---
name: correlation-regression-and-causal-claim-control
description: >
  Analyses relationships between variables properly and holds the line between
  association and causation: correlation and what it hides, regression at a
  working level, the standard confounding structures, an operational language
  pass over a draft, and the specific designs that do license a causal claim. Use
  for "is there a relationship between these", "run a regression", "what does
  controlling for that mean", "does X cause Y", "can we say this caused that",
  "the client wants to say it drove the result", "why did the coefficient change
  sign", or "is this correlation meaningful".
category: 05 Quantitative Analysis
ref: "05.06"
tier: 1
inherits: [K2, K3, K4, K5]
---

# Correlation, Regression and Causal Claim Control

## 1. One-line description
Analyses the relationship between two or more variables at a working professional level, and operates the library's causal firewall: it explains what a correlation coefficient conceals, what a regression coefficient does and does not mean, the confounding structures that make an association misleading, the designs that genuinely license a causal claim, and how to hold that line with a stakeholder who wants the claim anyway.

## 2. What this skill is used for

**The research problem it solves.** Almost every research finding that gets acted on is acted on causally. The report says two things are associated; the meeting decides to change one of them in order to move the other. That step is taken silently, by everybody, all the time, and most of the time nothing in the analysis licensed it. The problem is not ignorance of the slogan that correlation is not causation, which everybody can recite. It is that the slogan gives no help at all with the specific questions that matter: which structures actually produce a misleading association, how to recognise one in your own data, what "controlling for" achieves and what it cannot achieve, why adding a control variable sometimes makes a result worse rather than better, and which designs do license the claim. Alongside this sits a second and quieter failure: relationship analysis done badly in its own right. A correlation coefficient computed across a restricted range, or driven by four outliers, or summarising a relationship that is not remotely linear, reported as a single number that several completely different scatter patterns would produce. This skill covers both, because the causal error is usually built on top of a relationship that was not read carefully in the first place.

**Where it sits in the research lifecycle.** After description and testing, wherever a question concerns the relationship between variables rather than a difference between groups. It also runs as a checking pass over a finished draft from any other analysis, because causal language enters at the writing stage more often than at the analysis stage.

**Typical use cases.**
- Assessing the relationship between two measures, and reading what the coefficient hides.
- Estimating an association while holding other variables constant, and stating what that does and does not establish.
- Diagnosing why a coefficient changed sign or size when a variable was added to a model.
- Recognising a confounding structure in a dataset: common cause, mediator, collider, selection, reverse causation.
- Running a language pass over a draft report to bring causal claims back within what the design supports.
- Advising on the design that would license the causal claim a stakeholder wants.
- Auditing a supplied model whose conclusions are being read causally.

**Who uses it.** Quantitative researchers and analysts building or reading models; research directors reviewing claims before they leave the building; product and UX researchers relating behavioural measures to outcomes; academic and public sector researchers working with observational data; anyone who has to explain to a stakeholder why the deck cannot say what they want it to say.

## 3. When to use it

- The question is about the relationship between two or more variables rather than a difference between groups.
- An association has been found and someone is about to act on it as though it were causal.
- A model's coefficients are unstable, changed sign when a variable was added, or do not match the bivariate picture.
- A correlation has been reported and it needs checking for range restriction, outliers or non-linearity.
- A draft report or deck needs a causal language pass before it goes out.
- A stakeholder wants an attribution claim and someone has to explain what would be required to make it.
- A quasi-experimental or longitudinal analysis is being considered and its assumptions need stating and checking.
- A supplied model is being audited and the question is what its results actually support.

## 4. When NOT to use it

- **The question is whether two groups differ.** A difference between segments, waves or conditions is a testing question, and it belongs to **05.02 Statistical Testing**. Fitting a model to answer it adds assumptions without adding information.
- **The question is which of a set of attributes relates most strongly to an outcome.** That is **05.04 Driver Analysis**, which has its own approach selection, stability requirements and reporting standard. This skill supplies the confounding structures and the language control that 05.04 enforces, and takes over when the question becomes attribution rather than ranking.
- **An experiment exists or is feasible.** Where randomisation is available, use it and analyse it as one. **06.04 Experiment and A/B Test Analysis** covers design, allocation, primary outcome, and the analysis of a randomised comparison. No amount of observational modelling substitutes for random assignment, and modelling a randomised comparison as though it were observational discards the property that made it valuable.
- **The data cannot support a model at all.** A base too small for the number of terms, a heavily censored outcome, a predictor with almost no variation, or a dataset in which the key variables were measured on different bases. Fit statistics will be produced regardless; they will describe the sample rather than anything else. Report the bivariate picture with its bases and say the model was not estimable.
- **The relationship is a definitional or arithmetic one.** Regressing a total on one of its components, an index on an item inside it, or a variable on a recode of itself produces a strong result that carries no information. Check the construction of every variable before modelling it (**04.04**).
- **The causal question is the whole question and the design cannot be improved.** Where a decision genuinely depends on knowing whether X causes Y, and only cross-sectional self-report data exists, the honest deliverable is not a carefully hedged model. It is a statement that the question cannot be answered from this data, plus the design that would answer it. Per **K4 §9**, name what would close the gap.
- **A single number is wanted for a relationship that is not monotonic.** A correlation coefficient near zero on a strongly U-shaped relationship is arithmetically correct and substantively false. Where the shape is not monotonic, the answer is a description of the shape, not a coefficient.
- **The purpose is to produce a defensible-looking justification for a decision already taken.** Adding controls until a coefficient reaches the desired size and sign is a real practice and it is undetectable in the output. The protection is that the model specification and the order of models fitted are recorded before the results are seen, per **K4 §4.2**.

