Correlation is not a strategy: how to tell if two numbers are really linked

Here is a bet. Give me eight weeks of any two numbers from your brand.

I will find a pair that moves together like a married couple. I will not use any skill, just a spreadsheet and a little patience.

Then I will hand you a story about why. It will sound smart. It will probably be wrong.

Two numbers that rise together tell you almost nothing, because most business numbers rise together.

This page shows why that happens and how to catch it. It ends with a test you can run today in any spreadsheet. Every number below is made up.

The made-up brand and the made-up link

Picture a small brand that sells chew toys for dogs. It runs ads, and it sells on its own store.

Over eight weeks, ad spend went up and orders went up. Here are both, week by week.

Put them through the usual formula for how closely two lines move together. The answer is about 0.91. A perfect match scores 1.0, and no link at all scores 0.

That looks like a clear win for ads. The agency email writes itself.

But look at what the chart really shows. Both lines go up because time went by. The brand was growing. Almost everything grew with it.

Why unrelated numbers look linked

There are three common reasons. Each one fools smart people.

• A shared trend. Both numbers grow with the business, so any two of them rise together.
• A hidden third factor. Something else lifts both. Australia’s statistics office gives the classic case. Ice cream and sunscreen sales both climb in hot weather, so they look linked, yet neither causes the other (Australian Bureau of Statistics).
• Pure luck. Look at enough pairs and some will match by chance. One well-known site collects absurd pairs, and it warns that a big enough dataset will give strong links “completely at random” (Spurious Correlations).

Wikipedia names this problem a spurious relationship. Two things are tied together by “coincidence or the presence of a certain third, unseen factor” (Wikipedia).

A brand has plenty of hidden third factors. A price cut. A rival out of stock. A holiday. A big wholesale order. Each one can lift several numbers in the same week, and no single tool records all of them.

That is a blameless problem. The owner did not miss anything. The facts just live in different systems.

The dog toy example, taken apart

Back to the made-up brand. Say we ask a better question.

Not “did both numbers go up?” But “in the weeks when ad spend jumped, did orders jump too?”

To answer it, look at the change from each week to the next.

Run the same formula on these seven pairs of changes. The score is about -0.2.

The link just vanished. The weeks with the biggest ad jumps did not have the biggest order jumps. In week 4, spend rose by 7 and orders fell by 20.

So what were the ads doing? We cannot say yet. Maybe nothing. Maybe a lot, with a delay. The point is that the first chart gave us no right to claim a link.

Run this test: the change-and-shuffle test

You need a spreadsheet and two columns of weekly numbers. Use at least 26 weeks if you have them. Eight is only for the example.

1. Write the two columns. For example, weekly ad spend and weekly orders. Use closed weeks only, never the current one.
2. Make two new columns of changes. Each cell is this week minus last week.
3. Score the changes. Use the CORREL function on the two change columns. Write the score down. This is your real score.
4. Shuffle one column. Randomly reorder the weeks of one change column, so ad jumps no longer line up with order jumps. Score the pair again.
5. Repeat 20 times and write down each score. This is how a permutation test works: you rearrange the data and count how often chance matches your result (Wikipedia).
6. Count. How many of the 20 shuffled scores are as strong as your real one, in either direction?

What a pass looks like. Your real score is stronger than nearly all of the shuffles. Maybe 19 or 20 of them are weaker. Even then you have a strong hint, not proof.

What a fail looks like. Several shuffles match or beat your real score. That means chance can produce your result easily. Treat the link as noise.

One more check for a pass. Split your weeks in half and run the test on each half. A real link should show up in both.

Why use changes instead of totals? Totals carry the shared trend. Changes strip most of it out. It is not perfect, but it removes the cheapest false link.

What the test cannot tell you

A pass is still not a cause. Two traps remain.

• A delay. Ads may pay off a week or two later. Try lining one column up one week later and repeat.
• A hidden event. A promotion might have lifted both in the same week. The test cannot see an event nobody wrote down.

To prove a cause, you need a controlled test. Keep one group of shoppers or one region as it was, change the thing for another, and compare. Pausing an ad for two weeks in one region is a simple version.

If your ads send shoppers to Amazon, that is a place where a link hides. Amazon Attribution is Amazon’s tool that measures “the on-Amazon impact of your marketing strategies across non-Amazon channels” (Amazon Ads). Our post on whether Meta ads drive Amazon sales shows how to read it.

For the full difference between a link and a cause, see incrementality vs attribution.

A quick scan for bad links in your own reports

Before you believe a link, ask these.

Where this goes wrong with AI

Ask an AI app why sales rose, and it will give you a neat story. It will use whatever links it finds in the numbers you pasted in.

An AI is quick at finding patterns. It does not know which ones are shared trends unless someone tells it. It also cannot know about the price cut that never made it into the export.

So the risk is wrong inputs answered with confidence. Fix the inputs first. Write down what each number means, keep a log of events, and ask the AI to test a link the way this page does. Our guide to AI-ready data covers the setup.

The short version

Most business numbers trend, so most pairs look linked. Compare changes, not totals, and shuffle the weeks to see if chance matches you.

A pass earns a link a place on your list of things to check, and a controlled test is what proves a cause. Do not change a budget on a line chart alone.

Synthesis is built around this idea. It writes the business down once so every number means one thing, checks every number against its source, and keeps the AI you already use on those numbers. See what a brand brain is for the bigger picture.