In statistics, one of the most basic activities we do is computing summaries of variables. These summaries might be as simple as an average, or more complex. Let's look at some simple examples.

When you read the results of a medical trial, you will see things such as "The average age of subjects in this trial was 55 years in the treatment group, and 54 years in the control group."

As another example, let's look at one from the world of baseball.

Batting Leaders per Team

These two examples have a lot in common, even if they don't appear to when first reading. In the first example, we have a dataset from a medical trial. We want to break up the dataset into two groups, treatment and control, and then compute the sample average for age within each group.

In the second example, we want to break up the dataset into 30 groups, one for each MLB team, and then compute the maximum batting average within each group.

So what is in common?

In each case we have

1. A dataset that can be broken up into groups
2. We want to break it up into groups
3. Within each group, we want to apply a function

The following table summarizes the situation.

The tapply function can solve both of these problems for us!

The tapply function is simple to use. First, we will generate some data.

> ## generate data for medical example
> medical.example <-
    data.frame(patient = 1:100,
               age = rnorm(100, mean = 60, sd = 12),
               treatment = gl(2, 50,
                 labels = c("Treatment", "Control")))
> summary(medical.example)
    patient            age             treatment 
 Min.   :  1.00   Min.   : 29.40   Treatment:50  
 1st Qu.: 25.75   1st Qu.: 54.31   Control  :50  
 Median : 50.50   Median : 61.24                 
 Mean   : 50.50   Mean   : 61.29                 
 3rd Qu.: 75.25   3rd Qu.: 66.22                 
 Max.   :100.00   Max.   :102.47                  
> ## generate data for baseball example
> ## 5 teams with 5 players per team
> 
> baseball.example <-
    data.frame(team = gl(5, 5,
                 labels = paste("Team", LETTERS[1:5])),
               player = sample(letters, 25),
               batting.average = runif(25, .200, .400))
> summary(baseball.example)
     team       player   batting.average 
 Team A:5   a      : 1   Min.   :0.2172  
 Team B:5   c      : 1   1st Qu.:0.2553  
 Team C:5   d      : 1   Median :0.2854  
 Team D:5   e      : 1   Mean   :0.2887  
 Team E:5   f      : 1   3rd Qu.:0.3013  
            g      : 1   Max.   :0.3859  
            (Other):19                    

Now we have some sample data. Using tapply is now straightforward. In general, the call to the function will look like the example in the first comment. Then, actual calls to the function using the data we defined above are shown.

> ## Generic Example
> ## tapply(Summary Variable, Group Variable, Function)
> 
> ## Medical Example
> tapply(medical.example$age, medical.example$treatment, mean)
Treatment   Control 
 62.26883  60.30371  
> ## Baseball Example
> tapply(baseball.example$batting.average, baseball.example$team,
         max)
   Team A    Team B    Team C    Team D    Team E 
0.3784396 0.3012680 0.3488655 0.2962828 0.3858841  

The tapply function is useful when we need to break up a vector into groups defined by some classifying factor, compute a function on the subsets, and return the results in a convenient form. You can even specify multiple factors as the grouping variable, for example treatment and sex, or team and handedness.