## 5. Required inputs

**Required. Without these the skill cannot run. If absent, ask; if no answer is available and work must proceed, state the assumption at the point where it bites, per K5 §5.**

- **The relationship question, stated precisely**: which variable is the outcome, which is the predictor of interest, and what the answer would be used for. "Is there a relationship between session frequency and renewal?" not "model the data".
- **Respondent-level or record-level data** with the variables on the same units and the same base.
- **The measurement definition of every variable**: wording, scale, direction, units, how derived variables were constructed, and what the missing codes are. Per **K4 §6.2**, none of this is inferred from a variable name.
- **The design that produced the data**: cross-sectional, repeated cross-section, panel, observational record, or experimental. This determines what any result can license, and it is the single most important input in the skill.
- **The base for the analysis** after missing-data treatment, alongside the achieved sample.

**Optional, and what each one adds.**

- **A stated prior structure**: what is believed to cause what, and through what. This is what makes it possible to decide which variables to control for, and without it control-variable selection is guesswork that can make the estimate worse rather than better. It is the most valuable optional input in this skill.
- **Temporal information**: when each variable was measured, or a panel structure. Establishes temporal order, which is a necessary condition for a causal claim and rules out one whole class of alternative explanation.
- **A source of exogenous variation**: a randomisation, a policy change, an eligibility threshold, a staged rollout. Converts an observational question into a quasi-experimental one and is what makes the designs in Step 9 available.
- **Behavioural or transactional data** alongside self-report. Reduces common-method variance, which inflates every association measured within a single questionnaire.
- **A comparison group unaffected by the event or intervention.** Turns a before-and-after into a design that can control for what would have happened anyway.
- **Prior evidence on the same relationship.** Establishes whether this result is consistent with a body of work, which is one of the few things that strengthens a causal reading from observational data.

## 6. Questions to ask before starting

1. **What decision turns on this, and does it require a causal answer?** Determines the whole shape of the work. Many questions framed causally are satisfied by an associational answer once the decision is examined. *Default if unanswered:* assume the answer will be read causally, and write the constraint explicitly into the output.
2. **What produced this data, and is there any source of exogenous variation in it?** Determines which designs are available. *Default:* assume cross-sectional observational, and state that no causal claim is licensed.
3. **What is believed to cause what?** Determines which variables should be controlled for, which must not be, and what the model is testing. *Default:* ask for a prior structure; if none is available, control only for variables that plainly precede both the predictor and the outcome, and say that control-variable selection was made without a specified structure.
4. **When was each variable measured?** Determines whether temporal order can be established, and whether reverse causation can be excluded. *Default:* if everything was measured at once, state that temporal order is unknown and that reverse causation is unexcluded.
5. **Who is in this dataset, and how did they get here?** Determines the selection risk. A sample of current customers, active users, survey completers or people who reached a page is a selected sample, and selection can create associations that do not exist in the population. *Default:* describe the selection mechanism explicitly and reason about what it could induce.
6. **What is the range of each variable in this sample compared with the population of interest?** Determines whether range restriction is attenuating the relationship. *Default:* report the observed range beside the coefficient.
7. **Who will read this, and what will they do with it?** Determines how strongly the causal constraint has to be built into the output rather than stated once. *Default:* assume the result will be quoted without its caveats, and write the headline so that it survives being quoted alone.

## 7. Step-by-step methodology

**Step 1. Write the relationship question and the causal question separately.** Two lines. The relationship question is what the data can address: "is session frequency associated with renewal, and how strongly?" The causal question is what the business wants: "would increasing session frequency increase renewal?" Writing both down at the start prevents the second quietly replacing the first in the write-up, which is where the substitution normally happens. *Correct result:* two written questions, and a note on which of them the design can answer.

**Step 2. Look at the scatter before computing anything.** A correlation coefficient is a summary of a shape, and several completely different shapes produce the same coefficient. Plot the two variables and read four things. **Linearity:** is the relationship a straight line, a curve, a threshold or a plateau? A coefficient near zero on a U-shaped relationship is correct and useless. **Outliers:** are a handful of points doing most of the work? On modest samples, removing four points can halve a coefficient or double it, and a coefficient driven by outliers is a statement about those cases, not about the relationship. **Clusters:** does the cloud contain two groups, so that the overall relationship is produced by the difference between them rather than by any relationship inside either? **Range:** does the data cover the range that matters? *Correct result:* a written one-line reading of the shape before any coefficient is quoted, and no coefficient reported for a relationship that is not monotonic.

