Simpson's Paradox

“A trend can appear, disappear, or reverse when data are split into groups.”

01 / PLAINLY

What it means, plainly

Simpson's paradox occurs when a relationship seen in the total changes after the data are divided by another variable. The total and the subgroups represent different comparisons.

02 / CONTEXT

A little more

The paradox occurs when an aggregate association changes after stratifying by a third variable. Arithmetic alone cannot decide which comparison answers the causal or descriptive question.

03 / WHY IT MATTERS

Why it matters

It warns that an overall average can hide how cases were distributed, while splitting data without a causal reason can also mislead.

04 / EXAMPLE

A familiar example

Treatment A wins within mild and severe cases, yet B looks better overall because it received a larger share of mild cases.

05 / LIMIT

What it does not mean

Disaggregation is not always right either; a variable may be a confounder, mediator, or result of selection.

06 / NOTICE

Notice it in your day

Make two small groups where A has a better rate than B in each, but receives more difficult cases. Add the totals and notice how the question changes.

FINAL NOTE

The idea worth keeping

Before choosing totals or subgroups, sketch how the data were generated.

QUESTIONS / 02

Questions people still have

What changes in Simpson's paradox?

An aggregate association can disappear or reverse after data are split by a third variable.

Should you always prefer the subgroup result?

No. The choice depends on how the data arose and which question is being asked.