Chapter 11 Experiments: Dealing with Real–World Challenges
We will learn to assess balance with R in this chapter. We need the following libraries
11.1 Assess Balance
Let’s use the ProgramEffectiveness
data set from the AER
package to assess balance. The ProgramEffectiveness
data set contains 32 observations on four variables31. The data are used to examine whether a new method of teaching economics improved performance in later economics courses. The variables are grade coded as a factor with levels “increase” and “decrease”, average (grade point average), testscore (test score on economics test), and participation coded as a factor with levels “no” and “yes”. participation is the treatment in this case. We assess the balance below:
library(AER)
data("ProgramEffectiveness")
ProgramEffectiveness %$%
lm(average ~ participation) %>%
tidy()
# A tibble: 2 x 5
term estimate std.error statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl>
1 (Intercept) 3.10 0.112 27.8 5.97e-23
2 participationyes 0.0367 0.169 0.218 8.29e- 1
# A tibble: 2 x 5
term estimate std.error statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl>
1 (Intercept) 21.6 0.929 23.2 1.01e-20
2 participationyes 0.873 1.40 0.622 5.39e- 1
For each variable, we can conclude that the treatment is balanced.
11.2 Estimate ITT Model
We estimate the ITT model below:
Call:
lm(formula = as.numeric(grade) ~ participation)
Residuals:
Min 1Q Median 3Q Max
-0.571 -0.167 -0.167 0.429 0.833
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.167 0.105 11.13 0.0000000000035 ***
participationyes 0.405 0.158 2.56 0.016 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.445 on 30 degrees of freedom
Multiple R-squared: 0.179, Adjusted R-squared: 0.151
F-statistic: 6.53 on 1 and 30 DF, p-value: 0.0159
We can reject the null hypothesis of no effect and conclude that participation increased the test score on later tests.
?AER::ProgramEffectiveness for more information
↩︎