Average treatment effect from potential outcomes

\(ATE = E[Y(1) - Y(0)]\). The two arms may be the same units seen under both conditions (paired = TRUE) or different units. The distinction is explicit rather than inferred from matching lengths, because the variance formulas differ sharply: pairing uses \(Var(Y(1) - Y(0))/n\), which accounts for the covariance between arms, while independent arms use \(s_1^2/n_1 + s_0^2/n_0\). With strongly correlated arms the paired standard error is many times smaller, so guessing would mis-state every interval.

Usage

morie_ate_potential_outcomes(y1, y0, paired = TRUE, alpha = 0.05)

Arguments

y1, y0

Potential outcomes under treatment and control.

paired

Treat the arrays as the same units under both arms.

alpha

Significance level for the interval.

Value

Named list with ate, se, ci_low, ci_high, statistic, p_value, df, n1, n0, paired, method.

Details

Mirrors morie.fn.ate_d.

References

Rubin DB (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66(5), 688-701. Holland PW (1986). Statistics and causal inference. JASA, 81(396), 945-960.

Examples

set.seed(1)
morie_ate_potential_outcomes(rnorm(50, 2), rnorm(50))$ate
#> [1] 1.983122