Calculating Statistics for Groups

In general, the functions used to calculate summary statistics for a single group are the same functions used to calculate summary statistics for multiple groups.

The examples below use data from the mtcars data set.

Base R

The aggregate() function is a function that can be used to calculate a statistics for many groups. This function is automatically loaded when R is started.

Mean for Each Group

with(mtcars, aggregate(mpg ~ gear, FUN = mean))

##   gear      mpg
## 1    3 16.10667
## 2    4 24.53333
## 3    5 21.38000

Median for Each Group

with(mtcars, aggregate(mpg ~ gear, FUN = median))

##   gear  mpg
## 1    3 15.5
## 2    4 22.8
## 3    5 19.7

Sample Standard Deviation for Each Group

with(mtcars, aggregate(mpg ~ gear, FUN = sd))

##   gear      mpg
## 1    3 3.371618
## 2    4 5.276764
## 3    5 6.658979

Tidyverse

The dplyr package makes calculating statistics for multiple groups easy. This process is the same as calculating summary statistics for a sinble group with one additional step. See the dplyr section of the summary statistics page for details.

library(dplyr)
mtcars %>% 
  group_by(gear) %>% 
  summarize( Min = min(mpg),
             Q1 = quantile(mpg, .25),
             Avg_MPG = mean(mpg), 
             Q3 = quantile(mpg, .75),
             Max = max(mpg)
             )

## # A tibble: 3 x 6
##   gear    Min    Q1 Avg_MPG    Q3   Max
##   <fct> <dbl> <dbl>   <dbl> <dbl> <dbl>
## 1 3      10.4  14.5    16.1  18.4  21.5
## 2 4      17.8  21      24.5  28.1  33.9
## 3 5      15    15.8    21.4  26    30.4

mosaic

The mosaic package makes changes to some of the basic functions in R so that they may use the ~ operator to calculate summary statistics for groups. It also modifies functions to better handle missing data.

Summary Statistics for Each Group

library(mosaic) # Loads the mosaic package
favstats(mpg ~ gear, data = mtcars)

##   gear  min   Q1 median     Q3  max     mean       sd  n missing
## 1    3 10.4 14.5   15.5 18.400 21.5 16.10667 3.371618 15       0
## 2    4 17.8 21.0   22.8 28.075 33.9 24.53333 5.276764 12       0
## 3    5 15.0 15.8   19.7 26.000 30.4 21.38000 6.658979  5       0

Mean for Each Group

library(mosaic) # Loads the mosaic package
mean(mtcars$mpg ~ mtcars$gear)

##        3        4        5 
## 16.10667 24.53333 21.38000

Mathematicss, Computer Science, and Statistics Department Gustavus Adolphus College