Experiment 3: 100 games as a tibble – Hands-on Data Science

The data set Let's Make a Deal: 100 games with three doors holds 100 games with exactly the facts you just had as vectors, plus the first name of the player. The games were generated for this exercise and do not come from a recording of the show. A table whose columns are vectors of equal length and whose rows each describe one game is called a tibble in the tidyverse. You work with the functions of dplyr, which reshape a table step by step, joined by the pipe |>.

On your own computer you load the tidyverse and read the file with read_csv(); your own games from the previous phase work the same way, from the CSV file or with readRDS() from the RDS file.

library(tidyverse)
monty_hall <- read_csv("lets_make_a_deal.csv")
my_games <- as_tibble(readRDS("monty_hall_games.rds"))

In the boxes of this experiment dplyr is already loaded and the table is there as monty_hall.

First look

How many rows and columns does the table have, and what type is each column?

monty_hall

SHOW THE SOLUTION

glimpse(monty_hall)

The printed table already says it in its header: 100 × 5, that is 100 rows and five columns, and under every column name its type. A tibble shows only the first ten rows so that the output stays readable. glimpse() turns the table around and shows every column as a line with its type and first values: the first name and the decision as text (<chr>), the doors as numbers (<int> here, <dbl> after read_csv()).

Columns and rows

Try each step in a run of its own:

Get the column prize_door once with select() and once with pull(). What is the difference?
Select the columns prize_door and decision together.
Show the first ten and the last ten rows.
Show all columns except contestant.
Sort the table by prize_door, ascending and descending.

monty_hall |>
  select(prize_door)

SHOW THE SOLUTION

monty_hall |> select(prize_door)              # 1.: a table with one column
monty_hall |> pull(prize_door)                # 1.: a vector
monty_hall |> select(prize_door, decision)    # 2.
monty_hall |> slice_head(n = 10)              # 3.
monty_hall |> slice_tail(n = 10)              # 3.
monty_hall |> select(-contestant)             # 4.
monty_hall |> arrange(prize_door)             # 5.
monty_hall |> arrange(desc(prize_door))       # 5.

Each of these functions takes a table and returns a table again; only pull() takes a column out as a vector, as you know it from the previous phase. A minus before the name leaves a column out.

Who won?

Add a column won to the table with mutate(), following the same rule as in Experiment 2.
Use filter() to create a new table that holds only the games won. How many of them were won by switching, how many by staying? count() counts the rows per value of a column.
How often does staying win in these 100 games, and how often switching? group_by() splits the table into groups, and summarize() condenses each group into one row.
Turn decision into a factor and look at its levels. What is that good for?

monty_hall |>
  mutate(won = FALSE)

SHOW THE SOLUTION

monty_hall <- monty_hall |>
  mutate(won = (decision == "stay" & prize_door == contestant_choice) |
    (decision == "switch" & prize_door != contestant_choice))

games_won <- monty_hall |>
  filter(won)
games_won |>
  count(decision)

monty_hall |>
  group_by(decision) |>
  summarize(games = n(), rate = mean(won))

Of the 49 games won, 30 were won by staying and 19 by switching. That looks like an advantage for staying, but it is a trap: players stayed in 74 games and switched in only 26. Only the shares can be compared, and they show the opposite: staying wins 41 percent of the games, switching 73 percent.

mutate(decision = factor(decision)) turns the column into a factor with the levels stay and switch, and glimpse() then shows <fct>. A factor knows all allowed values; typos stand out, and tables and charts show the categories in a fixed order.