---
name: statistics
description: Use when the user asks about statistics or probability, e.g. normality, Q-Q plot, Shapiro-Wilk weights or W, p-values, variance, t-test, Wilcoxon, bootstrap, probability space, Bayes, Bayesian learning, normal distribution, density function (PDF), mean/std, classification metrics (accuracy, precision, recall, F1, confusion matrix).
---

# Statistics explainer

Explain for a learner who finds math hard:

1. Plain-language idea first (one or two sentences, no symbols).
2. A tiny worked example with small numbers.
3. Only then the formula, and define every symbol.

Style rule (from the author's `posts/.agents/AGENTS.md`): never put a LaTeX `=` sign on a separate line; keep the `=` on the same line as its left-hand side, otherwise the markdown table of contents breaks.

## Explaining Shapiro-Wilk

Read the Q-Q post below first. Start with its five-value example and explain one component at a time: paired gaps and fixed weights give A; squared distances from the mean give B; then W = A/B.

- Weights depend only on sample size. They are related to normal order statistics, but are not the Q-Q x values.
- A alone has no good/bad cutoff. B is a sum of squared deviations; sample variance is B/(n-1).
- Explain why the ratio works through the post's clearly labelled simplified pattern-multiplication example. The actual weights are covariance-adjusted; do not present the simplified example as the Shapiro algorithm.
- Both A and B involve squaring. Do not claim only B squares an outlier or that W is literally ordinary Q-Q correlation.
- Explain p using an imagined reference table of normal samples of the same size. SciPy uses published approximations, not a fresh simulation. Small p means evidence against normality, not the probability that the data is normal.
- Do not automatically reject a t-test because Shapiro rejects normality. Consider independence, skew, outliers, sample size and the target statistic. Wilcoxon signed-rank is not assumption-free or a mean test; log transforms require strictly positive inputs.

## Relevant posts

Before answering a question on one of these topics, read the matching post (view the repo-relative path, which sits next to `skills/` in the installed plugin) and cite it by name. If the file is missing locally, use the GitHub URL.

- **Defining Probability** — probability space, sample space, events, assigning probabilities (fair die example). `posts/defining_probability.md` — https://github.com/AndresNamm/blogg/blob/main/posts/defining_probability.md
- **Normal Distribution & Probability Density** — Q&A on the normal PDF, why it integrates to 1, what a density value means. `posts/normal_distribution_density.md` — https://github.com/AndresNamm/blogg/blob/main/posts/normal_distribution_density.md
- **Idea Behind Bayesian Learning** — Bayes formula, putting a probability distribution on model parameters instead of a single point estimate. `posts/intro_to_bayesian_learning.md` — https://github.com/AndresNamm/blogg/blob/main/posts/intro_to_bayesian_learning.md
- **Classification Metrics** — accuracy, precision, recall and related metrics from TP/TN/FP/FN. `posts/metrics.md` — https://github.com/AndresNamm/blogg/blob/main/posts/metrics.md
- **Q-Q Plot and Shapiro-Wilk Test** — normal quantiles versus weights, worked A/B calculations, pattern matching, variance versus sum of squares, and p-values from the normal reference distribution. `posts/qq_plot_and_shapiro_wilk.md` — https://github.com/AndresNamm/blogg/blob/main/posts/qq_plot_and_shapiro_wilk.md