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An R Companion for the Handbook of Biological Statistics

Salvatore S. Mangiafico

Standard Error of the Mean

The standard error of the mean can be calculated with standard functions in the native stats package.  The describe function in the psych package includes the standard error of the mean along with other descriptive statistics.  This function is useful to summarize multiple variables in a data frame.

 

Introduction

Similar statistics

See the Handbook for information on these topics.

 

Example

Standard error example

 

### --------------------------------------------------------------
### Standard error example, p. 115
### --------------------------------------------------------------

Input =("
Stream                     Fish
 Mill_Creek_1                76
 Mill_Creek_2               102
 North_Branch_Rock_Creek_1   12
 North_Branch_Rock_Creek_2   39
 Rock_Creek_1                55
 Rock_Creek_2                93
 Rock_Creek_3                98
 Rock_Creek_4                53
 Turkey_Branch              102
")

Data = read.table(textConnection(Input),header=TRUE)


### Calculate standard error manually

sd(Data$ Fish, na.rm=TRUE) /  
   sqrt(length(Data$Fish[!is.na(Data$ Fish)]))      # Standard error

 

[1] 10.69527

 

 

###  Use describe function from psych package for standard error
###  Also works on whole data frames

library(psych)

describe(Data$ Fish,
               type=2)        # Type of skew and kurtosis

 

 

  vars n mean    sd median trimmed  mad min max range  skew kurtosis   se

1    1 9   70 32.09     76      70 34.1  12 102    90 -0.65    -0.69 10.7

 

#     #     #

 

 

How to calculate the standard error

Methods are described in the “Example” section above.