dispdist: Estimated ATE distribution display, summary and significance testing

Description

Function for displaying, summarizing and producing p-values from the estimated average treatment effect (ATE) distribution

Usage

dispdist(distout, ate, quantiles = c(0.025, 0.975), display.plot = TRUE)

Arguments

distout

randomization distribution of estimated ATEs, as output from gendist().

ate

scalar hypothesized treatment effect for significance testing.

quantiles

vector of quantiles of the randomization distribution to be returned. Default is equal-tailed 95% intervals.

display.plot

logical for displaying a histogram for the randomization distribution with hypothesized treatment effect overlay. Default is TRUE.

Value

two.tailed.p.value: two-tailed p-value: twice the smaller of the two one-tailed p-values, as advocated by Rosenbaum (2002)
two.tailed.p.value.abs: two-tailed p-value: proportion of randomizations yielding absolute estimated ATE greater than or equal to absolute hypothesized ATE
greater.p.value: one-tailed p-value: proportion of randomizations yielding estimated ATE greater than or equal to hypothesized ATE
lesser.p.value: one-tailed p-value: proportion of randomizations yielding estimated ATE less than or equal to hypothesized ATE
quantile: specified quantiles of the randomization distribution
sd: standard deviation of the randomization distribution
exp.val: expected value of the randomization distribution

References

Gerber, Alan S. and Donald P. Green. 2012. Field Experiments: Design, Analysis, and Interpretation. New York: W.W. Norton.

Rosenbaum, Paul R. 2002. Observational Studies. 2nd ed. New York: Springer.

Samii, Cyrus and Peter M. Aronow. 2012. On Equivalencies Between Design-Based and Regression-Based Variance Estimators for Randomized Experiments. Statistics and Probability Letters. 82(2): 365-370. http://dx.doi.org/10.1016/j.spl.2011.10.024

Examples

Run this code

y <- c(8,6,2,0,3,1,1,1,2,2,0,1,0,2,2,4,1,1) 
Z <- c(1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0)
cluster <- c(1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9)
block <- c(rep(1,4),rep(2,6),rep(3,8))

perms <- genperms(Z,blockvar=block, clustvar=cluster) # all possible permutations
probs <- genprobexact(Z,blockvar=block, clustvar=cluster) # probability of treatment
ate <- estate(y,Z,prob=probs) # estimate the ATE

## Conduct Sharp Null Hypothesis Test of Zero Effect for Each Unit

Ys <- genouts(y,Z,ate=0) # generate potential outcomes under sharp null of no effect
distout <- gendist(Ys,perms, prob=probs) # generate sampling dist. under sharp null
dispdist(distout, ate)  # display characteristics of sampling dist. for inference

## Generate Sampling Distribution Around Estimated ATE

Ys <- genouts(y,Z,ate=ate) ## generate potential outcomes under tau = ATE
distout <- gendist(Ys,perms, prob=probs) # generate sampling dist. under tau = ATE
dispdist(distout, ate)  ## display characteristics of sampling dist. for inference