SE = \sigma / sqrt(n)

where:

  1. = 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.

    Figure of Using the standard error formula

    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.

    Figure of Using the plotrix package

    Syntax

    std.error(x,na.rm)

    Parameters

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

    Example

    library("plotrix")

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

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

print(op)

# [1] 7.564996

    That’s it!

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