Example: Aggregation Statistics

Summarizing a data set

The most straight forward function which returns some aggregated statistical information about a data set is summary.

a <- c("A", "B", "C", "A", "B", "A", "A")
b <- c("X", "X", "X", "X", "Y", "Y", "Y")
c <- c(1, 2, 3, 4, 5, 6, 7)
d <- c(10, 20, 30, 40, 50, 60, 70)
df <- data.frame(Cat1 = a, Cat2 = b, Val1 = c, Val2 = d)
summary(df)

##  Cat1  Cat2       Val1          Val2   
##  A:4   X:4   Min.   :1.0   Min.   :10  
##  B:2   Y:3   1st Qu.:2.5   1st Qu.:25  
##  C:1         Median :4.0   Median :40  
##              Mean   :4.0   Mean   :40  
##              3rd Qu.:5.5   3rd Qu.:55  
##              Max.   :7.0   Max.   :70

It provides the minimum, maximum, mean and median value of each numerical column along with the first and third quartile (i.e. the values separating 25% from 75% and 75% from 100% of the data). Non-numeric columns are summarized by counting the individual values (which will be ommitted after the first few rows so it is only informative for columns with just a few different character values).

The information of summary can also be obtained by specific functions but these will return only the same numbers if applied to a single column. For example the min function will return the minimum value of all values supplied to it. This leads to a return of 1 no matter if it is applied to column Val1 or to columns Val1 and Val2:

min(df[,3])

## [1] 1

min(df[,3:4])

## [1] 1

The other functions included in summary are

max(df$Val1)

## [1] 7

quantile(df$Val1,  probs = c(0.25, 0.75))

## 25% 75% 
## 2.5 5.5

mean(df$Val1)

## [1] 4

median(df$Val1)

## [1] 4

Aggregated statistics

If you are interested in aggregated statistics in terms of sums or means across columns or rows, you can use one of the rowSums, rowMeans, colSums, or colMeans functions.

df  # Just print the data frame so you can easily understand the results

##   Cat1 Cat2 Val1 Val2
## 1    A    X    1   10
## 2    B    X    2   20
## 3    C    X    3   30
## 4    A    X    4   40
## 5    B    Y    5   50
## 6    A    Y    6   60
## 7    A    Y    7   70

rowSums(df[,3:4])

## [1] 11 22 33 44 55 66 77

rowMeans(df[,3:4])

## [1]  5.5 11.0 16.5 22.0 27.5 33.0 38.5

colSums(df[,3:4])

## Val1 Val2 
##   28  280

colMeans(df[,3:4])

## Val1 Val2 
##    4   40

For other summary statistics across rows or if you want to define a grouping variable which controls the summary statistics, the aggregate function is very helpfull.

aggregate(df[,3:4], by = list(df$Cat1), FUN = median)

##   Group.1 Val1 Val2
## 1       A  5.0   50
## 2       B  3.5   35
## 3       C  3.0   30

Please note that the grouping elements (parameter “by”) have to be supplied as list so if you want to use a column of a data frame, use the list function to convert the factor to a list.

Of course, one can also use more than one grouping variable.

aggregate(df[,3:4], by = list(df$Cat1, df$Cat2), FUN = sum)

##   Group.1 Group.2 Val1 Val2
## 1       A       X    5   50
## 2       B       X    2   20
## 3       C       X    3   30
## 4       A       Y   13  130
## 5       B       Y    5   50

In some cases it is usefull to construct a specific aggregation key, so think of that easy possibility if you run into problems. As one example: imagine that the aggregate function can not use more than one grouping variable. To get the same result as in the line above, one can define a key consisting of the entries of column Cat1 and Cat2 (sorting is different but who cares):

df$key <- paste0(df$Cat1, df$Cat2)
aggregate(df[,3:4], by = list(df$key), FUN = sum)

##   Group.1 Val1 Val2
## 1      AX    5   50
## 2      AY   13  130
## 3      BX    2   20
## 4      BY    5   50
## 5      CX    3   30