The Analyst's Path

Scatter plot

A relationship message says two measured variables move together, and there is essentially one form: position on two common scales, one point per unit of observation. A scatter plot with fifteen or more points is the only chart that lets a reader see the strength of a relationship, its shape, and the observations that do not fit. A scatter licenses you to say that two variables are associated, to state how strongly, and to name the observations that break the pattern.

4 min readPart of Chart-Choice Grammar: Match the Chart to the MessageOpen in course mode

Advertisement

A relationship message says two measured variables move together, and there is essentially one form: position on two common scales, one point per unit of observation. A scatter plot with fifteen or more points is the only chart that lets a reader see the strength of a relationship, its shape, and the observations that do not fit.

What does a bar chart of group means erase?

Most analysts reach for a bar chart of group means instead. It's worth seeing what that erases.

Take fourteen synthetic US software companies, each with a net revenue retention figure and a revenue growth rate, and split them at 110% retention. The low group averages 19.0% growth, the high group averages 32.875%, and a two-bar chart of those two numbers is technically accurate. It's also nearly a lie, because the fastest-growing company in the low group grew 31%, which beats three of the eight companies in the high group. A reader looking at two bars concludes that retention above 110% means faster growth, full stop. A reader looking at the scatter sees a real upward relationship with substantial overlap, which is a different and more useful belief.

Advertisement

What can you claim from a scatter plot?

Compute the relationship. Don't just describe it. For that panel, Pearson's correlation coefficient is 0.8928, so r squared is 0.7970 and 20.30% of the variation in growth is not explained by retention at all. The fitted line has a slope of 0.9990, meaning one additional point of retention is associated with about one additional point of growth across this range, and the residuals run from 7.50 points above the line to 8.48 points below it. Those numbers belong on or beside the chart, because they are what turns a shape into a claim a reader can check.

This is the place for the line about causation, and it needs stating carefully. A scatter licenses you to say that two variables are associated, to state how strongly, and to name the observations that break the pattern. It doesn't license a causal claim in either direction, and the reason has nothing to do with philosophical delicacy. Retention could raise growth. Fast growth could flatter retention, because a company adding customers quickly has a young base that has not yet had time to leave. A third factor, a product in an expanding category, could raise both. All three stories fit the same scatter, and choosing between them takes an argument the chart cannot supply.

Write the title accordingly. "Retention and growth move together, and retention explains about 80% of the variation in growth" is defensible from this chart. "Improving retention drives growth" is not, and the difference is one word.

What about a third variable, or very few points?

A third variable can go into the point size, which makes a bubble chart, and it comes with a caution: area is read poorly, so a bubble tells you an order of magnitude and not a value. If the third variable's exact value matters, use small multiples of scatters instead and split on the third variable. Three-dimensional scatters are ruled out entirely, for the reason section 9 gives.

Fewer than about a dozen points and the scatter stops being a scatter. With eight observations you are looking at a pattern the eye will find whether or not it exists, and the form that won't mislead is a labelled table with the correlation stated, plus a sentence naming how few observations it rests on.

Advertisement

Part of the course

This page is part of Chart-Choice Grammar: Match the Chart to the Message (PR2.01), in Phase 2: Financial statement analysis and quality of earnings. The module's flashcards and its quiz are in the app.