# Inspect an association without calling it a content effect

Constructed teaching cases with full context. No actual people, accounts, payments, research participants or forecasts.

Pair the same eligible observations, inspect their units, time and group structure, then describe the relationship and its sensitivity. A correlation coefficient summarizes a particular linear association; it does not establish causation, exclude a curved relationship or validate an audience-wide rule. Keep the actual data and alternative explanations with the conclusion.

## Write the two variables and actual paired unit

A question might relate editing minutes to a post’s response-event count at a fixed age. Pair both values to the same post and preserve missing values, source and age. Sorting each column independently destroys those pairs; matching by a similar title can join different posts.

Keep counts, proportions and exposure opportunities explicit. A larger follower base or longer observation age may affect both variables. If a denominator or source is missing, do not infer it from another metric simply to obtain a complete scatter plot.

## Inspect shape and variation before a single coefficient

NIST’s scatter-plot guidance considers linear/nonlinear structure, changing variation and unusual observations, and distinguishes association from causation. Draw actual paired points without presenting an interpolated line as extra data. The complete constructed pairs in the packet can be inspected directly as a table.

Pearson correlation describes linear association and is undefined when either variable has no variation. A coefficient near zero can hide a curved pattern. A large magnitude can be driven by a single point or a shared time trend; neither makes a causal interpretation valid.

## Keep time, groups and plausible common causes

Inspect whether a calendar trend, author, topic or distribution change structures the pairs. More publishing and more impressions may both occur during a campaign period without the added posts alone causing the difference. Subgroup analysis also needs adequate comparable observations, not a search for a favorable subset.

A useful next step may be to improve measurement, examine a specific mechanism or design a proper comparison. Do not choose a new posting rule solely because the coefficient is high in a handful of selected posts. Keep the claim observational unless the actual design supports more.

## Resolve three constructed association claims

C1 — Constructed pairs (1,2),(2,4),(3,6),(4,8),(5,10) have Pearson r=1. Decision: describe the exact linear pattern and ask whether time or another shared factor structures it. Outcome: perfect association in five entered pairs, not proof that doubling the first variable causes the second to double.

C2 — Constructed pairs x=−2,−1,0,1,2 and y=4,1,0,1,4 have r=0 but the exact relation y=x². Decision: retain the full table and nonlinear pattern. Outcome: zero linear coefficient does not establish independence or no relationship.

C3 — Constructed pairs (1,2),(2,4),(3,3),(4,1),(20,20) have r=0.972. Without the final point, r=−0.4. Decision: verify that unusual observation, retain it if valid and report both the full result and sensitivity. Outcome: not permission to delete the point that contradicts the preferred story.

| Pair | x | y = x² |
| --- | --- | --- |
| 1 | −2 | 4 |
| 2 | −1 | 1 |
| 3 | 0 | 0 |
| 4 | 1 | 1 |
| 5 | 2 | 4 |

## Make a source check rather than an automatic exclusion

An unusual point may be a real event, a wrong unit, a data-entry error or another source problem. Keep the original and correction evidence. Report any exclusion rule and its rationale, including whether it was chosen after seeing the result. Do not silently replace an unavailable value with zero.

A complete association note states sample/pairing, metric age, coefficient if appropriate, shape, sensitive points and plausible alternatives. It does not turn a scatter plot into a prediction interval or a controlled experiment. Useful interpretation can end with an unresolved causal question.

## Retain the pairs and bounded interpretation

The worksheet keeps paired unit, two variable definitions, source, selection, missingness, plot/table review, optional coefficient and sensitivity decision. The offline fixture runner reproduces these exact numerical examples; it neither validates a real analytics export nor collects private profile data.

Primary guidance was read on 1 November 2026. All pairs are constructed. No real content, audience, campaign or causal result was observed, and this exercise is not another original population study.

## Primary sources

- [NIST: scatter plots, shapes and association limits](https://www.itl.nist.gov/div898/handbook/eda/section3/eda33q.htm)