Descriptive statistics by group in R

Problem

We'd like to report descriptive statistics in R by a grouping variable and subsetting the output statistics.

Solution

We will use the data frame iris, columns Sepal.Length and Sepal.Width and grouping by Species. In our example, we want to return the mean, the standard deviation, the skewness and kurtosis.

Subset of descriptive statistics by group

library(psych)
# Variables by index
d <- describeBy(iris[1:2], group = iris$Species)
# Two options to subset the statistics:
lapply(d, "[", , c(3, 4, 11, 12))
lapply(d, subset, , c(3, 4, 11, 12)) 

# Variables by name
i <- match(c("Sepal.Length", "Petal.Length"), names(iris))
d <- describeBy(iris[i], group = iris$Species)
lapply(d, subset, , c("mean", "sd", "skew", "kurtosis")) 

$setosa
             mean   sd skew kurtosis
Sepal.Length 5.01 0.35 0.11    -0.45
Sepal.Width  3.43 0.38 0.04     0.60

$versicolor
             mean   sd  skew kurtosis
Sepal.Length 5.94 0.52  0.10    -0.69
Sepal.Width  2.77 0.31 -0.34    -0.55

$virginica
             mean   sd skew kurtosis
Sepal.Length 6.59 0.64 0.11    -0.20
Sepal.Width  2.97 0.32 0.34     0.38

Subset of descriptive statistics without grouping

# Seleccionamos las columnas deseadas de la tabla
d <- describe(iris[1:2])
# Subsetting output statistics
d[, c(3, 4, 11, 12)]

             mean   sd skew kurtosis
Sepal.Length 5.84 0.83 0.31    -0.61
Sepal.Width  3.06 0.44 0.31     0.14

References

• Descriptive statistics in R

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

Subconjunto de estadísticas descriptivas en R

Problema

Deseamos calcular las estadísticas descriptivas para unas variables de un data frame. Esta vez, queremos seleccionar tanto las estadísticas como las variables de la tabla.

Solución

Utilizaremos el data frame iris, pero solamente para las columnas Sepal.Length y Sepal.Width. En nuestro ejemplo, calcularemos la media (mean), la desviación típica (SD), la asimetría (skewness) y la curtosis (kurtosis). Pero

Para una tabla

library("psych")
# Seleccionamos las columnas deseadas de la tabla
d <- describe(iris[1:2])
# Seleccionamos las estadísticas deseadas
d[, c(3, 4, 11, 12)]

             mean   sd skew kurtosis
Sepal.Length 5.84 0.83 0.31    -0.61
Sepal.Width  3.06 0.44 0.31     0.14

Estadísticas por grupo

# Variables por índice
d <- describeBy(iris[1:2], group = iris$Species)
# Dos opciones para seleccionar las estadísticas
# de la lista de data frames
lapply(d, "[", , c(3, 4, 11, 12))
lapply(d, subset, , c(3, 4, 11, 12)) 

# Variables por nombre
i <- match(c("Sepal.Length", "Petal.Length"), names(iris))
d <- describeBy(iris[i], group = iris$Species)
lapply(d, subset, , c("mean", "sd", "skew", "kurtosis")) 

$setosa
             mean   sd skew kurtosis
Sepal.Length 5.01 0.35 0.11    -0.45
Sepal.Width  3.43 0.38 0.04     0.60

$versicolor
             mean   sd  skew kurtosis
Sepal.Length 5.94 0.52  0.10    -0.69
Sepal.Width  2.77 0.31 -0.34    -0.55

$virginica
             mean   sd skew kurtosis
Sepal.Length 6.59 0.64 0.11    -0.20
Sepal.Width  2.97 0.32 0.34     0.38

Referencias

• Estadísticas descriptivas en R
• Introducción al diagrama de caja (box plot) en R
• Regresión lineal simple para principiantes en R

Estadísticas descriptivas en R

Problema

Deseamos calcular estadísticas descriptivas a nuestros datos.

Solución

Vamos a ver algunas de las fórmulas que hemos visto de manera dispersa en otras entradas.

Función summary

# Para una sola 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 

# Para una tabla (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  

Función fivenum

Resumen con los 5 números de Tukey empleados en los diagramas de caja: mínimo, bigote inferior, mediana, bigote superior, máximo

# Para una variable solamente
fivenum(iris$Sepal.Width)

[1] 2.0 2.8 3.0 3.3 4.4

Función boxplot.stats

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

Podemos acceder a los elementos de la lista anterior, con el símbolo $ seguido del elemento de la lista:

$stats - vector con los 5 números de Tukey.
$n - número de observaciones.
$conf - intervalo de confianza para la media.
$out- los valores de los valores atípicos (outliers).

Con el paquete psych

Para una tabla

install.packages("psych")
require("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

Estadísticas por grupo

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

Referencias

• Subcojunto de estadísticas descriptivas en R
• Introducción al diagrama de caja (box plot) en R
• Regresión lineal simple para principiantes en R