Topic guide

When can a study support a causal explanation?

Separate an observed relationship from a specified intervention contrast and inspect the assumptions connecting them.

For: Readers evaluating claims that one behaviour, exposure or intervention changes another outcome.

Begin here

  1. NPTEL — National Programme on Technology Enhanced Learning · Source-checked annotation

    Lecture 25 : Univariate and Bivariate Scatter Plots

    NPTEL — National Programme on Technology Enhanced Learning Speaker not established foundation Duration unknown

    The scatterplot examples begin with what the observations actually show. Use them as a descriptive starting point before moving to the separate causal question in the reading.

An association tells you that observations vary together. A causal question asks what would change under a specified intervention. Those questions can use the same variables while requiring different evidence. Begin with the scatterplot lecture: describe the pattern before supplying an explanation. Then ask what decision or action the causal claim is about. A slope is not yet an answer to that question.

In an original example, students who spend more time revising tend to obtain higher marks. More revision might help. Prior knowledge, motivation or available study time might also affect both variables. Exam difficulty could change the pattern across classes. Sketch these possibilities before choosing an analysis. A correlation is useful descriptive information, but selecting the explanation requires knowledge of how the data were generated. NPTEL scatterplots and correlation sequence.

The counterfactual approach compares outcomes under alternative interventions. An individual is observed under one actual course of events; the other outcome is missing. Randomisation can support comparisons of average effects, while the realised study still requires attention to its conduct and analysis. Hernán and Robins develop this distinction in Chapters 1 and 2 of Causal Inference: What If. The book is a deeper continuation, not a claim that every causal question has one simple formula.

For one common approach to observational data, Chapter 3 makes the needed assumptions explicit. The intervention must be sufficiently well defined and connected to the observed exposure. The measured information must support an appropriate comparison without remaining confounding, and the relevant groups must have a positive chance of each treatment being compared. These are commonly called consistency, exchangeability and positivity. They are substantive requirements, not boxes certified by a small p-value. Inspected book version, Chapter 3.

Return to revision time. “Make everyone study more” is underspecified. Compare offering a defined revision session with not offering it, in a particular population over a particular period. That is a different intervention from compelling an extra hour of solitary study. Write down which effect you want before deciding whether existing records can inform it. If the records contain no comparable students receiving one of the alternatives, a neat regression output cannot manufacture that comparison.

The regression videos contribute statistical mechanics and a useful warning about overfitting; they do not teach a complete causal-identification strategy. Keep prediction, description and causal estimation as separate aims when reading their examples. A model can predict well without explaining an intervention’s effect, and a causal estimate can remain uncertain even when the association is strong.

End with a short assumption audit. Name the intervention, comparison, population, outcome and follow-up period. Draw two plausible causal stories, identify an observation that would distinguish them, and state one assumption that the available data cannot verify. The aim is a more explicit claim with visible limits, not a stronger conclusion obtained by adding the word “causal”.

Build the connection

  1. NPTEL — National Programme on Technology Enhanced Learning · Source-checked annotation

    Lecture 28 : Correlation Coefficient

    NPTEL — National Programme on Technology Enhanced Learning Speaker not established intermediate Duration unknown

    Summarise association. Correlation is symmetric, so its calculation alone cannot supply a direction of causation.

  2. NPTEL — National Programme on Technology Enhanced Learning · Source-checked annotation

    Probability and Statistics: Review - Part 2

    NPTEL — National Programme on Technology Enhanced Learning Speaker not established intermediate Duration unknown

    Check a special-case claim. The joint-Gaussian discussion shows why a statistical relationship cannot be detached from its assumptions.

  3. NPTEL — National Programme on Technology Enhanced Learning · Source-checked annotation

    Statistic for linear regression

    NPTEL — National Programme on Technology Enhanced Learning Speaker not established intermediate Duration unknown

    Inspect the model. A regression slope and its statistical assumptions are a different object from an identified intervention effect.

