Do you vary more than you differ from other people?
Most research about how people work describes people on average. Whether any of it can tell one particular person what to change is a separate question, and almost nobody asks it. I write about that gap.
Where this ends up: the best number I had for that gap turns out to be an artefact of how the researchers built their comparison, and I am publishing that rather than keeping it. The argument survives. The number does not.
Evidence One statistic appeared to prove the gap is enormous. A 2018 paper in the Proceedings of the National Academy of Sciences, one of the journals a finding has to pass through to be taken seriously (Fisher, Medaglia & Jeronimus, 2018). The variation inside one person is roughly 8 times the variation between people. 7.85 to 1.
In other words, how much you change from one day to the next is eight times bigger than how much you differ from the person next to you. If that were true, describing someone by their average would be close to useless, and everything I write about would matter enormously.
I wanted it to be true. I no longer think it is.
They took studies where people were measured over and over, mostly for weeks. Then each measurement was used twice. Once as a point inside one person’s record. Once as a stand-in for a whole person in a pooled group, with the same 78 people in every one of those groups.
The second use is the problem. That between-person figure is not the spread of people. It is the spread of 78 group averages, one for each moment, with the same 78 people in every one. Those averages barely move, and not only because averages are smooth. The same people sit in every one, so the differences between people cancel out exactly. What is left is the average of 78 people’s momentary wobbles. So the comparison sets the within-person figure against how much the group average wobbles from moment to moment. The first is always bigger, for any group of people you measured, and the size of the ratio is set mostly by how many people went into each average, not by how people differ from one another.
You can watch it happen. The spread of those averages shrinks in proportion to the square root of how many people go into each one. One of their samples had 78 people, so every average pooled 78 people, and the square root of 78 is 8.83. The five ratios they reported for that sample ran from 7.04 to 9.92, straddling it. Another sample had 83 people; the square root of 83 is 9.11, and its two ratios were 9.14 and 9.25. Not every sample lands there. One with 64 people came out near 4, which shared timing can explain; one with 63 came out at 10 and 13, which I cannot.
Correction. I got the mechanism wrong the first time. I wrote that one sample measured people 78 times each and that the spread of averages shrinks with the square root of how many measurements you took. The 78 is the number of people in that sample. Each of them was measured about 130 times. The authors then drew 78 of those measurements per person to make a square grid, which is why the same number turns up twice, and why my arithmetic came out right anyway. Averaging one person’s measurements over time does not shrink the differences between people at all. Averaging across the same people, moment after moment, cancels them completely. The spread shrinks with the square root of the number of people in each average, not the number of measurements. The square root of 78 is still 8.83, so the number stands. The reason I gave for it does not. One more thing: the paper never says whether its within-person figure is the typical person’s own spread or the spread of people’s averages, so my earlier phrase "one person’s raw bounce" assumed something the paper does not state. The argument about the between-person figure holds either way.
The clearest sign sits in their own table. Depressed mood, rated 0 to 100, in a study that mixed 43 people with anxiety or depression and 35 healthy controls. The figure the paper labels the spread between people was 2.77. That would mean everyone in the study has the same average mood within about 3 points out of 100. Nobody believes that about people. It is what you get when you measure how precise an average is and then call it the spread of a population.
Losing the number does not settle the question against me. The argument that group statistics do not describe individuals is mathematical and it stands on its own. The experience-sampling work stands too, in a narrower form than it usually gets quoted in. What died is one number, and it was the best-known one I had.
When I first published this I wrote that I had not found a published paper making the criticism. There is one, for the paper’s correlation results rather than its spread figures: a letter in the same journal argued the between-person quantity was behaving like the standard error of an estimate, and the authors replied that their figure was not a proxy for within-person variation but a third thing, a measure of how unstable cross-sectional estimates were, adding that it may be inappropriate to use one to draw inferences about the other (Hamaker & Ryan, 2019, and the authors’ reply). That concession is most of my argument, made by the people best placed to make it. What remains mine is applying the same reading to the spread table, where the paper never defines what its between-person column is computed over. The arithmetic fits only one answer. A statistician could still tell me I have the numerator wrong.
I set myself a rule. Go looking for the study that contradicts you before you publish. This one contradicted me and it was on my side.
Where this stops. Fisher, Medaglia and Jeronimus 2018, PNAS 115(27), open access at PMC6142277. The authors gesture at the mechanism themselves in their discussion. I have not seen a published paper making this criticism, so I am stating it as a reading of their own reported numbers rather than as an accepted correction.
What would change my mind. A response showing the between-person column is a spread of raw scores rather than of means.