Engineering Statistics

Engineering Statistics

Overview

Pure-Python statistics for engineering data summaries:

• Mean, median, standard deviation, min/max.
• Mean confidence interval (t-table if degrees of freedom in the

built-in table, normal approximation otherwise).

• Simple linear regression (one predictor): slope, intercept, R², and SSE.

The implementation deliberately stays in the Python standard library so the skill is fast and dependency-light.

Prerequisites

1. uv available.

When to Use

• Summarising a small batch of lab measurements.
• Computing a CI for the mean of a sample.
• Fitting a single-predictor linear regression for a sanity check.

Don't use for

• Autocorrelated process time-series (time-series-process-data-analysis).
• Censored lab data with below-LOQ values (censored-regression).
• Compositional data (compositional-data-analysis).
• Hierarchical / multi-level models (bayesian-hierarchical-process-models).
• Multi-predictor regression (use statsmodels or scikit-learn).

Utility Scripts

• uv run scripts/engg_stats.py describe --values "12.3,12.5,12.1,12.4" --output /tmp/desc.json
• uv run scripts/engg_stats.py mean-ci --values "12.3,12.5,12.1,12.4" --confidence 0.95 --output /tmp/ci.json
• uv run scripts/engg_stats.py linear-regression --x "1,2,3,4,5" --y "2.1,3.9,6.1,8.0,10.1" --output /tmp/reg.json

Procedure

1. Confirm the data is i.i.d.-like (no obvious autocorrelation, no

censoring, not a composition).

1. Run the desired summary.
2. If the CI is for a process value and you suspect autocorrelation, use

time-series-process-data-analysis instead.

Pitfalls

• Treating SPC data as i.i.d.; lag-1 autocorrelation > 0.3 invalidates

the t-CI for the mean.

• Using R² as a goodness-of-fit metric without checking residuals.
• Ignoring outliers; one or two leverage points can drive the regression.
• Computing a CI on fewer than 5 data points and reporting it as

precise.

• Using mean ± 2 SD as a "95% interval" when the data is not normal.
• Reporting the slope of a linear fit with insignificant slope (CI crosses

zero) as if it had physical meaning.

• Standardising the predictor before fitting and forgetting to back-

transform the slope to original units.

• Using sample standard deviation s where population standard deviation

sigma is needed (e.g. capability indices).

Fallback Strategies

• For larger or more complex problems, switch to statsmodels or

scikit-learn (not in this skill).

• If the t-table degrees of freedom are missing for an unusual df, the

script falls back to a normal-approximation CI with a warning.

Verification

• Run the listed script with representative inputs and an --output file when a deterministic calculation is available.
• Confirm the JSON result contains ok: true, expected units, and no unhandled warnings.
• Check result magnitudes against the stated assumptions, references, and a hand calculation or known operating range before reporting them.

References

• references/reporting.md — guidance for reporting CIs and regressions.

Anti-Patterns

• Reporting "p = 0.04 so the effect is real" without checking residuals.
• Computing a CI without naming the assumed sampling distribution.
• Using linear regression on a clearly non-linear trend.

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: jskherman
• Source: jskherman/engg-skills
• License: Apache-2.0

Install and usage instructions live in the source repository linked above.