GRIM · SPRITE

SPRITE

SPRITE (sample parameter reconstruction via iterative techniques) goes from summary statistics back to data. Given a mean, an SD, n and the lowest and highest possible answers, it looks for sets of whole-number answers that produce exactly those numbers, and shows them as bar charts.

How the search works

  1. Draw n random answers on the scale.
  2. Nudge single answers up or down until the mean rounds to the reported one.
  3. Pick one answer to raise and another to lower, choosing them so the SD moves toward the target while the mean stays put. Sometimes only one answer is moved, if the mean still rounds the same way.
  4. Repeat until the SD rounds to the reported value, or give up after a fixed number of steps.
  5. Run the whole thing again to collect several different datasets, and stop when new runs keep returning ones already found.

The checker follows the authors' R implementations (rSPRITE and rsprite2) step for step, in a background thread so the page stays responsive. Each answer set it shows has been checked with exact arithmetic: its mean and SD round to what you entered.

What it adds to GRIM and GRIMMER

It knows the scale. A mean and SD can pass both earlier tests and still be impossible because, on a 1–5 scale, nothing spreads that far. SPRITE then finds nothing, and the checker also computes the possible SD range for that mean directly. When the answers can only be a few values, the checker also counts every possible sample and reports exactly how many match, so a "none found" becomes a proof.

Worked examples from the preprint

Self-refilling soup bowls. 31 people estimated a mean of 9.8 ounces with an SD of 9.2. If nobody could have estimated more than 18 ounces, the largest SD possible with that mean is 9.08, so no dataset exists; from a maximum of 19 onward, datasets appear, as the preprint reports.

A complete count. For a 1–7 scale, n = 20, mean 3.45 and SD 2.06, the preprint notes that a complete search (CORVIDS) finds 107 datasets. The checker's own count gives the same 107.

Carrots taken. In the preprint, 45 children took a mean of 19.4 carrots (SD 19.9), and the authors' SPRITE runs first found datasets with a maximum of 41. Exact arithmetic puts the boundary one lower: with a maximum of 40, a handful of extreme datasets exist (about half the children taking none and the rest taking nearly all 40), which this checker's SPRITE finds and which rsprite2 finds too. With a maximum of 39 none can exist. Either way the conclusion stands: the numbers need a pile-up at both ends.

How to read the charts

Look at the family of shapes rather than one chart. If every dataset that fits is piled up at both ends of the scale, or needs a few extreme answers, that is worth a question about how the data were collected. But SPRITE does not sample datasets in proportion to how likely they are, and the share of charts with some feature is not a probability. A random search can also miss rare solutions, which is why the complete count is shown whenever it is feasible.

Source

Heathers, J. A., Anaya, J., van der Zee, T., & Brown, N. J. L. (2018). Recovering data from summary statistics: Sample Parameter Reconstruction via Iterative TEchniques (SPRITE). PeerJ Preprints, 6:e26968v1. doi:10.7287/peerj.preprints.26968v1.

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