Vectors

In the game with three doors a car stands behind one of three doors, the player picks a door, the host opens another one with a goat, and the player stays with the choice or switches. Whoever records many games has a series of values for each fact: the doors with the car, the first choices, the decisions. In R such a series is called a vector, and almost everything in R is one. A single number is a vector too, just with one value; hence the [1] before every output.

Building vectors

With c() (for combine) you put values together into a vector, here the doors behind which the car stood in five games:

prize_door <- c(2, 1, 3, 3, 1)
prize_door

There is a shortcut for sequences of numbers: 1:5 is the vector of the numbers from 1 to 5, such as the numbers of the five games.

Five games give several vectors of the same length, one per fact. The first position in every vector belongs to the first game, the second to the second, and so on. Suppose we had also asked the five players their age:

prize_door <- c(2, 1, 3, 3, 1)
contestant_choice <- c(2, 3, 1, 1, 1)
decision <- c("stay", "switch", "stay", "switch", "switch")
age <- c(56, 55, 47, 32, 74)

Calculating with vectors

When you calculate with a vector, R calculates with every single value, here the age of the five players one year later:

age <- c(56, 55, 47, 32, 74)
age + 1

R combines two vectors of the same length position by position, the first value with the first, the second with the second. If five players played several times, this gives each one's share of games won:

played <- c(3, 1, 2, 4, 2)
won <- c(2, 0, 1, 3, 1)
won / played

That is exactly what makes R so convenient for data: a column of a table is a vector, and a calculation applies to all rows at once, without a loop. The door numbers, on the other hand, are not for calculating, since they are names and not amounts.

Functions for vectors

Many functions summarise a vector into a single value, for example sum(), mean(), min(), max() and length():

age <- c(56, 55, 47, 32, 74)
mean(age)

Try the others in the box too by replacing mean with another name. length(prize_door) tells you how many games are recorded.

Picking out single values

Square brackets give you access to positions of a vector. Counting starts at 1, so prize_door[2] is the door with the car in the second game:

prize_door <- c(2, 1, 3, 3, 1)
prize_door[2]

A vector of positions fits into the brackets too, for example prize_door[c(1, 3)] for the first and the third game, or prize_door[2:4] for games 2 to 4. A minus leaves a position out: prize_door[-1] is everything except the first game.

Comparing

Was the first choice already right? Questions like this start with a comparison. Like calculating, a comparison applies to each value on its own and gives TRUE or FALSE for every position:

prize_door <- c(2, 1, 3, 3, 1)
contestant_choice <- c(2, 3, 1, 1, 1)
prize_door == contestant_choice

In the first and the fifth game the first choice was right. Equality is checked with two equals signs; a single = is an assignment like the arrow <-. You compare text the same way, in quotes: decision == "switch". Numbers can also be compared by size, as in age > 50.

Combining conditions

& means "and", | means "or", and ! reverses a logical value. Whoever stayed and was right at once won by staying:

prize_door <- c(2, 1, 3, 3, 1)
contestant_choice <- c(2, 3, 1, 1, 1)
decision <- c("stay", "switch", "stay", "switch", "switch")
decision == "stay" & prize_door == contestant_choice

Only the first game meets both conditions. With | it would be all games for which at least one of the two holds.

Checking against a list

When a value is to belong to a selection, a chain of | quickly gets long. %in% checks for every value whether it occurs in another vector, for example whether a player is one of those who played several times:

contestant <- c("Mia", "Jonas", "Lea", "Mia", "Tom")
contestant %in% c("Mia", "Tom")

Counting and shares

When you calculate with logical values, TRUE counts as 1 and FALSE as 0. So sum() of a comparison is the number of hits and mean() their share:

prize_door <- c(2, 1, 3, 3, 1)
contestant_choice <- c(2, 3, 1, 1, 1)
sum(prize_door == contestant_choice)

Replace sum with mean in the box: 0.4 means that in two of five games the first choice was right. You will write these two lines all the time when analysing data.

Selecting with a condition

A comparison also fits into the square brackets. Then R picks out only the positions where it gives TRUE, here the age of those who switched:

age <- c(56, 55, 47, 32, 74)
decision <- c("stay", "switch", "stay", "switch", "switch")
age[decision == "switch"]

That is how two groups can be compared: mean(age[decision == "switch"]) against mean(age[decision == "stay"]).

Key points

• c() builds a vector, 1:10 a sequence of numbers; the positions of several vectors belong together when they describe the same game.
• Calculations and comparisons apply to every value, two vectors are combined position by position; equal is ==.
• & is "and", | is "or", ! reverses; %in% checks against a list.
• sum(), mean(), length() and their relatives summarise a vector; sum() of a comparison counts the hits, mean() gives their share.
• [ ] picks out positions, counted from 1, or with a condition exactly those for which it holds.