# Engineering Statistics

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- **Type:** Skill
- **Install:** `agentstack add skill-jskherman-engg-skills-engineering-statistics`
- **Verified:** Yes — security-reviewed for prompt injection and unsafe behavior
- **Seller:** [jskherman](https://agentstack.voostack.com/s/jskherman)
- **Installs:** 0
- **Category:** [Agent Skills](https://agentstack.voostack.com/c/agent-skills)
- **Latest version:** 0.1.0
- **License:** Apache-2.0
- **Upstream author:** [jskherman](https://github.com/jskherman)
- **Source:** https://github.com/jskherman/engg-skills/tree/main/skills/engineering-statistics

## Install

```sh
agentstack add skill-jskherman-engg-skills-engineering-statistics
```

Requires the [AgentStack CLI](https://agentstack.voostack.com/docs/cli). Works with Claude Code, Cursor, and any MCP-compatible agent.

## About

# 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).
2. Run the desired summary.
3. 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](https://github.com/jskherman)
- **Source:** [jskherman/engg-skills](https://github.com/jskherman/engg-skills)
- **License:** Apache-2.0

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

## Pricing

- **Free** — Free

## Security capabilities

Automated source analysis of v0.1.0 — what this tool can access:

- **Network access:** no
- **Filesystem access:** no
- **Shell / process execution:** no
- **Environment & secrets:** no
- **Dynamic code execution:** no

*"Yes" means the capability is present in the source — more access means more to trust, not that it is unsafe.*


## Versions

- **0.1.0** — security scan: passed — Imported from the upstream source.

## Links

- Listing page: https://agentstack.voostack.com/l/skill-jskherman-engg-skills-engineering-statistics
- Seller: https://agentstack.voostack.com/s/jskherman
- Browse the marketplace: https://agentstack.voostack.com/browse

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