**Step 3. Compute the coefficient, and report what constrains it.** Choose the measure from the data: a product-moment coefficient for two roughly linear interval measures, a rank-based coefficient for ordinal data or a monotonic but non-linear relationship, and an appropriate measure of association for categorical data. Then report the three things that change how it should be read. **Range restriction** attenuates a coefficient, sometimes drastically: a study of current customers cannot see the relationship among people who left, and a study of high performers cannot see the relationship across the full ability range. This is why a modest coefficient in a restricted sample can correspond to a strong relationship in the population. **Measurement reliability** attenuates it too: two noisy measures cannot correlate highly even when the underlying constructs are strongly related, so a low coefficient between single-item measures may be a statement about the items. **Squared coefficient as shared variance** is the standard interpretive aid and it is routinely over-read: a coefficient of 0.3 corresponds to about 9% shared variance, which sounds negligible and can still be substantively important. *Correct result:* every coefficient reported with n, the observed range of both variables, and one line on the shape it summarises.

**Step 4. Move to regression when the question involves more than two variables, and be precise about what a coefficient means.** A regression coefficient is the average difference in the outcome associated with a one-unit difference in the predictor, **among cases that are alike on the other variables in the model**. Three consequences follow, and they are the source of most misreading. It is a comparison between different cases, not a prediction of what happens if you change something for one case. "Alike on the other variables" means alike on the variables in the model and only those. And where the predictors are correlated, the coefficient describes the part of the predictor that is not shared with the others, which may be a small and substantively odd residue. Standardised coefficients allow comparison between predictors on different scales at the cost of being sample-dependent; unstandardised coefficients are interpretable in real units and should be reported wherever the units mean something. *Correct result:* every coefficient stated in the form "among cases alike on [the listed variables], a difference of one unit in X is associated with a difference of Z in Y", with the conditioning set named.

**Step 5. Say what "controlling for" achieves, and what it cannot.** Controlling for a variable removes the part of the association that runs through it, as measured. Four limits are permanent. It only removes what was measured, so an unmeasured confounder is untouched. It only removes it as well as the measure captures it, so a noisily measured confounder is only partly controlled and the residual bias can be substantial. **Controlling for the wrong variable makes the estimate worse:** conditioning on a mediator removes part of the effect you are trying to estimate, and conditioning on a collider creates an association that does not exist. And a model with many controls is not more rigorous than one with few; it is a different model, answering a different question, and the difference has to be justified rather than assumed. *Correct result:* an explicit statement of which variables are controlled, why each, and which known confounders are not measured.

**Step 6. Check the assumptions, and read what a violation means substantively.** Linearity in the modelled relationship: check residuals against fitted values, and against each predictor. Independence of observations: clustered data (multiple records per person, per site, per household) violates it and understates standard errors, sometimes severely. Constant error variance: heteroscedasticity does not bias coefficients but does bias their standard errors, and robust standard errors are the usual answer. Distribution of residuals rather than of the raw variables, which matters most on small samples. Influential cases: a case with high leverage and a large residual can move a coefficient on its own, and should be identified and reported rather than silently removed. Multicollinearity: correlated predictors inflate standard errors and destabilise individual coefficients without harming the model's overall fit, which is why a model can predict well while none of its coefficients is interpretable (see **05.04**, Step 6). *Correct result:* a diagnostics record, with any violation named, the action taken, and what the violation implies for the interpretation rather than only for the arithmetic.

**Step 7. Report fit without over-reading it.** The share of variance accounted for describes how well the model predicts within this sample, and nothing else. It is not the share of the outcome that is caused by the predictors, not a measure of whether the model is correctly specified, and not comparable across models with different outcomes or different samples. It rises whenever a variable is added, which is why an adjusted or out-of-sample measure is preferable when models are being compared. **A high value with a wrong specification is entirely possible, and a low value can accompany a correctly specified and important relationship**, particularly where individual behaviour is inherently variable. Report it with the base, the predictor set and the outcome definition, and say what the unexplained share is likely to contain. *Correct result:* fit reported as a description of prediction within this sample, with a one-line reading.

**Step 8. Work through the five confounding structures against your own data.** This is the analytical core of the skill. For each, the question is not whether it is possible in principle but whether it is plausible here, given what is known about how the data arose.

