Mary (a woman) is choosing between restaurants A and B to take her friend, John (a man), out for dinner.

Restaurant A has an average rating of 4.1 and restaurant B of 4.3.

But looking at ratings by gender, among men, restaurant A has a rating of 4.0 and restaurant B of 3.8. Among women, restaurant A has a rating of 4.6 and restaurant B of 4.4. It seems that men and women separately prefer restaurant A but together they prefer restaurant B!

1. Draw a Paik-Agresti diagram conditioning on the gender with restaurant on the horizontal axis and average ratings on the vertical axis to explain how this apparent contradiction could arise.
2. Draw a causal graph describing the relationships among the three variables: restaurant, gender and ratings.
3. Assuming that there are no other significant factors related to restaurant ratings, what kind of variable is gender in this context?
4. Which restaurant should Mary choose? Why?