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Correlation is not causation

Two things can rise or fall together without one causing the other. A trend shows a relationship, not the reason, so a hidden third factor may explain both.

Part of: VCE Applied Computing - U1O1 - Data analysis — Module 67, VCE Data Analytics - U3O1 - Data Analytics — Module 92, VCE Data Analytics - U3O2 - Analysis and Design — Module 71, VCE Data Analytics - U4O1 - Development and Evaluation — Module 39, 9-10 Digital Technologies: Analysing and visualising data — Module 14, ACARA Digital Technologies Years 7–8 — Analysing and Visualising Data — Module 50, ACARA Digital Technologies Years 9–10 — Acquiring and Validating Data — Module 116, ACARA Digital Technologies Years 9–10 — Analysing and Visualising Data — Module 46

Understanding Correlation is not causation in VCE Spreadsheets, SQL & Visualisation

What it does: One outside factor (the hot weather) drives both variables, so they seem linked even though neither causes the other. Careful wording describes the relationship and admits that a cause has not been proven. Negative correlation means one variable rises while the other falls. The study and test score example is a positive correlation. A trend shows a relationship, not the reason. You need more evidence, such as a controlled experiment, to show cause. Matching trends only show correlation. Coincidence or a hidden third factor can produce the same pattern. A better conclusion is 'more study time is linked to better marks', and other factors such as motivation may also play a part.

Common mistakes: CORREL compares two variables, so it needs two data sets. It should be r <- CORREL(ice, burns). A negative correlation means r is below 0. The test should be IF r < 0 THEN.

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This module's key terms are also in a printable crossword (Modules 55–70) and word search (Modules 55–86).

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Learning
Duo
Ice cream sales and sunburn cases both rise in summer. What is the best conclusion?
Hot sunny weather could be a hidden third factor affecting bothEating ice cream causes sunburn
Matches
Sales of sunscreen rose with sales of ice cream, so sunscreen causes ice cream sales.
↓
This treats a correlation as a cause. Hot weather is the hidden third factor behind both.
Applying
Meanings
Term
correlation is not causation
Meaning
Two things can rise or fall together without one causing the other. A trend shows a relationship, not the reason, so a hidden third factor may explain both.
Practice
Ice cream sales and shark attacks rise together.
Testing
Gaps
=(B2:B30,C2:C30)
Check Answer
Spots
2burns <- [4, 9, 14]
3r <- CORREL(ice)

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Quick Questions

1. Ice cream sales and sunburn cases both rise in summer. What is the best conclusion?
A. Hot sunny weather could be a hidden third factor affecting both ✓
B. Eating ice cream causes sunburn
Hot weather leads to more ice cream sales and more time in the sun. The two trends are linked by a third factor, not by one causing the other.
2. Which statement describes a negative correlation?
A. As hours of screen time go up, sleep hours go down ✓
B. As hours of study go up, test scores go up
Negative correlation means one variable rises while the other falls. The study and test score example is a positive correlation.
3. A scatter plot shows a strong positive correlation between two variables. What does this tell you?
A. The variables tend to rise together, but it does not prove why ✓
B. Changing one variable will definitely change the other
A trend shows a relationship, not the reason. You need more evidence, such as a controlled experiment, to show cause.
4. Which conclusion is worded more carefully?
A. Sleeping more makes students score higher
B. Students who sleep more tend to score higher, so there may be a link ✓
Careful wording uses phrases like 'tend to', 'is linked to' and 'may be', which show a relationship without claiming a cause.
5. Towns with more fire trucks sent to a fire have more fire damage. What is a likely hidden third factor?
A. The colour of the fire trucks
B. The size of the fire ✓
Bigger fires need more trucks and also cause more damage. The fire size explains both, so the trucks do not cause the damage.

Match the Pairs

Ice cream sales and shark attacks both rise in summer → A positive correlation: two things rise together, but neither one causes the other
Hours of gaming up, test scores down → A negative correlation: as one variable rises, the other falls
A hidden third factor can explain why two variables move together → Hot weather -> more ice cream sales AND more swimmers at the beach
A careful conclusion says the data shows a link, not a cause → The data shows a link between sleep and marks, but more evidence is needed
Sales of sunscreen rose with sales of ice cream, so sunscreen causes ice cream sales. → This treats a correlation as a cause. Hot weather is the hidden third factor behind both.
The scatter plot slopes upward, which proves that more study time causes better marks. → 'Proves' and 'causes' are too strong. A trend shows a relationship, not the reason for it.

Key Term

correlation is not causation
Two things can rise or fall together without one causing the other. A trend shows a relationship, not the reason, so a hidden third factor may explain both.

Fill in the Blanks

1. =CORREL(B2:B30,C2:C30)
Hint: Type the spreadsheet function that measures how strongly two columns are related.
2. Negative correlation: one rises, other falls
Hint: Type the word that describes what the second variable does in a negative correlation.
3. Hidden third factor may explain both
Hint: Type the number word for the extra factor that can cause both variables to change.
4. A is linked to B, not caused by B
Hint: Type the careful word that describes a relationship without claiming a cause.
5. r near -1 means strong negative correlation
Hint: Type the value of r that shows a perfect negative correlation.

Spot the Error

Question 1
A ice <- [20, 35, 50]
B burns <- [4, 9, 14]
C r <- CORREL(ice)
Line C — CORREL compares two variables, so it needs two data sets. It should be r <- CORREL(ice, burns).
Question 2
A r <- -0.8
B IF r > 0 THEN
C PRINT 'negative correlation'
D ENDIF
Line B — A negative correlation means r is below 0. The test should be IF r < 0 THEN.
Question 3
A r <- 0.1
B IF ABS(r) > 0.3 THEN
C PRINT 'weak link'
D ENDIF
Line B — A weak link means the size of r is small, so the test should be ABS(r) < 0.3. With > it would run for strong links.
Question 4
A temp <- [10, 20, 30]
B heater <- [90, 50, 10]
C type <- 'positive'
D PRINT type & ' correlation'
Line C — As temperature rises, heater use falls. That is a negative correlation, so type should be 'negative'.
Question 5
A r <- 0.85
B PRINT 'A causes B'
C PRINT 'Cause is unproven'
Line B — A strong r only shows a relationship. A careful conclusion says A is linked to B, not that A causes B.

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