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Edit: This post originally appeared on my WordPress blog on September 20, 2009. I present it here in its original form.

The R Function of the Day series will focus on describing in plain language how certain R functions work, focusing on simple examples that you can apply to gain insight into your own data.

Today, I will discuss the tapply function.

### What situation is tapply useful in?

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.

Team Player Batting Average
Minnesota Twins Joe Mauer .374
Seattle Mariners Ichiro Suzuki .355
Boston Red Sox Kevin Youkilis .309

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.

Example Group Variable Summary Variable Function
Medical Example Treatment age mean
Baseball Example Team batting average max

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

### How do I use tapply?

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

```

### Summary of tapply

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.