unsum: reconstruct raw data from summary statistics

The goal of unsum is to undo summarization: reconstruct all possible samples that may underlie a given set of summary statistics. It currently supports sets of mean, SD, sample size, and scale bounds. This can be useful in forensic metascience to identify impossible or implausible reported numbers.

The package features CLOSURE: Complete Listing of Original Samples of Underlying Raw Evidence, a fast algorithm implemented in Rust. Go to Get started to learn how to use it.

CLOSURE is exhaustive, which makes it computationally intensive. If your code takes too long to run, consider using SPRITE instead (see Previous work below).

Installation

You can install unsum with either of these:

remotes::install_github("lhdjung/unsum")
# or
pak::pkg_install("unsum")

Your R version should be 4.2.0 or more recent.

Demo

Start with closure_generate(), the package’s main function. It creates all possible samples:

library(unsum)

data <- closure_generate(
  mean = "2.7",
  sd = "1.9",
  n = 130,
  scale_min = 1,
  scale_max = 5
)
#> → Just a second...

data
#> $inputs
#> # A tibble: 1 × 7
#>   mean  sd        n scale_min scale_max rounding   threshold
#>   <chr> <chr> <dbl>     <dbl>     <dbl> <chr>          <dbl>
#> 1 2.7   1.9     130         1         5 up_or_down         5
#> 
#> $metrics
#> # A tibble: 1 × 5
#>   samples_initial samples_all values_all horns horns_uniform
#>             <int>       <int>      <int> <dbl>         <dbl>
#> 1              15        5359     696670 0.881           0.5
#> 
#> $frequency
#> # A tibble: 5 × 4
#>   value f_average f_absolute f_relative
#>   <int>     <dbl>      <int>      <dbl>
#> 1     1     67.0      358972     0.515 
#> 2     2      5.63      30170     0.0433
#> 3     3      4.09      21940     0.0315
#> 4     4      5.63      30162     0.0433
#> 5     5     47.7      255426     0.367 
#> 
#> $results
#> # A tibble: 5,359 × 2
#>       id sample     
#>    <int> <list>     
#>  1     1 <int [130]>
#>  2     2 <int [130]>
#>  3     3 <int [130]>
#>  4     4 <int [130]>
#>  5     5 <int [130]>
#>  6     6 <int [130]>
#>  7     7 <int [130]>
#>  8     8 <int [130]>
#>  9     9 <int [130]>
#> 10    10 <int [130]>
#> # ℹ 5,349 more rows

Visualize the overall distribution of values found in the samples:

closure_plot_bar(data)

Previous work

SPRITE generates random datasets that could have led to the reported statistics. CLOSURE is exhaustive, so it always finds all possible datasets, not just a random sample of them. For the same reason, SPRITE runs fast when CLOSURE may take too long.

GRIM and GRIMMER test reported summary statistics for consistency, but CLOSURE is the ultimate consistency test: if it finds at least one distribution, the statistics are consistent; and if not, they cannot all be correct.

CORVIDS deserves credit as the first technique to reconstruct all possible underlying datasets. However, it takes very long to run, often prohibitively so. This is partly because the code is written in Python, but the algorithm is also inherently much more complex than CLOSURE.

About

The CLOSURE algorithm was originally written in Python by Nathanael Larigaldie. The R package unsum provides easy access to an optimized implementation in Rust, closure-core, via the amazing extendr framework. Rust code tends to run much faster than R or Python code, which is required for many applications of CLOSURE.