- **Common cause (confounding).** A third variable causes both X and Y, so they move together with no path between them. Recognise it by asking what could produce both. It is the structure everyone knows, and controlling for the common cause removes the spurious association if, and only if, the common cause is measured and measured well.
- **Mediator.** X causes M causes Y. Here the association between X and Y is real and causal, but controlling for M will make it disappear, which looks like a refutation and is not. Recognise it by asking whether the candidate control sits on the path between X and Y in time and in mechanism. **Controlling for a mediator is a common and serious error, because it removes exactly the effect you were trying to measure.**
- **Collider.** X and Y both cause C, and conditioning on C creates an association between X and Y that does not otherwise exist. This is the structure practitioners find least intuitive and it is very common in applied work, because colliders are frequently the variables that define the sample. If two independent qualities both raise the chance of appearing in the dataset, they will be negatively associated inside it. Recognise it by asking whether the control variable, or the selection into the sample, is a consequence of both X and Y.
- **Selection effect.** A special and pervasive case of the collider: who is in the data is determined by something related to both variables. Current customers, active users, survey responders, people who completed a journey, firms that survived. The association inside a selected sample can differ in size and in sign from the association in the population. Recognise it by describing precisely how a unit came to be in the dataset.
- **Reverse causation.** Y causes X rather than X causing Y, or both run in a loop. Recognise it by asking whether the outcome could plausibly influence the predictor, which in attitudinal data it usually can: satisfied customers report better experiences partly because they are satisfied. Cross-sectional self-report data cannot distinguish the directions at all, and where the two variables were measured in the same instrument, the halo running from outcome to predictor is a live and usually unquantifiable part of the association.

*Correct result:* a short written assessment of each of the five against this specific dataset, naming the plausible candidates rather than listing the structures generically. This assessment goes into the output, because it is the evidence that the causal reading was considered rather than assumed away.

**Step 9. Name the design that would license the claim, and check it against what you have.** Three families license causal inference, and each carries requirements that must be stated and checked rather than asserted.

- **Randomised experiment.** Assignment to condition is random, so groups are alike on everything measured and unmeasured in expectation. The requirements are that randomisation actually occurred and was preserved, that the comparison is analysed as assigned rather than as treated, that attrition is balanced, and that the outcome and analysis were specified in advance. This is the strongest licence available and it is the reason to run an experiment where one is feasible (**06.04**).
- **Valid quasi-experiment.** Where assignment was not random but something outside the units' control created variation that behaves as though it were: a staged rollout, an eligibility threshold, a policy change affecting one group and not another, a natural comparison group. The standard forms compare changes over time between an affected and an unaffected group, exploit a threshold at which treatment changes sharply, or use an external factor that affects the outcome only through the treatment. Each rests on an assumption that cannot be proved from the data: that the groups would have moved in parallel absent the intervention, that units did not manipulate their position around the threshold, that the external factor has no other route to the outcome. **The assumption is stated explicitly, and evidence for it is provided (pre-period parallel movement, density around the threshold, placebo outcomes) rather than asserted.**
- **Longitudinal design with temporal order established and confounders addressed.** Predictor measured before outcome, with baseline outcome controlled so that the analysis concerns change rather than level, and with the plausible confounders measured at baseline. This is weaker than the first two and is often the best available. It rules out reverse causation for the measured period and it does not rule out unmeasured common causes, which must be acknowledged.

**Wherever a causal claim is made, the licensing design is named in the same paragraph as the claim.** Not in a methods appendix, not in a footnote. A reader encountering the claim encounters the reason it is permitted. *Correct result:* either a causal claim with its design named beside it, or no causal claim.

**Step 10. Run the language pass over the draft.** This is an operational check, applied to a finished document, and it belongs to this skill regardless of which skill produced the document. Take the draft, including headings, chart titles, bullet fragments and the executive summary, and mark every construction that asserts a causal relationship. The prohibited set from **K4 §3.2**: "drives", "leads to", "causes", "results in", "the impact of", "the effect of", "improving X will increase Y", "because customers found X, they did Y", and the bare "so" or "therefore" joining two findings. Then add the constructions that smuggle causation in without a verb: a heading of the form "why customers churn" over correlational evidence; a chart title reading "what improves retention"; an arrow in a diagram; a recommendation whose logic only works if the association is causal. For each one, either replace it with associational language or attach the licensing design. **The executive summary is where this fails most often**, because it is written last, compressed hardest, and read most. *Correct result:* a marked-up draft with every instance resolved, and a note of how many were found, since a high count is a signal about the analysis rather than about the writing.

**Step 11. Handle the stakeholder who wants the claim anyway.** This is a professional situation with a correct handling, and refusing without helping is not it (**K4 §9**). Four moves, in order. **Say what the evidence supports, precisely and without hedging**, so that the strength of what you do have is not lost in the process of declining what you do not. **Explain the specific alternative explanation, not the general principle.** "Correlation is not causation" persuades nobody; "the customers who use this feature are the ones who were already going to renew, and we can see that in their tenure profile" does, because it names a rival account the stakeholder can evaluate. **Name what would settle it**, with the design, roughly what it would cost and how long it would take, because a stakeholder who wants an answer will usually take a route to one. **Offer the strongest honest formulation** for the document: the association with its size, the temporal information if any exists, the confounders that were addressed, the rival explanations that could not be excluded, and, where the decision must be made anyway, a statement of what is being assumed if the organisation acts as though the relationship were causal. That last move is often the most useful thing this skill produces, because it makes the assumption visible and reviewable instead of buried. *Correct result:* a written position that a stakeholder can act on, in which the assumption being made is explicit and owned.

