3.6 Relational Operators in R

Goal: Compare callback rates for white sounding names to black sounding names, so we need to be able to filter by race.

Good news: We have several relational operators in R that evaluate logical statements:

• ==, <, >, <=, >=, !=
• We have a statement and R evaluates it as TRUE or FALSE

## for each observation, does the value of race equal "black"?
resume$race == "black"

By putting this logical statement within [ ], we are asking R to take the mean() of the variable resume$call for the subset of observations for which this logical statement is TRUE.

mean(resume$call[resume$race == "black"])

## [1] 0.06447639

Ultimately, each of these paths has led us to a place where we can estimate the average treatment effect by calculation the difference in means: the difference in callback rates for black and white applicants.

We said the ATE = \(\bar{Y}(treatment) - \bar{Y}(control)\)

ate <- mean(resume$call[resume$race == "black"]) - 
  mean(resume$call[resume$race == "white"])
ate

## [1] -0.03203285

How can we interpret this? Do white applicants have an advantage?