PSLE Science Reality Lab Vol No.249 | “Correlation r = 0.80” — Does That Prove One Variable Causes the Other?

Stable internal ID: PSLE-SCI-REALITY-0249

Wait, what? A news-style infographic shows a scatterplot of two measurements and prints “correlation r = 0.80.” The caption says, “This proves that increasing X causes Y to increase.”

The number can describe a strong linear association in the dataset. It does not, by itself, identify the cause.

NIST describes the correlation coefficient as a measure of the linear relationship between two variables, ranging from −1 to +1. A positive value means the variables tend to increase together in a linear pattern; a negative value means one tends to decrease as the other increases. But an association can arise because X influences Y, Y influences X, a third factor influences both, the sample is selected in a particular way, or several mechanisms act together.

This is not a lesson in distrusting graphs. It is a lesson in making the claim match the evidence. The 2026 PSLE Science assessment objectives include interpreting and analysing information, evaluating observations, information and methods, and communicating explanations and reasoning. The 2023 Primary Science syllabus also emphasises healthy scepticism and considering more than one plausible explanation. A learner seeing a striking scatterplot should be curious before being certain.

Quick Answer

No. A correlation of r = 0.80 can be evidence of a strong positive linear association in the observed data. It does not alone prove that changing one variable causes the other to change.

Ask:

What exactly were the two variables?
How were the data collected?
What does the scatterplot actually look like?
Could another variable affect both?
Could the direction run the other way?
Was one variable deliberately changed while other important conditions were controlled?
Does independent evidence support a mechanism?

The Owned Learner Job

This Reality Lab owns one narrow real-world communication job: how to evaluate a chart, infographic or headline that uses a correlation coefficient as if it were direct proof of cause and effect.

It does not own correlation mathematics, regression, probability or causal inference as standalone topics. Those concepts remain with their broader owners. Here the coefficient is treated as a communication object a young science learner may encounter.

Rebuild the Evidence Object

Imagine an original dataset from 12 school gardens. The first variable is the number of hours of sunlight measured at each garden. The second is average plant height after a defined growing period. The scatterplot trends upward and the calculated Pearson correlation is r = 0.80.

What can we say?

Observed: gardens with more measured sunlight tended to have taller plants in this dataset.
Quantified: the two variables had a fairly strong positive linear association.
Not yet proven: the difference in sunlight alone caused the height differences.

Why not? The gardens may also differ in water, soil, plant variety, fertiliser, pest damage, temperature or starting plant size.

Association Is a Pattern, Causation Is a Mechanism Claim

An association says two quantities vary together in a dataset. A causal claim says changing one quantity produces a change in another through some process.

The second claim is stronger. Stronger claims require stronger evidence.

For a Primary learner, remember this sentence:

A pattern can suggest a question. It does not automatically answer the question of cause.

Worked Case 1: The Third Variable

Across 20 days, ice-cream sales and the number of people swimming at a pool both rise together. The correlation is strong.

Does buying ice cream cause people to swim? Does swimming cause ice-cream sales?

A third variable—hot weather—could increase both. The observed association is real, but the causal story is different from the first explanation that came to mind.

The learner habit is not to shout “correlation is useless.” The association can still be useful evidence. The habit is to ask what other explanation could generate it.

Worked Case 2: Reverse Direction

In a set of ponds, the amount of algae and the number of grazing snails are positively associated. A headline says, “More snails cause more algae.”

Another possibility is that ponds with more algae provide more food, allowing more snails to survive. Or a third environmental factor may affect both. Without a suitable investigation, the direction of cause remains unresolved.

Worked Case 3: A Hidden Group Creates the Pattern

A report combines data from seedlings of two species. Species A tends to be both older and taller when measured; species B tends to be younger and shorter. Across all plants, age and height correlate strongly.

Age may indeed affect height, but the mixed species also contribute to the pattern. If the claim is “one extra day of age causes this exact increase in any seedling,” the combined scatterplot is not enough.

Worked Case 4: High r Does Not Mean “80% Correct”

A pupil sees r = 0.80 and says, “The graph is 80% accurate.” That is not what the coefficient means.

The correlation coefficient is unitless and describes the direction and strength of a linear association. It is not a test score, percentage of data points that are correct, percentage chance that the claim is true, or percentage accuracy of the instruments.

This matters because percentages feel familiar. Scientific symbols must be read according to their definitions, not converted into whatever percentage story sounds intuitive.

Worked Case 5: A Strong Curve Can Have a Misleading Linear Correlation

Imagine plant growth increases as temperature rises from very cold to moderate, then decreases when temperature becomes too high. The relationship is curved. A single linear correlation coefficient can fail to describe that shape well.

Therefore never read r without looking at the scatterplot. The number summarises one aspect of the pattern; it does not replace the data picture.

Representation Check: Look at the Points Before the Caption

Are there many points or only a few?
Do the points form a roughly linear pattern?
Are there separate clusters?
Is one extreme point pulling the line?
Were axes truncated in a way that makes the pattern look stronger?
Are both variables measured on comparable groups and times?

A correlation coefficient should be read with the plot that produced it, not as a floating badge detached from the evidence.

Comparison Check: Are We Comparing Like With Like?

