---
name: Statistical Modeling & Multivariate Statistics
description: Choose and run the right statistical model — regression, multivariate methods, hypothesis tests, inference — then report effect sizes and uncertainty honestly, so a decision rests on evidence rather than a p-value taken out of context.
audience: analyst · researcher · growth marketer · data-curious PM
---

# Statistical Modeling & Multivariate Statistics

## What this is
A method for applied statistics on business and product data: framing a question as a testable model, fitting it, checking assumptions, and reporting the result with effect size and confidence — not just a yes/no from a significance test.

## What this is NOT
- **Not a p-value vending machine.** It reports effect sizes and intervals, never "p < 0.05, therefore true." It refuses p-hacking, HARKing, and cherry-picked subgroups.
- **Not causal inference by default.** Correlation is labelled correlation; causal claims require a design (experiment, natural experiment, or explicit assumptions) and are flagged as such.
- **Not a substitute for a statistician** on high-stakes inference, clinical/financial risk models, or regulated model validation (SR 11-7).

## When to use
Modelling a relationship (regression), reducing or grouping many variables (PCA, factor/cluster analysis), comparing groups (t-test, ANOVA), or checking whether an observed difference is signal or noise.

## Operating principle
Assumptions first, model second, story last. State what the model assumes, test it, and let the size of the effect — with its uncertainty — carry the conclusion. "Not significant" is a real, reportable finding.

## Capabilities
- **Model selection & fit** — Goal: the right model for the data and question. Method: match outcome type (linear/logistic/count), check linearity/normality/homoscedasticity/independence, handle multicollinearity (VIF), report coefficients with CIs. Output: a fitted model + a plain-English reading of each driver. Quality bar: every assumption is checked and its violation disclosed, not ignored.
- **Multivariate methods** — Goal: structure in many variables. Method: PCA/factor analysis for reduction, k-means/hierarchical for segmentation, with the number of components/clusters justified (scree, silhouette) not guessed. Output: the reduced/segmented structure + a stability note. Quality bar: segments are validated for stability, not just the first clustering that looked tidy.
- **Hypothesis testing & inference** — Goal: is this signal or noise. Method: pick the correct test, state H0/H1, report effect size + CI + power, correct for multiple comparisons. Output: the test result framed by effect size. Quality bar: no significance claim without an effect size; multiple tests are corrected; underpowered results say so.

## A worked example
"Does the new onboarding lift activation?" → Logistic regression of activation on variant + controls; assumptions checked; odds ratio 1.34 (95% CI 1.08–1.66), a real but modest lift, reported with the interval — not "significant, ship it." If the design wasn't randomised, the write-up says "associational, confounders possible."

## Guardrails & escalation
Causal or high-stakes inference → a statistician + an explicit design. Regulated risk models → model-risk governance (SR 11-7). Predictive deployment → the ML for Business skill. Every figure labelled measured or estimated.

## References
Standard applied-statistics canon (regression, ANOVA, PCA/factor analysis, hypothesis testing, power analysis); APA statistical-reporting norms; SR 11-7 for regulated models. Verify method choice with a statistician for high-stakes work.