One number cannot describe a step function

Every widely used Big Five instrument reports a facet as a single number. That number is a claim: it asserts you have a characteristic level of the trait, and that variation around it is either small or uninteresting.

For most facets and most people, that claim is defensible. This project concerns the cases where it is not — and where the deviation is not noise but the most descriptively important feature of the trait in that person.

The clearest case is Agreeableness. Its Altruism and Sympathy items are written about people in general — the needy, strangers, humanity at large:

“I am concerned about others.”
“I sympathize with the homeless.”
“I feel sympathy for those who are worse off than myself.”

Someone whose warmth is strongly conditional on closeness — guarded toward strangers, close to unconditional toward a small circle — has no accurate way to answer. Any single response overstates one and understates the other. The instrument returns approximately the mean of a distribution the respondent does not have.

Two people can score identically on Altruism and be completely different:

• Person A — consistently moderate helpfulness toward everyone.
• Person B — near-zero toward strangers, near-total toward the inner circle.

These are not the same person. They behave differently in most situations that matter — in caregiving, in crisis, in how they form relationships, in where finite attention goes. A measurement model that cannot distinguish them is not merely imprecise; it is describing somebody who does not exist.

The gradient, not the point.

Selected facets are administered four times, at four ordered levels of closeness — your inner circle, friends, acquaintances, strangers — and the shape of the resulting curve is the object of measurement.

  expression
      ^
  7   |  *----*                      flat      — the usual model fits
      |
  5   |  *----*
      |         \                    tapers    — ordinary modulation
  3   |          *----*
      |  *----*
  1   |          \____*----*         step      — a boundary, and it matters
      +---------------------------->            which side you are on
       inner  friends  acq.  strangers

Four points rather than two, because a two-point difference score is statistically unusable — its reliability lands around .27 with our item counts, and can go negative. Four ordered points support an exact decomposition into level, slope and curvature whose precision can be calculated rather than assumed.

Each measured trait is asked about three different ways, and those three do not always agree with each other. Someone whose embarrassment in front of strangers is extreme, while the other two statements about the same trait stay level, produces a facet curve that is the mean of a disagreement — a gentle slope that looks unremarkable, with the interesting part averaged away.

That is the identical error the instrument was built to catch, occurring inside a single facet rather than across a person. So the results page draws the spread of the three statements behind every curve, always, rather than only when a threshold is crossed. Where they agree the band collapses onto the line; where they pull apart it opens, and the eye lands on the disagreement without needing to be told.

Ten facets, chosen so the central hypothesis can fail. Three are predicted flat and one is predicted to run backwards — without those, a gradient would be indistinguishable from someone simply agreeing with everything.

This section exists because the honest answer to “is this new?” is partly, and the parts that are not new should be said first.

Clifton (2014) had people rate their Big Five as experienced with each of thirty individual members of their social network, and found that expression varied with how central the other person was. A closeness gradient in Big Five expression has therefore already been demonstrated. No claim of novelty for the phenomenon is available here, and none is made.

Repeating one item set across several relational targets is also established — Fraley et al.’s ECR-RS does it with four attachment targets, and self-concept differentiation (Donahue et al., 1993) has measured cross-role variability since the nineties.

What is plausibly new is narrower:

• Facet-level resolution. Prior work is domain-level or adjective-level.
• Signed, directional profiles. Self-concept differentiation discards direction by construction — and direction is exactly the information we want.
• Closeness as the ordering axis rather than social role, which connects trait expression to the discounting and moral-circle literatures rather than to role theory.

Taken at face value, that result predicts this instrument will find nothing. We cite it ourselves, prominently, because a reviewer who finds it first will use it to end the conversation.

The distinction we depend on is this: they manipulated the comparison standard — rate yourself relative to close others. We manipulate the behavioural target — how you actually behave toward close others. Those are different psychological operations. The first asks you to re-anchor a self-assessment; the second asks about a different set of behaviours.

Frame-of-reference research that manipulates target or domain does move scores substantially — a meta-analysis found contextualised measures achieve criterion validity of .24 against .11 for non-contextualised ones.

But the distinction is carried entirely by item wording, which makes it an engineering constraint rather than an argument. Every stem in our instrument is written as behaviour toward a target and must be unreadable as a comparison. You can read all of them on the methods page.

If our gradients also come out at d < .05, the honest conclusion is that Lenhausen et al. were measuring the same thing, and the construct does not exist. We will say so.

Recorded before any data was collected, so they cannot be revised afterwards. The construct is not supported if any of these holds:

1. The frames do not separate. Ring-framed scores differ by d < .05, replicating the null above.
2. No differentiation across traits. The conduct controls gate as much as Altruism, and Anger does not reverse. That would indicate a response-style artifact rather than gating.
3. Measurement non-invariance across rings. Without it, a between-ring difference reflects the items behaving differently rather than the person differing.
4. Inadequate reliability. If the combined index is not stable enough for individual interpretation, we withdraw individual feedback and report population findings only.
5. No incremental validity. If contraction predicts nothing beyond overall trait level, self-concept differentiation, neuroticism, and existing closeness measures, then it reduces to things already measurable at a fraction of the item cost.

• Not IRB-approved institutional research. An independent project, run openly.
• Not clinical, not diagnostic, not a screen for anything.
• Never for hiring, admissions, or any evaluative decision about another person.
• Not population norms. The reference sample is self-selected internet volunteers — young, English-speaking, and not representative. Every percentile on this site says which group it refers to.

There is also a well-documented trap in reports like these: people accept randomly generated personality descriptions as accurate about themselves, and the vaguer and more flattering the prose, the higher the acceptance. That is why our interpretation stays tied to specific numbers, hedged by their uncertainty, and occasionally unflattering.