## 8. Analytical framework

    Question → Shape → Association → Conditioning → Structures → Design → Language → Claim

**Question.** The relationship question and the causal question, written separately.
**Shape.** The scatter, read before any coefficient.
**Association.** The coefficient or model estimate, with base, range and reliability constraints.
**Conditioning.** What was controlled for, why each variable, and what remains unmeasured.
**Structures.** The five confounding structures assessed against this dataset by name.
**Design.** What produced the data, and therefore what it can license.
**Language.** The operational pass over the draft.
**Claim.** What may be written, capped by the design.

The framework has one absolute rule: **the claim gate is set by the design gate, not by the strength of the association.** A very strong association from a cross-sectional design licenses no causal claim at all, and a modest one from a randomised design licenses a causal claim about its measured effect. Practitioners consistently reverse this, treating a large or highly significant association as though its size were evidence about its direction, and it is not.

Against the **K2** evidence chain, this skill governs the boundary between Finding and Interpretation for relationship claims, and the specific move it prevents is the silent interpretation described in **K2 §2.2**.

## 9. Output format

**1. Question block.** The relationship question, the causal question, and a statement of which the design can answer.

**2. Design statement.** What produced the data, when each variable was measured, how units entered the sample, and therefore what class of claim is available.

**3. Relationship description**, per pair examined.

| Pair | Shape (one line) | Coefficient and type | n | Observed range, X and Y | Outliers or influential cases | Notes on restriction or reliability |
|---|---|---|---|---|---|---|

**4. Model table**, where a model was fitted.

| Term | Coefficient (unstandardised) | Standardised | CI | p | Conditioning set | Interpretation in words |
|---|---|---|---|---|---|---|

With: outcome definition, predictor set, base after missing-data treatment, achieved sample, fit measure and its reading, and the diagnostics record.

**5. Confounding assessment.** One row per structure, named against this dataset.

| Structure | Plausible candidate here | Measured? | Action taken | Residual risk |
|---|---|---|---|---|

**6. Causal position.** One paragraph stating what the design licenses, the licensing design if a causal claim is made, and the rival explanations that could not be excluded.

**7. Language pass record.** Instances found, instances resolved, and how each was resolved.

**8. If the organisation acts anyway.** Where a decision will be taken on an associational finding, the assumption being made, stated in one sentence, and what would falsify it.

**Where the evidence is thin**, the format is not filled. A relationship that is not monotonic gets a description of its shape and no coefficient. A model that could not be estimated gets the bivariate picture and a statement of why. A causal question the design cannot answer gets Section 6 saying so and the design that would answer it, not a hedged model presented as an approximation. Per **K4 §1**, a slot for a coefficient is not evidence that a coefficient means anything.

## 10. Quality checks

Run before any relationship result is presented. **K4 §8** runs anyway; these are specific to this task.

1. Was the scatter examined before any coefficient was computed or quoted?
2. Is any coefficient reported for a relationship that is not monotonic?
3. Have influential cases been identified, and is their effect on the estimate reported rather than silently removed?
4. Is the observed range of both variables reported alongside every coefficient, and is range restriction assessed?
5. Is every regression coefficient stated with its conditioning set named in words?
6. Is any variable controlled for that sits on the causal path between the predictor and the outcome?
7. Has the possibility of conditioning on a collider, or of selection into the sample acting as one, been assessed explicitly?
8. Have all five confounding structures been assessed against this dataset by name, rather than listed generically?
9. Is temporal order established for any claim that depends on it, and is reverse causation addressed where it cannot be?
10. Is the fit measure reported with the base, predictor set and outcome definition, and read as prediction within this sample only?
11. Does every causal claim name its licensing design in the same paragraph?
12. For any quasi-experimental claim, is the identifying assumption stated, and is evidence for it provided rather than asserted?
13. Has the language pass been run over headings, chart titles and the executive summary, not only the body?
14. Does the headline finding survive being quoted without its caveats, or does it become a causal claim when separated from them?
15. Where the organisation will act on an associational finding, is the assumption being made written down?

