Chapter 13 — Correlation, Causation, and Controlled Comparisons

PyPI workbook run (Track D)

From inside your Track D workbook folder (created by pystatsv1 workbook init --track d --dest ...), run:

pystatsv1 workbook run |trackd_run|

Outputs are written under outputs/track_d/ by default. If you’re unsure what a file is for, start with Track D Outputs Guide.

To see the full chapter-by-chapter run map (D00–D23), see Track D chapter index (PyPI).

Optional: write to a custom output folder:

pystatsv1 workbook run |trackd_run| --outdir outputs/track_d_custom

Interpretation prompts (quick self-check):

  • What is the accounting or business measurement goal in this chapter?

  • Which invariant/check would catch a “numbers look fine but are wrong” mistake here?

This chapter is about not fooling yourself (or your stakeholders) when you see two lines move together.

Accountants are trained to explain variances. The trap is when a tidy story turns into a causal claim: “X increased, so X caused Y.” Often, a third factor (seasonality, activity level, headcount) moves both.

What you’ll build in this chapter

Using the North Shore Outfitters (NSO) running case, you’ll produce a small “correlation audit” pack:

  • A naïve correlation (two variables move together).

  • A controlled comparison (same correlation after “controlling for” a third variable).

  • A short executive memo explaining what you can and cannot claim.

Key terms (accounting ↔ data)

Correlation (r)

A number from -1 to +1 that measures linear co-movement. It is not proof of cause.

Causation

A claim that changing X would change Y (a “do” statement). Requires design, not vibes.

Confounder / third variable

A variable Z that influences both X and Y, creating a misleading relationship.

Control variable

The variable(s) you hold constant (or adjust for) to isolate a relationship of interest.

Partial correlation (controlled correlation)

Correlation between X and Y after removing the linear effect of Z from both.

Running case inputs

The script reads NSO v1 synthetic outputs (created earlier in Track D), especially:

  • gl_journal.csv — transaction-level general ledger entries.

  • statements_is_monthly.csv — income statement summaries (used for sanity checks).

Outputs

When you run the Chapter 13 script, it writes:

  • ch13_controlled_comparisons_design.json — pre-committed variables + controls.

  • ch13_correlation_summary.json — correlations, partial correlations, and notes.

  • ch13_correlation_memo.md — a CFO-style memo (what we know / don’t know).

  • figures/ + ch13_figures_manifest.csv — plots and a manifest for docs/RTD.

How to run

From the repo root:

make business-ch13

Or directly:

python -m scripts.business_ch13_correlation_causation_controlled_comparisons \
  --datadir data/synthetic/nso_v1 \
  --outdir outputs/track_d \
  --seed 123

How to interpret the results (what “good” looks like)

  1. Naïve correlation is a prompt, not an answer. It tells you “look here,” not “this caused that.”

  2. Controlled comparisons shrink bad stories. If Revenue correlates with Payroll Taxes, the real driver may be Payroll Expense. Partial correlation helps you say: “The Revenue–PayrollTax link mostly disappears once we control for Payroll.”

  3. Write the correct sentence. Bad: “Revenue causes payroll taxes.” Better: “Revenue and payroll taxes move together, but payroll explains most of that relationship. A causal claim would require a designed change (e.g., staffing policy) and a comparison group.”

End-of-chapter problems

  1. Confounding variable Find two NSO metrics that move together and propose a plausible third variable that drives both. Write the “wrong” story and then correct it.

  2. Narrative correction Rewrite an overconfident causal statement into a defensible statement that acknowledges confounding.

  3. Controlled comparison Pick a control variable and recompute the relationship (partial correlation). Explain why the control is reasonable in accounting terms.