Descriptive statistics in R

Problem

We'd like to compute descriptive statistics in R.

Solution

The summary function returns a set of summary statistics for the input (a vector, data frame or model).

# For a variable
summary(iris$Sepal.Length)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  4.300   5.100   5.800   5.843   6.400   7.900 

# For a data frame
summary(iris)

  Sepal.Length    Sepal.Width     Petal.Length    Petal.Width          Species  
 Min.   :4.300   Min.   :2.000   Min.   :1.000   Min.   :0.100   setosa    :50  
 1st Qu.:5.100   1st Qu.:2.800   1st Qu.:1.600   1st Qu.:0.300   versicolor:50  
 Median :5.800   Median :3.000   Median :4.350   Median :1.300   virginica :50  
 Mean   :5.843   Mean   :3.057   Mean   :3.758   Mean   :1.199                  
 3rd Qu.:6.400   3rd Qu.:3.300   3rd Qu.:5.100   3rd Qu.:1.800                  
 Max.   :7.900   Max.   :4.400   Max.   :6.900   Max.   :2.500  

The fivenum function returns Tukey's five number summary (minimum, lower-hinge, median, upper-hinge, maximum) for the input data.

# For a variable
fivenum(iris$Sepal.Width)

[1] 2.0 2.8 3.0 3.3 4.4

The boxplot.stats function returns the statistics necessary for producing box plots.

boxplot.stats(iris$Sepal.Width)

$stats
[1] 2.2 2.8 3.0 3.3 4.0

$n
[1] 150

$conf
[1] 2.935497 3.064503

$out
[1] 4.4 4.1 4.2 2.0

To return a specific statistic we type boxplot.stats(iris$Sepal.Width) followed by:

$stats - vector with Tukey's five number summary.
$n - the number of non-NA observations.
$conf - the lower and upper extremes of the ‘notch’.
$out- outliers.

The psych package

For a data frame

library(psych)
describe(iris)

             vars   n mean   sd median trimmed  mad
Sepal.Length    1 150 5.84 0.83   5.80    5.81 1.04
Sepal.Width     2 150 3.06 0.44   3.00    3.04 0.44
Petal.Length    3 150 3.76 1.77   4.35    3.76 1.85
Petal.Width     4 150 1.20 0.76   1.30    1.18 1.04
Species*        5 150  NaN   NA     NA     NaN   NA
             min  max range  skew kurtosis   se
Sepal.Length 4.3  7.9   3.6  0.31    -0.61 0.07
Sepal.Width  2.0  4.4   2.4  0.31     0.14 0.04
Petal.Length 1.0  6.9   5.9 -0.27    -1.42 0.14
Petal.Width  0.1  2.5   2.4 -0.10    -1.36 0.06
Species*     Inf -Inf  -Inf    NA       NA   NA

Statistics by group

describeBy(iris, group = iris$Species)

group: setosa
             vars  n mean   sd median trimmed  mad
Sepal.Length    1 50 5.01 0.35    5.0    5.00 0.30
Sepal.Width     2 50 3.43 0.38    3.4    3.42 0.37
Petal.Length    3 50 1.46 0.17    1.5    1.46 0.15
Petal.Width     4 50 0.25 0.11    0.2    0.24 0.00
Species*        5 50  NaN   NA     NA     NaN   NA
             min  max range skew kurtosis   se
Sepal.Length 4.3  5.8   1.5 0.11    -0.45 0.05
Sepal.Width  2.3  4.4   2.1 0.04     0.60 0.05
Petal.Length 1.0  1.9   0.9 0.10     0.65 0.02
Petal.Width  0.1  0.6   0.5 1.18     1.26 0.01
Species*     Inf -Inf  -Inf   NA       NA   NA
--------------------------------------- 
group: versicolor
             vars  n mean   sd median trimmed  mad
Sepal.Length    1 50 5.94 0.52   5.90    5.94 0.52
Sepal.Width     2 50 2.77 0.31   2.80    2.78 0.30
Petal.Length    3 50 4.26 0.47   4.35    4.29 0.52
Petal.Width     4 50 1.33 0.20   1.30    1.32 0.22
Species*        5 50  NaN   NA     NA     NaN   NA
             min  max range  skew kurtosis   se
Sepal.Length 4.9  7.0   2.1  0.10    -0.69 0.07
Sepal.Width  2.0  3.4   1.4 -0.34    -0.55 0.04
Petal.Length 3.0  5.1   2.1 -0.57    -0.19 0.07
Petal.Width  1.0  1.8   0.8 -0.03    -0.59 0.03
Species*     Inf -Inf  -Inf    NA       NA   NA
--------------------------------------- 
group: virginica
             vars  n mean   sd median trimmed  mad
Sepal.Length    1 50 6.59 0.64   6.50    6.57 0.59
Sepal.Width     2 50 2.97 0.32   3.00    2.96 0.30
Petal.Length    3 50 5.55 0.55   5.55    5.51 0.67
Petal.Width     4 50 2.03 0.27   2.00    2.03 0.30
Species*        5 50  NaN   NA     NA     NaN   NA
             min  max range  skew kurtosis   se
Sepal.Length 4.9  7.9   3.0  0.11    -0.20 0.09
Sepal.Width  2.2  3.8   1.6  0.34     0.38 0.05
Petal.Length 4.5  6.9   2.4  0.52    -0.37 0.08
Petal.Width  1.4  2.5   1.1 -0.12    -0.75 0.04
Species*     Inf -Inf  -Inf    NA       NA   NA