## 11. Common failure modes

| Failure | How to recognise it | How to prevent it |
|---|---|---|
| **Coefficient without shape** | A correlation quoted with no plot examined; a near-zero coefficient on a visibly curved relationship | Step 2 before any number; no coefficient on a non-monotonic relationship |
| **Outlier-driven relationship** | A coefficient that halves when four cases are removed | Influential-case diagnostics reported; the estimate with and without shown |
| **Range restriction misread** | A weak relationship in a sample of high performers or current customers, reported as weak in general | Observed range reported; the selected nature of the sample stated |
| **Controlling for a mediator** | An effect that disappears when a variable on the causal path is added, reported as a refutation | Prior structure specified before control selection; Step 5 |
| **Collider conditioning** | An association that appears only inside a filtered sample, or after a control was added | Step 8; the selection mechanism described in words |
| **Control inflation** | A model with twenty controls presented as more rigorous than one with three | Each control justified by the structure; more controls is a different question, not a better answer |
| **Fit read as causal share** | "The model explains 40% of churn" read as 40% of churn being caused by the predictors | Step 7 reading attached to every fit measure |
| **Significance read as direction** | A very small p-value taken as evidence that the causal reading is safe | The claim gate is the design gate; stated in the framework and enforced in Section 12 |
| **Temporal order assumed** | A cross-sectional association written up in the order the analyst expects it to run | Measurement timing recorded per variable; reverse causation assessed explicitly |
| **Specification search** | Controls added or removed until the coefficient looks right, with no record of the models tried | Specification and model order recorded before results are seen; all models fitted reported |
| **Caveat that does not survive compression** | Careful language in the body, "drives" in the summary and on the chart title | Language pass covers headings, titles and summary; the headline must survive being quoted alone |
| **AI: fluent causal narrative** | A well-written explanatory account of why one variable moves another, from correlational data | Step 10 as a required pass; **K4 §3.2** applied to headings and fragments, not only sentences |
| **AI: inventing a mechanism** | A plausible causal story supplied to explain an association, presented as interpretation rather than hypothesis | Mechanisms are hypotheses under **K3 §4.3**, labelled, with the validation named |
| **AI: hedging uniformly instead of differentiating** | Every relationship qualified identically, so the reader cannot tell the strong from the weak | **K3 §1**; calibrate, and state strong associational findings strongly |

## 12. AI guardrails

Universal prohibitions are inherited from **K4** and are not repeated here. **K4 §3.2** is the governing rule for this skill and is binding in full; the following operationalise it.

1. **Never make a causal claim without naming the licensing design in the same paragraph.** A causal claim whose design is in an appendix is an unlicensed claim.
2. **Never allow a causal construction in a heading, a chart title, a bullet fragment or an executive summary** that would not be permitted in the body. These are where the claim survives the edit.
3. **Never treat the strength or the significance of an association as evidence about its direction.** No association, however large, licenses a causal reading that the design does not.
4. **Never report a correlation coefficient without having examined the shape of the relationship**, and never report one at all where the relationship is not monotonic.
5. **Never control for a variable without stating why**, and never control for a variable that plausibly lies on the path between the predictor and the outcome without saying what that does to the estimate.
6. **Never present a model with more controls as more rigorous.** Say what question each specification answers.
7. **Never supply a causal mechanism as interpretation.** An explanation of why two variables are associated is a hypothesis, labelled as one, with the validation named (**K3 §4.3**).
8. **Never omit the confounding assessment.** A relationship result without a named assessment of common cause, mediation, collider, selection and reverse causation against this specific dataset is incomplete.
9. **Never report a quasi-experimental result without its identifying assumption and the evidence offered for it.** The assumption is not a caveat; it is the thing the claim rests on.
10. **Never add or remove controls after seeing the coefficient in order to improve it.** Where specifications were explored, all of them are reported with the order in which they were fitted.
11. **Never let a stakeholder's preference change the claim.** Per **K4 §9**, state what the evidence supports, name the rival explanation, name the design that would settle it, and offer the strongest honest formulation. A stated preference is information about the stakeholder (**K4 §4.2**).

## 13. Best-practice principles

1. **The design decides what you may say; the data decides how strongly you may say it.** These are two separate questions and they are constantly conflated. A large, precise, highly significant association from an observational design still licenses nothing causal.
2. **A coefficient is a summary of a picture, and you must look at the picture.** Several very different scatter patterns produce the same coefficient, and one of them is a straight line, one is a curve, one is a cloud with an outlier, and one is two clusters. Reporting the number without having seen which one you have is not analysis.
3. **"Controlling for" is a much weaker operation than it sounds.** It removes what was measured, as well as it was measured, and only that. A noisy measure of a confounder leaves most of the confounding in place while creating the impression that it has been dealt with.
4. **Adding a control can make things worse.** This is the single most useful thing an analyst can learn here. Mediators and colliders are common, and conditioning on either produces a wrong answer with the appearance of extra rigour.
5. **The selection mechanism is part of the data.** How a unit came to be in the dataset determines what associations can exist inside it. Describe it in words before modelling, every time.
6. **Reverse causation is the default suspicion in attitudinal data, not an exotic one.** People who are happy with an outcome rate its components more favourably. Any model built inside one questionnaire is measuring some of that.
7. **Name the rival explanation, not the principle.** In a room, "correlation is not causation" is heard as pedantry. A specific, plausible alternative account that the stakeholder can evaluate is heard as analysis, and it is what actually changes decisions.
8. **The executive summary is where the firewall breaks.** It is written last, compressed hardest, and read by the people who act. Run the language pass on it separately and last.
9. **Write the headline so it survives being quoted alone.** Any caveat that lives in a following sentence will eventually be detached from the claim it qualifies. Build the qualification into the sentence.
10. **A modest association can matter and a strong one can be trivial.** Effect size in context, reach and the cost of acting determine importance; the coefficient does not.
11. **Where a decision must be made on associational evidence, make the assumption explicit and owned.** This is more useful than either refusing or capitulating, because it converts a hidden causal assumption into a stated one that somebody can review when the results come in.
12. **The best answer to a causal question is usually a different study.** Naming the design, its cost and its timing is more valuable than any amount of careful hedging around data that cannot answer the question.