Suppose sunlight is measured across whole gardens but plant height is measured from only the three tallest plants in each garden. The variables may be paired, but the sampling choices can distort the association.

Before trusting a strong-looking r, check what each point represents, how groups were selected, and whether measurement methods stayed consistent.

Method Check: Observation Versus Intervention

An observational dataset records what happens without deliberately assigning conditions. It can reveal patterns and generate hypotheses. An experiment can go further by deliberately changing one factor while controlling important alternatives where possible.

If we want to test whether light causes a change in seedling growth, a stronger design may use similar seedlings assigned to different light conditions while water, soil, container size and other relevant factors are kept comparable.

Even then, the conclusion should match the tested organisms and conditions. An experiment does not create unlimited causation claims either.

Alternative Explanations to Keep Alive

X may influence Y.
Y may influence X.
A third variable may influence both.
Several variables may act together.
Selection of the sample may create the pattern.
Measurement method may create or strengthen the apparent association.
The pattern may differ outside the observed range or population.

You do not have to believe all possibilities equally. You keep them available until evidence rules them in or out.

What Evidence Strengthens a Causal Claim?

A well-designed experiment where the proposed cause is changed deliberately.
Important alternative variables are controlled or accounted for.
The effect appears repeatedly in independent studies or trials.
A plausible scientific mechanism connects cause and effect.
The timing makes sense: the proposed cause occurs before the effect.
Different methods point toward the same explanation.
The effect changes in a sensible way when the proposed cause changes.

What Weakens It?

The only evidence is one observational correlation.
The sample is tiny or strongly selected.
The scatterplot contains separate groups that were ignored.
A third variable provides a plausible alternative explanation.
The proposed cause occurs after the supposed effect.
The relationship disappears when important conditions are controlled.
The coefficient is high only because of one extreme point.

How Far Can the Conclusion Travel?

From r = 0.80, a careful statement can be:

In this dataset, the two measured variables showed a strong positive linear association.

Without further evidence, do not automatically upgrade that to:

“X causes Y.”
“Y causes X.”
“The relationship is 80% accurate.”
“80% of Y is caused by X.”
“The same relationship must hold in every population and condition.”

Tempting but Invalid Reasoning

“The dots slope upward, so X causes Y.” An upward association does not establish direction or exclude third variables.
“r = 0.80 means 80% of the points are right.” r is not a percentage-correct score.
“r is close to 1, so there cannot be another cause.” A strong association can still arise from shared causes or linked conditions.
“r = 0 means there is no relationship.” Pearson r measures linear association; a curved relationship can be missed.
“Correlation never matters.” Correlation can be valuable evidence. The mistake is asking it to prove more than it can.

PSLE-Style Transfer Case: Fan Speed and Evaporation

A pupil records natural classroom fan settings over ten days and the amount of water lost from an open dish. Days with faster fan settings tend to show more water loss. The pupil concludes, “Fan speed definitely caused the difference.”

A stronger response is:

The data show an association between fan setting and water loss, but other conditions such as temperature, humidity and starting water amount may also differ. A controlled investigation changing fan speed while keeping relevant conditions similar would give stronger evidence about causation.

Explained Practice

Practice 1

A chart shows r = −0.75 between shade cover and soil temperature. What does the negative sign tell you?

Answer: In the dataset, higher values of one variable tended to go with lower values of the other in a fairly strong linear pattern. It does not by itself prove shade caused the temperature difference.

Practice 2

Two variables have r = 0.85. Can you say the measurements are 85% accurate?

Answer: No. Correlation strength and measurement accuracy are different scientific quantities.

Practice 3

Plant height and fertiliser amount correlate strongly, but larger pots also received more fertiliser. What alternative explanation should you test?

Answer: Pot size may affect growth and is mixed with fertiliser amount. A better investigation would separate these variables.

Practice 4

A scatterplot forms a clear U-shape but r is near zero. Does that prove there is no relationship?

Answer: No. Pearson correlation summarises linear association. The visible curved pattern is important evidence that the coefficient alone does not describe.

Delayed Independent Return: Three Arrows

Tomorrow, draw X and Y and test three possible diagrams: X → Y, Y → X, and X ← Z → Y. Explain how all three could produce an association between X and Y. If you can do that, a correlation headline will no longer force you into one causal story too early.

Parent and Tutor Teaching Guide

Use an intentionally silly dataset first. Across several days, draw both ice-cream sales and fan use rising with temperature. Ask the learner whether buying ice cream turns fans on. Then reveal temperature as the common factor. The humour helps the distinction stick without becoming cynical about statistics.

Next, give a genuine science example where causation is plausible, such as light level and photosynthetic activity. Ask what additional experiment would strengthen the causal claim. This prevents the learner from memorising the unhelpful slogan “correlation means nothing.”

The desired habit is balanced: association is evidence; causation is a stronger explanation that needs a stronger bridge.

Route to Existing Canonical PSLE Science Owners

Authoritative Sources

Quiet Return

A strong pattern deserves attention. It does not deserve a cause invented faster than the evidence can support.

When you see r = 0.80, say what the number has earned: a strong positive linear association in this dataset.

Then ask the scientific question that matters next: what evidence would distinguish the possible causes?

Small Group Tutorials