# Reaction-time summary methods: calculation and claim sheet

Published: 2026-10-21  
Evidence type: deterministic methods example plus targeted narrative review  
Data provenance: constructed trial lists only; no participant, customer, account or telemetry data

## Calculation

For an eligible trial list `x` of length `n`:

- mean = `sum(x) / n`
- median = the middle ordered value for odd `n`
- nominal 20% trimmed mean = sort `x`, remove `floor(0.20 * n)` values from each tail, then average the remainder
- fastest = `min(x)`

Each example has nine trials, so the trimming rule removes one value from each tail and averages seven. The term “20%” names the prespecified per-tail proportion; integer rounding means one of nine values (11.1%) is actually removed from each tail in this small example.

Run `python3 calculate.py` to reproduce all displayed values and assert them against the CSV.

## Interpretation boundary

The examples show how four summaries respond to two deliberately different changes: one slower tail value and a constant 40 ms shift to every value. They do not estimate a population, validate a cutoff, recommend a universal primary outcome, or establish why a response was slow.

A real comparison must define task/version, device and input method, trial eligibility, anticipations and interruptions, correct/error/omission handling, trial count, summary statistic and comparison rule. These decisions should be made before checking which rule makes a session look better.

## Source checks

- Ratcliff (1993), DOI `10.1037/0033-2909.114.3.510`: evaluated RT outlier methods, including transformations and cutoffs.
- Miller (1988), DOI `10.1037/0096-1523.14.3.539`: warned about sample-median bias under skew and unequal trial counts.
- Rousselet & Wilcox (2020), DOI `10.15626/MP.2019.1630`: replicated and extended the median-bias analysis, demonstrated a bootstrap correction, and argued that different distributional questions require different methods.
- Miller (2023), DOI `10.15626/MP.2020.2472`: compared power for means, medians and bias-corrected medians in simulations.
- Miller (2023), DOI `10.1037/xge0001450`: simulation assessment of common outlier-exclusion procedures.

This is a targeted narrative methods note, not a systematic review. Literature search, drafting, calculations and source checks used an OpenAI automated assistant. Automated consistency checks passed; there was no independent human methods review or journal peer review.