## 14. Worked example

**INPUT**

A fictional collaboration software company, Ardent Loop, wants to know whether use of its shared-templates feature increases account renewal, because a proposed roadmap investment depends on it. Available data: 4,200 business accounts, with feature usage logs for the past year, account tenure, seat count, industry, support ticket volume, and renewal outcome at the end of the year. The product team's opening position is that accounts using shared templates renew at 91% against 74% for non-users, "so templates drive retention".

**PROCESS**

*Step 1, two questions.* Relationship question: is shared-template usage associated with renewal, and how strongly? Causal question: would getting more accounts to use shared templates increase renewal? The design can address the first.

*Step 2, shape.* Usage is heavily right-skewed, with a long tail of very heavy users. Plotted against renewal rate by usage decile, the relationship is not linear: renewal rises steeply from zero usage to light usage, then flattens almost completely above the third decile. **This is a threshold, not a gradient**, and it matters enormously to the roadmap question: the association is with any usage at all, not with more usage. A single coefficient across the range would have concealed this entirely.

*Step 3, association.* The raw gap is 17 points. Reported with both bases and the observed range.

*Step 5, conditioning.* Seat count, tenure and industry are controlled. Support ticket volume is deliberately not controlled, and the reason is recorded: it plausibly sits on the path (heavier use may generate more tickets, and ticket experience may affect renewal), so conditioning on it would remove part of whatever effect exists.

*Step 8, structures assessed against this dataset.* **Common cause:** account health, engagement and the presence of an internal champion would produce both template usage and renewal. None of these is measured directly; seat count and tenure are weak proxies. This is the dominant risk and it is stated as such. **Mediator:** support tickets, handled above. **Collider:** none conditioned on in the model, but the sample itself is a candidate, addressed next. **Selection:** the dataset is accounts that existed at the start of the year, so accounts that churned in their first months are absent, and those are exactly the accounts least likely to have adopted any feature. The selected sample therefore excludes the cases that would most weaken the association. Quantified as far as possible: 340 accounts churned before the observation window and are not in the 4,200. **Reverse causation:** accounts that had already decided to renew, or were expanding, would invest in configuring templates. Since usage and renewal are measured over overlapping periods, this cannot be excluded from the annual figures.

*The judgement call.* Usage is logged monthly, so temporal order can be partly recovered. Restricting the analysis to usage in the first quarter and renewal at year end establishes that usage preceded the outcome, at the cost of dropping accounts that joined mid-year and reducing the base to 3,180. **Judgement:** the temporal version is weaker in precision and much stronger in what it licenses, so both are run and reported together. In the temporal version, controlling for seat count, tenure, industry and first-quarter activity level overall, the association between first-quarter template usage and renewal falls from 17 points to about 6 points, interval 2 to 10. Most of the raw gap was general account activity, not templates specifically. This is the most useful number in the analysis and it would not have existed without the temporal restriction.

*Step 9, design.* No randomisation, no eligibility threshold, no staged rollout in the history. A quasi-experimental option does exist for the future: the feature is being extended to a second product tier in stages, which would supply a staged-rollout comparison. Noted as the route to an answer.

*Step 10, language pass.* Eleven causal constructions found in the draft. The chart title "what drives renewal" is changed to "renewal rate by first-quarter template usage". The heading "why accounts churn" becomes "characteristics associated with non-renewal". Three instances of "drives" and two of "leads to" are replaced. The executive summary contained the only remaining instance of "increases", which is removed. The count of eleven is reported, because it indicates how strongly the causal reading was embedded in the framing.

*Step 11, the stakeholder.* The product team is told plainly what the evidence supports: template usage in the first quarter is associated with a 6-point higher renewal rate among accounts alike on size, tenure, industry and overall activity, and the relationship is a threshold rather than a gradient. The rival explanation is named specifically: accounts with an internal champion adopt features and renew, and templates may be a marker of that rather than a cause of it. The design that would settle it is named: the staged tier rollout, analysed as a comparison between the affected and unaffected groups, with the parallel-movement assumption checked on the pre-period. And the assumption is written down: if the roadmap proceeds on this evidence, the organisation is assuming that at least part of the 6-point association reflects the feature rather than the kind of account that adopts it, and the staged rollout will test that within two quarters.

