12 Causal Inference

Outline how to solve the Pearl, Glymour, and Jewell (2016) exercises in R.

12.1 Study question 1.3.2

Data:

library(tidyverse)
ed <- tibble(Gender = c("M","M","M","M","F","F","F","F"),
             eLevel = c("U","H","C","G","U","H","C","G"),
             num    = c(112,231,595,242,136,189,763,172)) %>%
  mutate(total = sum(num))

which we tabulate as

ed %>%
  kable()

Gender	eLevel	num	total
M	U	112	2440
M	H	231	2440
M	C	595	2440
M	G	242	2440
F	U	136	2440
F	H	189	2440
F	C	763	2440
F	G	172	2440

12.2 Exercises and answers

12.2.1 Find \(P(eLevel = H)\)

ed %>%
  filter(eLevel == "H") %>%
  mutate(p_H = sum(num)/total) %>%
  kable()

Gender	eLevel	num	total	p_H
M	H	231	2440	0.1721311
F	H	189	2440	0.1721311

12.2.2 Find \(P(eLevel = H\ \vee \ Gender = F)\)

ed %>%
  filter(Gender == "F" | eLevel == "H") %>%
  mutate(p_HorF = sum(num)/total) %>%
  kable()

Gender	eLevel	num	total	p_HorF
M	H	231	2440	0.6110656
F	U	136	2440	0.6110656
F	H	189	2440	0.6110656
F	C	763	2440	0.6110656
F	G	172	2440	0.6110656

12.2.3 Find \(P(eLevel = H\ |\ Gender = F)\)

ed %>%
  filter(Gender == "F") %>%
  mutate(tcond = sum(num)) %>% 
  filter(eLevel == "H") %>%
  mutate(p_HgivenF = sum(num)/tcond) %>%
  kable()

Gender	eLevel	num	total	tcond	p_HgivenF
F	H	189	2440	1260	0.15

12.2.4 Find \(P(Gender = F\ | \ eLevel = H)\)

ed %>%
  filter(eLevel == "H") %>%
  mutate(tcond = sum(num)) %>% 
  filter(Gender == "F") %>%
  mutate(p_FgivenH = sum(num)/tcond) %>%
  kable()

Gender	eLevel	num	total	tcond	p_FgivenH
F	H	189	2440	420	0.45