  4. NPTEL — National Programme on Technology Enhanced Learning · Source-checked annotation

    Hypothesis testing in linear regression

    NPTEL — National Programme on Technology Enhanced Learning Speaker not established intermediate Duration unknown

    Separate prediction from explanation. The checked overfitting and prediction-interval examples reveal why fitting observations is not the same task as explaining them causally.

  5. NPTEL — National Programme on Technology Enhanced Learning · Source-checked annotation

    Hypothesis testing of means

    NPTEL — National Programme on Technology Enhanced Learning Speaker not established intermediate Duration unknown

    Inspect the comparison. Paired and separate-group analyses require knowing how the observations arose; a test name does not supply that history.

Write two causal stories

For the invented revision-time example, specify a concrete intervention and draw two different explanations for the association with marks. State the comparison needed to distinguish them, then name one assumption that remains untestable from the observed association alone.

Exercise or methods at source ↗

Read alongside

Go into the full course →

Next step

Work through Chapters 1–3 of What If, then identify the assumptions behind one observational claim in your own subject.

Limits of this route

The video descriptions were checked against identified official-transcript excerpts, not complete viewing. An accessible official media endpoint is not evidence that every frame played. Teaching examples are not independent validation of the underlying scientific or clinical claims. The causal account is based on selected book passages; it does not cover all identification strategies, time-varying treatment or selection bias. The revision example is hypothetical.

Sources and editorial check · 2026-11-07

Specific primary reading passages and each selected video’s identified official-transcript excerpts; full viewing and scientific peer review are not claimed.

Checked by agent. This is not human peer review.

  1. Hernán and Robins — Causal Inference: What If, download labelled 19 August 2026

    Retrieved 2026-11-07. Inspected identified excerpts only: first 2,200 extracted characters of PDF pages 8, 12, 13, 14; the extracted text of pages 22, 24, 36, 37, 39, 41, 42 and 44. These cover causal questions, counterfactuals, randomisation, consistency, exchangeability and positivity. No whole-book reading claimed.

  2. Lecture 25 : Univariate and Bivariate Scatter Plots

    Retrieved 2026-11-07. Selected excerpts only: segment 0 (header) first 1118 characters; segment 1 (01:42) first 1400 characters; segment 12 (25:38) first 1069 characters; segment 23 (36:02) first 1400 characters. No complete transcript reading or full video viewing claimed.

  3. Lecture 28 : Correlation Coefficient

    Retrieved 2026-11-07. Selected excerpts only: segment 0 (header) first 1400 characters; segment 1 (05:26) first 594 characters; segment 11 (24:59) first 1400 characters; segment 20 (51:24) first 400 characters. No complete transcript reading or full video viewing claimed.

  4. Probability and Statistics: Review - Part 2

    Retrieved 2026-11-07. Selected excerpts only: segment 0 (header) first 1400 characters; segment 1 (01:51) first 988 characters; segment 18 (39:39) first 1400 characters; segment 34 (65:49) first 1218 characters. No complete transcript reading or full video viewing claimed.

  5. Statistic for linear regression

    Retrieved 2026-11-07. Selected excerpts only: segment 0 (header) first 435 characters; segment 1 (00:23) first 1400 characters; segment 5 (26:32) first 1400 characters; segment 8 (35:04) first 1400 characters. No complete transcript reading or full video viewing claimed.

  6. Hypothesis testing in linear regression

    Retrieved 2026-11-07. Selected excerpts only: segment 0 (header) first 198 characters; segment 1 (00:09) first 0 characters; segment 8 (13:37) first 1400 characters; segment 14 (34:51) first 1400 characters. No complete transcript reading or full video viewing claimed.

  7. Hypothesis testing of means

    Retrieved 2026-11-07. Selected excerpts only: segment 0 (header) first 186 characters; segment 1 (00:09) first 636 characters; segment 12 (18:06) first 519 characters; segment 23 (40:14) first 1400 characters. No complete transcript reading or full video viewing claimed.

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