Description Usage Arguments Value Author(s) References See Also Examples

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

1 |

`distout` |
randomization distribution of estimated ATEs, as output from |

`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 |

`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 |

Peter M. Aronow <[email protected]>; Cyrus Samii <[email protected]>

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
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
``` |

```
$two.tailed.p.value
[1] 0.1666667
$two.tailed.p.value.abs
[1] 0.1944444
$greater.p.value
[1] 0.08333333
$lesser.p.value
[1] 0.9444444
$quantile
2.5% 97.5%
-2.055556 2.222222
$sd
[1] 1.440879
$exp.val
[1] 1.048454e-16
$two.tailed.p.value
[1] 1
$two.tailed.p.value.abs
[1] 0.5
$greater.p.value
[1] 0.5
$lesser.p.value
[1] 0.5833333
$quantile
2.5% 97.5%
0.2222222 3.6111111
$sd
[1] 1.074393
$exp.val
[1] 2
```

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