Two Binary Variables - Fisher’s Exact Test

library(tidyverse)

# Reading in the nfl drives data
drives <- read.csv("https://raw.githubusercontent.com/Shammalamala/STA4504/refs/heads/main/data/ch2/nfl%20drives.csv") 

Looking at the way drives can begin and end:

unique(drives$drive_start)

## [1] "Fumble"       "Interception" "Kickoff"      "Punt"

unique(drives$drive_end)

## [1] "Field Goal" "Punt"       "Touchdown"  "Turnover"

Motivating Question: Is a team more likely to score a touchdown after a turnover compared to a punt or kickoff?

Relative risk is often used for two binary variables, so let’s convert our data into two binary variables:

• drive_start: turnover - Interception/Fumble vs kick - Kickoff/Punt
• drive_end: TD - Touchdown vs noTD - Field Goal/Turnover/Punt

drives2 <- 
  drives |> 
  mutate(
    drive_start = if_else(drive_start %in% c("Interception", "Fumble"),
                          true = "turnover",
                          false = "kick") |> 
                  factor(),
         
    drive_end = if_else(drive_end == "Touchdown",
                        true = "TD",
                        false = "noTD") |> 
                factor()
  )

Next, let’s display the results in a two-way table using xtabs()

# Displaying a two-way table using xtabs()
drive_freq <- 
  xtabs(formula = ~ drive_start + drive_end, data = drives2)

drive_freq

##            drive_end
## drive_start noTD   TD
##    kick     4055 1200
##    turnover  571  239

And converting the table from counts to conditional proportions using prop.table(margin = "drive_start")

drive_freq |> 
  prop.table(margin = "drive_start") |> 
  
  round(digits = 3)

##            drive_end
## drive_start  noTD    TD
##    kick     0.772 0.228
##    turnover 0.705 0.295

c(
  'Pearson test:' = rstatix::chisq_test(drive_freq)$p,
  "Fisher's Test" = rstatix::fisher_test(drive_freq)$p
)

## Pearson test: Fisher's Test 
##  3.959419e-05  5.233613e-05

For a bigger than 2x2 table