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My research is on estimating average treatment effects using different machine learning models. However, I need a big data set with a truly randomised experiment in order to estimate the "true" average treatment effect. Does anybody have knowledge of such a data set that is publicly available? It does not matter what it is about, just that the treatment assignment is truly random.

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    What do you mean with "truly random". Clinical trials are randomised, there are a couple of data sets available to interested researchers. – Grimaldi Sep 23 '17 at 9:33
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I don't know what you mean exactly, and I assume you don't mean "double-blind" studies.

However, if you already had your own dataset: You can randomize that data yourself, and take averages of permuted values of interesting columns as a baseline.

Just augment + shuffle/permute the data table correctly, and you'll get a randomized dataset just as you need.

This code is from the Datacamp.com class "Foundations of inference" where this technique is demonstrated at length:

Dataset (2 columns, 40 rows):

sample(disc)
      sex      promote
1    male     promoted
2    male     not promoted
3    female   promoted 
...

R Code:

rep_sample_n <- function (tbl, size, replace = FALSE, reps = 1) 
{
    n <- nrow(tbl)
    i <- unlist(replicate(reps, sample.int(n, size, replace = replace), 
        simplify = FALSE))
    rep_tbl <- cbind(replicate = rep(1:reps, rep(size, reps)), 
        tbl[i, ])
    dplyr::group_by(rep_tbl, replicate)
}


# Sample the entire data frame 5 times
# Shuffle the "promote" variable within replicate
# Find the proportion of promoted in each replicate and sex 
#    -> get a simple distribution, should be around mean=0   
# Difference in proportion of promoted across sex grouped by gender
disc %>%
  rep_sample_n(size = nrow(disc), reps = 5) %>%
  mutate(prom_perm = sample(promote)) %>%
  group_by(replicate, sex) %>%
  summarize(prop_prom_perm = mean(prom_perm == "promoted"),
            prop_prom = mean(promote == "promoted"))  %>%
  summarize(diff_perm = diff(prop_prom_perm),
            diff_orig = diff(prop_prom))  # male - female

Result:

  replicate   diff_perm diff_orig
      <int>       <dbl>     <dbl>
         1  0.04166667 0.2916667
         2 -0.12500000 0.2916667
         3 -0.04166667 0.2916667
         4 -0.04166667 0.2916667
         5  0.12500000 0.2916667

This shows that 5 randomized datasets derived from the original show max +-12.5 % difference in people promoted, regardless of gender, whereas the original data show a mean difference of 29% difference (when grouped by gender).

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