**OUTPUT**

A question block with both questions; a design statement covering the observation window and how accounts entered it; a relationship description recording the threshold shape and the 340 excluded accounts; two model tables, cross-sectional and temporal, with conditioning sets in words; a confounding assessment naming account health as the dominant unmeasured common cause and describing the selection into the sample; a causal position stating that no causal claim is licensed and naming the staged rollout as the design that would license one; a language pass record of eleven instances; and a stated assumption for the decision.

**Researcher sign-off required.** The roadmap decision is a material investment resting on an associational finding with a named unmeasured confounder (**K5 §2.5**). The analysis states what is assumed if the investment proceeds; whether that assumption is acceptable is not an analytical judgement.

## 15. Advanced usage

**Sensitivity analysis for unmeasured confounding.** Where an unmeasured common cause is the dominant risk, it can be characterised even though it cannot be removed: how strongly would a confounder have to be related to both the predictor and the outcome to explain the whole association away? An association robust to any plausible confounder is meaningfully stronger than one that a modest unmeasured variable would erase, and stating the threshold is far more informative than acknowledging the risk in general terms.

**Interaction rather than separate models.** When the question is whether a relationship is stronger in one group than another, fitting two models and observing that one coefficient is significant and the other is not is not an answer. The difference between the two is itself an estimate requiring its own test, fitted as an interaction. This error is extremely common and reliably produces false claims about where an effect is concentrated.

**Clustered and multilevel data.** Where observations nest inside people, sites, households or organisations, treating them as independent understates standard errors, sometimes by a large factor. Cluster-robust standard errors are the minimum response; a multilevel model is appropriate where the group level is substantively interesting rather than a nuisance, and it also separates within-group from between-group relationships, which frequently differ in size and sometimes in sign.

**Mediation, done properly.** Where the question is how an effect operates rather than whether it exists, mediation analysis decomposes an association into direct and indirect parts. It rests on strong assumptions, particularly that there is no unmeasured confounding of the mediator-outcome relationship, which is rarely defensible in observational data and is often quietly ignored. Report it as a description of the model's structure, not as an established mechanism.

**Non-linear and threshold relationships.** Where a relationship plateaus, has a floor, or reverses, a linear term averages the regions and answers no question well. Model the shape: splines, bands or an explicit threshold term. In applied work the threshold reading is usually far more actionable than a slope, because it identifies where the change actually happens.

**Prediction versus explanation.** A model built to predict and a model built to estimate a relationship are different objects with different standards. A predictive model may include anything that improves out-of-sample accuracy, including consequences of the outcome, and its coefficients are not interpretable. An explanatory model has a specification driven by structure and is judged on whether the estimate is unbiased, not on fit. Confusing the two produces a model that predicts well and supports no conclusion at all.

**When the standard approach does not fit.** Where no design is available and the decision cannot wait, the deliverable is the association, the named rival explanations, the sensitivity threshold, and the explicit assumption the organisation will be making. This is a legitimate professional output and it is much better than either a hedged model or a refusal.

## 16. Skill chain

**Recommended previous skills**
- **05.01 Descriptive Analysis.** Hands over the distributions, ranges and base definitions that determine whether a relationship can be estimated and how a coefficient should be read.
- **05.02 Statistical Testing.** Hands over the difference-testing questions this skill does not cover, and the effect-size and interval discipline that applies to model estimates as well.
- **05.03 Cross-Tabulation.** Hands over the bivariate picture and the confounded banner points that a model is often brought in to separate.
- **01.04 Research Method Selection.** Determines, at design stage, whether the study will be able to answer a causal question at all, which is where this skill's constraints should first be applied.

**Recommended next skills**
- **06.04 Experiment and A/B Test Analysis.** Takes the causal question this skill cannot answer from observational data, and supplies the design that licenses the claim.
- **08.01 Finding to Insight Development.** Takes the associational finding and does the interpretation work, under the language constraints this skill sets.
- **08.04 Recommendation Development.** Takes the stated assumption from Step 11 and carries it into the recommendation, so that a decision taken on associational evidence records what it assumed.

**Runs well alongside**
- **05.04 Driver Analysis**, which depends on this skill's confounding structures and language control, and hands over whenever ranking becomes attribution.
- **05.05 Trend and Tracker Analysis**, whenever a movement over time is about to be attributed to an intervention.
- **13.03 AI Output Verification**, which runs the Step 10 language pass as an audit over finished deliverables produced anywhere in the library.
- **K4 §3.2**, which this skill operationalises, and **K3 §4**, which supplies the register for stating an association strongly without stating it causally.

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A Yazi Supplied Skill and resource.