Nova Academy — Lesson 011: Correlation & Causation — When Patterns Need Explanations

A pattern is the beginning of a question

Suppose ice-cream sales and park visits both increase in the same weeks. Perhaps ice cream encourages visits. Perhaps the park sends people toward ice cream. Or perhaps warmer weather makes both more likely. Observing two rising numbers does not tell us which explanation is right.

Our previous lesson was about uncertainty. This one asks how to investigate a proposed cause without confusing a compelling story with evidence.

1. Correlation describes how observations vary together

Two variables are positively associated when higher values of one tend to accompany higher values of the other. A negative association means higher values of one tend to accompany lower values of another. A weak linear association does not rule out more complicated relationships.

For numerical data, a Pearson correlation coefficient between −1 and +1 describes the direction and strength of a linear relationship. It does not identify which variable caused the other, if either did.

Read OpenStax Psychology 2e, Analyzing Findings for examples of scatterplots and correlation.

2. Causal explanations propose what produces a change

A causal question asks whether changing A would change B under appropriately comparable circumstances. We can draw A → B to record that hypothesis. But the arrow is a proposed relationship; drawing it does not prove it.

3. Find the hidden third factor

For the park example, draw two arrows on paper: Warmer weather → Ice-cream sales and Warmer weather → Park visits. Now consider whether temperature could explain part or all of the association. A variable that distorts the interpretation of a suspected cause and an outcome can be a confounder.

This diagram represents a possible mechanism, not verified measurements from a real town. Holidays, tourism, school schedules, or publicity might also matter.

4. Counterfactuals and fair comparisons

A counterfactual question asks: “What would the outcome have been if the suspected cause had been different, with the relevant circumstances otherwise comparable?” We cannot ordinarily observe both possibilities for the same event at the same instant.

Researchers address this difficulty through carefully designed experiments, comparison groups, repeated measurements, and observational causal-inference methods. Random assignment reduces systematic differences on average; it does not make one small test infallible.

The NIST Engineering Statistics Handbook explains the difference between an observed correlation and a causal relationship.

5. Mini-lab · Two paper airplanes, one question

15–20 MINUTES · PAPER EXPERIMENT OR DATA-ONLY OPTION

The suspected cause is wing design, while the outcome is flight distance. Make two planes using different designs. Use the same paper type, launch line, and thrower. Select an unobstructed indoor space, safely away from other people and breakable objects.

1. Before testing, write your prediction and why you think it may be true.
2. Flip a coin to determine whether A or B goes first in each pair of trials.
3. Measure five throws of each design; record every attempt, even the disappointing ones.
4. Calculate the mean of the five distances for each plane.
5. Identify three possible alternative influences, such as throwing force, folding differences, air flow, or measurement error.
6. Explain how you could improve the reliability of the comparison.

You can skip physical throws and work with these invented classroom data. They are not real experimental observations:

Plane	Five distances in meters	Mean
A	3.1, 3.0, 3.2, 3.3, 3.0	3.12
B	3.4, 3.1, 3.5, 3.3, 3.2	3.30

6. Improve the experiment

Suppose all five A throws occur before all five B throws. The thrower may improve with practice or tire over time. Randomizing the order helps prevent one design from systematically benefiting from its position in the session.

Other improvements include more trials, consistent folding measurements, a clearer distance-measurement rule, and repeating the comparison with other throwers. Even careful small experiments must report their uncertainty.

NIST also describes randomized block designs for situations in which nuisance factors such as operators or testing conditions matter.

7. What if a controlled experiment is impossible?

Some causal questions cannot be answered by assigning people or environments randomly. Certain experiments are unethical, expensive, or impossible. Observational studies, natural experiments, and other methods can still contribute causal evidence when their assumptions and alternative explanations are examined carefully.

Therefore, “correlation is not causation” is a warning against an unsupported leap, not a declaration that causal knowledge can never come from observational research.

8. Audit a causal headline

Find a public headline claiming something “causes,” “prevents,” “improves,” or “reduces” another outcome, or invent a fictional headline for this exercise. Then record three separate statements:

Avoid collecting private information or experimenting on other people. Keep the investigation to public sources or imaginary classroom examples.

9. Questions, interpretations, and the next model

A satisfying story can connect two dots. A careful explanation must survive comparison with plausible alternatives. Nova Academy treats that discipline as a foundation of inquiry: be imaginative in what you propose and precise about what has been established.

The previous ten lessons give us the tools to ask good causal questions: observe, test, verify, define, model, study feedback and emergence, examine connections, adapt, and report uncertainty.

10. Knowledge check

1. Do two variables rising together establish that one caused the other?
2. What could temperature explain in the park-and-ice-cream example?
3. What does a counterfactual question compare?
4. Why randomize the order of paper-airplane throws?
5. What is actually supported by the invented A and B data?
6. Can careful observational studies contribute to causal understanding without randomized experiments?

Reflection · When patterns need explanations

You can see a real pattern and still be mistaken about its source. The goal is not to become suspicious of everything. It is to remain curious enough to investigate the explanations that a pattern permits.

Takeaway: Name the association. Propose competing causes. Seek a fair comparison. Calculate carefully. Describe what the evidence does—and does not—show.

Completion: Identify a potential confounder, calculate both sample means, and explain one limit of the proposed causal claim. No tuition, enrollment, grades, or certificate required.

Sources & further learning

• OpenStax Psychology 2e — Analyzing Findings.
• NIST — Experiments and Experimental Design.
• NIST — Randomized Block Designs.

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Nova Academy is a free, non-accredited educational initiative of the Electric Icarus Project. The paper-airplane measurements are fictional teaching data, not published experimental findings.