8 Vectors
Vectors are one of the foundational data structures in R. They store, access and manipulate data efficiently, which makes them an indispensable building block in data analysis.
Getting Data
To understand the optimal strategy for the Monty Hall problem, we can start by simulating the game ourselves in a simple way. Imagine using three cups to represent the doors, with one person acting as the host and another as the contestant. The host hides a prize, such as a coin, under one of the cups, and the contestant makes an initial choice. Next, the host reveals a cup that does not contain the prize, and the contestant can either stay with their original choice or switch to the remaining cup. By repeating this process multiple times, for instance ten rounds, we can begin to gather data. But what kind of data should we collect?
The data we collect should allow us to perform the analysis needed to effectively address our research questions. As a general principle, when in doubt, it's better to record more data, since unnecessary information can always be removed later, but data that was never captured cannot be retrieved. So what kind of data should we record during the game?
Which cup contained the prize?
Which cup did the contestant choose initially?
Which cup was revealed by the host?
What decision did the contestant make (stay or switch)?
Did the contestant win?
This is a solid starting point, though there are additional details we could consider. For instance, recording the date and time of each experiment or noting who played the host and who played the contestant could also provide useful insights. We will keep these ideas in mind for future experiments, but for now, we will focus on a concise list of key variables from above.
We don't actually need to record whether the contestant won the prize, as we can logically infer this from the other observations. If we know the contestant's initial choice, where the prize is, and whether they stayed or switched, we can determine the outcome.
Representing the data in R
Imagine you played the game three times with a classmate and recorded the results on paper. The result could look something like this:
Although this is a well-structured summary of your simulation, it is not suitable for direct use in a programming language like R. To effectively analyze the games you played (and potentially many more), we need to consider how to represent this data in a format that R can handle.
Scalar values
First, let's focus on identifying which cup contained the prize in each game to help us organize the data step by step. This information can be represented as a single number between 1 and 3. For instance, in the first game, the prize was under cup 2, so the value would be 2. A single value like this, represented by a single number, is known as a scalar value, in contrast to a collection of values, which we call a vector.
To represent scalar values in R, we can store them as objects with descriptive names. This can be done using the assignment operator <-:
However, if we played 100 games, this approach would lead to 100 separate objects, each storing a single scalar value. While this technically works, it is impractical for data analysis, especially when we need to compare or relate the prize locations to other variables. A better solution would be to use vectors to store all the values in a more organized and manageable way.
Vectors
Instead of storing each prize value in separate objects, we can store all three values in a single object called a vector. The c() function allows us to create a vector by combining values, separated by commas:
There are two important characteristics of a vector. First, all elements of a vector must be of the same data type (in this case, numbers). Second, the elements of a vector are ordered, meaning each value has a specific position within the vector. This order is crucial when comparing elements across different vectors.
More than a vector
Exercises
Last updated
Was this helpful?