Will Rogers Phenomenon

If someone moves from group A to group B, both group averages can rise — without any value changing.

What is this about?

A joke by Will Rogers: when the "Okies" moved from Oklahoma to California, the average IQ rose in both states. That works if the movers are below the average of the old state but above the average of the new one: leaving raises one average, arriving raises the other. The overall average stays the same, because only the assignment changes. In medicine this is called stage migration: better diagnostics assign cases to other disease stages, so every stage looks better — without real progress. (The IQ joke is a pure statistics gag, not a real statement about anyone.)

How to proceed

1. Who can move? — set the number of willing-to-move Okies (outlined in purple in the plot).
2. Moving to California — "start wave" or control by hand from 0 to 100%.
3. Average IQ per state (①) and each person (②) — both average lines move to the right, the overall average stands still.
4. Concepts — why the overall mean is immune and what stage migration means.

What to watch for

It is not a real effect: not a single individual value changes, only a label (the place of residence) moves. Sum and count of all values stay the same — that is why the overall mean is immune.
The condition: both means rise exactly when the mover is below the average of the old group but above that of the new group.
Suspicious is: "all subgroups improve" but the overall value stagnates. Then it helps to compare the whole group or to apply the same classification consistently.

Things to try

Start the wave and notice that the overall average stays put while both state averages rise. Then change the number of willing-to-move Okies.

What's next?

In Simpson's Paradox, too, the conclusion depends on how cases are grouped: same data, different grouping, different result.

📋 Example — Okies Move to California

Will Rogers' quip: "When the Okies left Oklahoma and moved to California, they raised the average IQ of both states." 😄 The migrants are below Oklahoma's average but above California's average — they sit exactly in between. Question first: what happens to both states' averages when they move — do they rise, fall, or a mix? Slide the migration wave up (or click "▸ Start wave") and watch.

① Average IQ by State

Oklahoma 🤠

—

California 🏄

—

USA overall

—

unchanged by the move

Moved

of 12 willing to move

No one has moved yet — slide the migration wave up.

② Each Point = One Person · Position = IQ

top lane = Oklahoma · bottom lane = California · thick line = mean now · pale line = mean at start

Concepts

What is the Will Rogers phenomenon?

If you move a case from group A to B whose value lies below A's average but above B's average, the mean of both groups rises — even though no individual value changes. The overall average stays constant.

Why does the overall average stay the same?

A move only changes a label (place of residence), not a measured value (IQ). The sum and count of all values stay identical → the overall mean is immune to reclassification. Only the split shifts.

The serious side: stage migration

In medicine, better diagnostics reclassify cases into different disease stages — every stage looks better afterward, without any real progress (Feinstein 1985). Rankings and grading tiers are just as susceptible.

How to spot it / what to do?

Suspicious: "every subgroup improves," but the overall value stagnates. Solution: compare the overall group, or apply the same classification consistently. → Simpson's Paradox → Regression to the Mean

Will Rogers Phenomenon — when the Okies moved out, both states got smarter