Together is not the same as because

By the end of this lesson you can explain why two things rising together does not prove one causes the other.

Why it matters

"Children who eat breakfast do better at school, so breakfast makes children clever!" Maybe. Or maybe families with time for breakfast also have time for homework. Decisions built on the wrong cause waste money and help nobody.

The idea in plain words

When two things go up together and down together, data people say they are correlated: they move together. That is a fact you can see in the data.

But why they move together is a different question. There are three common reasons:

1. One really does cause the other.
2. A hidden third thing causes both.
3. It is a coincidence.

Correlation: two things moving together: when one is high, the other tends to be high (or low).

Cause: one thing making another happen.

Hidden cause (confounder): a third thing that drives both, making them move together even though neither causes the other.

Heat drives both sales. Watermelons do not make coconuts sell.

See it done

Data: stall-days.csv: 28 days of daily totals at Amara's stall (synthetic). Import it into a new tab. Column C is max_temp_c (the day's hottest temperature, made up), D is watermelons_sold, E is coconuts_sold.

Claim to check: "Selling watermelons makes people buy coconuts. Amara should put watermelons at the front to sell more coconuts."

1. Draw the two together. Select D1 to E29. Insert, Chart, and set Chart type to Scatter chart. Each dot is one day.

Scatter chart: a chart with one dot per row, placed by two numbers: one across, one up. It shows whether two things move together.

The dots climb from bottom left to top right. The two sales are correlated.

2. Name what you see. On days with more watermelons sold, more coconuts were sold too. They are correlated.
3. Ask: could something else drive both? What makes people want cold, juicy fruit? Hot weather.
4. Check the suspect. Make a scatter chart of temperature against coconuts: select C1 to C29, then hold Ctrl (⌘ on a Mac) and select E1 to E29, then Insert, Chart, Scatter chart. The dots climb too: hotter days, more coconuts. The same is true for watermelons.

Temperature and coconuts move together as well.

5. Decide. The heat is a better explanation than "watermelons cause coconuts". Putting watermelons at the front on a cool day would probably not sell more coconuts.
6. The rare bonus of synthetic data. We know the answer here, because the course team wrote the script that made this data. It makes hot days sell more of both fruits, and there is no link between the two fruits at all. With real data, you rarely know for sure, so you must stay careful.

Your turn, with help

"Towns with more fire engines have more fires. So fire engines cause fires." What is the hidden third thing?

Hint: what do towns with lots of fire engines also have lots of?

Show the answer

The size of the town. Bigger towns have more buildings (so more fires) and more fire engines. Size drives both.

Your turn, alone

1. "Pupils who own more books get better marks." Give one possible hidden cause.
2. In the real country data, countries with more people tend to give off more CO₂ in total. Is it fair to say "people cause CO₂"? What would you want to know first?
3. Correlation, cause, or both? "When it rains, more umbrellas are sold."
4. Write the one-sentence rule from this lesson in your own words.

Check your answers

1. For example: family income, or how much time parents have to read with them.
2. Partly: people use energy. But it is not the whole story. Per person, the amounts differ hugely (lesson 5.2), so how people live and how energy is made matters too. You would want CO₂ per person, and facts about the energy each country uses.
3. Both: they are correlated, and here rain really does cause people to buy umbrellas.
4. For example: "Two things moving together does not prove that one causes the other."

Watch out

• "Linked to" in headlines. It usually means "correlated with". It does not prove "causes".
• Stopping at the first explanation. Always ask: what else could make both of these go up?
• Swinging the other way. Correlation does not prove cause, but it does not rule it out either. Sometimes one thing really does cause the other (rain and umbrellas). Proving it needs more evidence, which you will meet in the statistics course.

Say it back

1. What is correlation?
2. What is a hidden cause?
3. What really drove both of Amara's fruit sales?

Show the answers

1. Two things moving together.
2. A third thing that drives both, so they move together without one causing the other.
3. The heat (the day's hottest temperature).

What is next

That ends Module 5. You now know five traps: cut-off axes, totals instead of rates, picked windows, averages that hide spread, and together-is-not-because. In Module 6 you put everything together and write your first data story, one that would not fall into any of them.