Correlation

People have always said that two numbers look related. The trouble was that eyes were the only instrument for checking. Put two lines on the same chart, have one person say they track each other and another say they don't, and the conversation has nowhere left to go. Both are looking at the same picture, so there's no way to argue that one of them looked harder.

The scale made it worse. Stretch one axis and the two lines snap into alignment; compress it and they drift apart. The same data could be made to leave opposite impressions.

A correlation coefficient hands that judgment to a number. However the chart is drawn, the value doesn't move, and while people may argue about whether 0.7 is large, they stop arguing about whether a relationship exists at all. A meeting that traded impressions turns into one working from a shared figure.

Take how far each value sits from its own average, multiply those distances pair by pair, average the products, and divide by how spread out the two values are so the result lands between -1 and 1. Multiplying the distances from the average is the whole idea. When one value is above its average and so is the other, the product is positive; when only one of them is, it's negative. If the products pile up with mostly the same sign, the two values move in the same direction.

There are three steps.

1. Collect the paired values. For each account, write the number of teammates invited last month next to the number of days the account logged in this month. Keep only accounts that have both.
2. For each row, multiply the two deviations from their averages, then add them up and take the average. If the average invite count is 3 and the average login count is 12 days, an account with 5 invites and 18 days gives (5-3) times (18-12), or 12. An account with 1 invite and 20 days gives (1-3) times (20-12), or -16.
3. Divide by how spread out each of the two values is. This step erases the units. Before it, the size of the number depends on whether you counted people or days; after it, the result falls between -1 and 1 and can be compared against any other pair.

Reading the result splits into sign and size. Positive means that when one value is high the other tends to be high; negative means that when one is high the other tends to be low. The closer the absolute value is to 1, the closer the pairs sit to a single straight line, and 0 means there's no straight-line relationship. A 0.72 says accounts that invited more people generally log in more often; a -0.41 says accounts with longer load times generally log in less.

Running the numbers takes one spreadsheet function or a one-line query.

Use the value as evidence only when the absolute number is large, the sample is big enough, and the scattered points fall roughly along a line. Miss any one of the three and you still get a number, just not one worth trusting.

What counts as large depends on the field. In instrument measurement even 0.9 is considered low, but since what a person does is decided by dozens of things at once, product data showing 0.3 is already a relationship worth examining. Roughly, above 0.7 reads as strong, 0.3 to 0.7 as worth a look, and under 0.1 as nothing — without treating those cutoffs as hard lines.

Sample size often matters more. A coefficient of 0.6 across eight accounts happens routinely when nothing is going on. The same 0.6 carries different weight from 8 accounts than from 800. With a small sample, check the confidence interval alongside the value, and if that interval crosses 0, don't claim a relationship.

Looking at the scatter of points is not a step to skip. This measure only detects straight-line relationships, so a relationship with any other shape comes out near 0. Notification frequency and retention behave exactly that way: retention climbs up to about two notifications a week, then falls once it passes ten, forming an upside-down U. Run a correlation across that and the rising half cancels the falling half, leaving something like 0.05. Reporting from that number alone that notifications have nothing to do with retention gets the conclusion exactly backwards. A single far-flung point can do similar damage — drop that one account and 0.8 can collapse to 0.2.

"Invites and retention came out at 0.62."

The two move together clearly enough to be worth digging into.

"There's a correlation, but I don't think we can call it the cause."

Pushing back on a proposal to change a feature based on things moving together.

"With a sample of 12, that number is risky."

Too few accounts, so the value could easily be coincidence.

At Pagedeck, Mia reaches for this most often when deciding which metric to examine first. She computes coefficients for five or six values against paid conversion and starts with whichever comes out largest. Last quarter, accounts that invited a teammate in their first week showed 0.62 against retention at six months.

What she did with that number wasn't propose a bigger invite button — it was go looking for a confounding variable, a hidden value that moves both sides. Splitting accounts by team size, the coefficient dropped to 0.2 among teams larger than 20. Heavy inviting and long retention were both coming from the team being large. Only after recalculating within groups matched on team size did she design the next experiment.

The most common error is reading a high coefficient as one thing causing the other. Seeing two values rise together, people naturally read the first as producing the second. But this number only reports that they moved together; it says nothing about which moved which. The order could be reversed, or a third value could be moving both. Decide on that misreading and you spend a quarter pushing invite counts up and retention stays exactly where it was.

Leaning too far the other way is also common: deciding the number is useless unless it proves causation. Teams that got burned once tend to land here. But the value of a coefficient isn't in proving a cause — it's in choosing where to dig first. Sweep a few dozen metrics for which ones move with your goal and the list of experiment candidates drops to five or six. Confirming a cause with something like an A/B test takes two weeks per run, so throwing away the step that narrows the field means picking what to test on instinct.