Methods

The public-domain IPIP-NEO-120 (Johnson, 2014): five domains, thirty facets, four items per facet, five-point scale. Administered unmodified, which is what makes the resulting scores comparable to published values and to Johnson’s public repository of 619,150 item-level cases. Any edit would forfeit that.

Items are interleaved so that all thirty facets appear once in each block of thirty. Pages are exactly thirty items for that reason: at that size, no two items from the same facet ever appear on screen together. Showing related items side by side inflates the correlation between them, which would inflate the reliability estimate, which would in turn make every confidence interval on the results page look narrower than it honestly is.

A facet score is the sum of its four items after reverse keying (range 4–20). A domain score is the mean of its six facet sums, also on 4–20 — not the sum of twenty-four items, which would give a 24–120 range and silently break every comparison to published values.

One missing item in a facet is prorated onto the full range; two makes the facet unscorable, and it is reported as unscorable rather than as a number. Prorating also widens the confidence interval, because a prorated four-item facet behaves like a three-item scale.

Every percentile is reported with an interval. The computation:

alpha    Cronbach's alpha, computed IN THE REFERENCE CELL
SEM      SD * sqrt(1 - alpha)                    standard error of measurement
T        M + alpha * (X - M)                     Kelley regressed true score
SE_est   SD * sqrt(alpha * (1 - alpha))          standard error of estimation
band     PR(T - z*SE_est) .. PR(T + z*SE_est)    z = 1.2816 at 80% coverage

The headline number is the percentile of the regressed true score, not of the observed score. Regression toward the mean is correct rather than conservative: when measurement is noisy, an extreme observed score is more likely to be partly noise than genuinely that extreme. The observed percentile is also returned, for comparability with instruments that report it.

Default coverage is 80%, not 95%. A 95% band on a four-item facet spans roughly forty percentile points and reads as “this test does not work”. Both are computed, the coverage is always labelled on screen, and 95% is available in exports.

When the facets inside a domain contradict each other, the domain score is the mean of a contradiction. Two gates, both required:

• Is the spread real? An omnibus chi-square over the facet z-scores, each weighted by its own error variance so that noisy facets count for less.
• Is it unusual? Against a threshold derived from the reference sample rather than asserted. This matters: under a common-factor model with typical loadings the expected within-person facet spread is already about 0.71 standard deviations, so a hand-picked threshold would flag most of the population.

Only the most extreme verdict suppresses the single number entirely. The outlying facets are named, because naming them is the useful part.

Ten facets administered at four ordered levels of closeness, three stems each, giving 120 items on a seven-point scale. Seven points rather than five because Agreeableness facets sit near ceiling toward close others, and truncation at the ceiling manufactures apparent gradients.

5.1  The rings

The middle rings are not padding. “Acquaintances” is deliberately concrete and distant, which bounds a real confound: people think about distant others more abstractly and answer from general impression rather than episodic memory, so part of any raw difference between “inner circle” and “people in general” would be an artefact of abstraction rather than of gating.

5.2  Why not a difference score

The intuitive statistic — inner circle minus strangers — throws away the two middle rings, and with them the only thing that distinguishes a gradual taper from a step. Since which of those it is is the substantive claim, that alone rules it out.

The usual argument against it is reliability: for a difference of two measurements, reliability is (ρ − ρ_xy) / (1 − ρ_xy), which collapses as the two measurements become more correlated. That argument is real but weaker than we previously claimed here. Under this instrument’s own assumptions the difference score reaches .61 against the linear contrast’s .66 — a genuine advantage, and a modest one.

5.3  Why not a hyperbolic discount rate

Social-discounting research fits a hyperbolic curve with a per-person rate k, and it is tempting to reuse. But there the distance is a rank position among a hundred named people — a genuinely ratio-scaled quantity, which is what makes the shape claim meaningful. Our four rings are ordinal categories. Coding them 1,2,3,4 versus 1,5,20,100 moves k by two orders of magnitude, and a parameter whose value is set by an arbitrary coding choice cannot be the headline.

5.4  What we use

An exact orthogonal decomposition of the four points into level, linear, quadratic and cubic components. It is closed-form, always defined, assumes only that the rings are ordered, and — decisively — its precision is computable rather than assumed.

Nothing in the theory predicts a cubic component in a four-point gradient, so that component serves as a per-person noise estimate at no extra item cost.

Reliability for an arbitrary contrast c is 1 − (c′Θc)/(c′Σc), with Θ the diagonal error covariance and Σ the observed covariance of the ring composites. It is closed-form, which is what lets us print these numbers instead of arguing about them.

Because the observed slope is measured at .66 rather than perfectly, roughly a third of it is expected to be noise. The results page therefore draws both: the observed curve solid, and the empirical-Bayes shrunken slope as a dashed straight line through it. The gap between what someone answered and what we would actually bet on is the honest content, and for a period that shrunken value was computed on every request and then never rendered.

5.5  When we refuse to name a shape

A four-point curve always looks like it has a shape. A label is reported only when a parametric bootstrap assigns it at least 0.60 probability, and the measurement had enough power to detect a gradient at all. That second condition matters more than it sounds: an omnibus test returns “flat” whenever it fails to detect a difference, and a badly imprecise measurement fails to detect anything — so without a power check, “you are the same with everyone” would be reported confidently whenever we could see least.

A third condition was added after review. Ten facets each labelled at 60% confidence accepts an expected four wrong labels per respondent, and a page that hands someone four confident wrong statements about themselves has done more damage than one that stays quiet. Candidate labels are therefore sorted by their posterior support and admitted only while the running mean of (1 − support) stays under a target of .20 — a direct Bayesian false-discovery-rate control, which needs no p-values and no independence assumption because it uses the bootstrap’s own posterior.

A fourth condition was added after we measured how badly the first three handled “flat”. Simulating 31,200 respondents whose true shape we knew, the power check turned out to catch only the extreme cases: roughly nine in ten curves labelled flat were gradients the instrument could not resolve, and each of those people was being told the single-number model described them well. The problem is not the threshold. Failing to reject a null is not evidence for it, and no amount of bootstrap agreement converts one into the other — a badly powered test agrees with itself about “flat” every single time.

Claiming sameness needs a test built to establish it. We now require an equivalence test: rather than asking whether the four rings differ, we ask whether every pair can be shown to differ by less than one scale point, and report flatness only when the answer is yes. Because that hypothesis is a union of six pairwise claims, rejecting it requires rejecting all six, which needs no multiplicity correction — each extra comparison makes the claim harder rather than easier to earn.

The honest consequence is that this instrument almost never earns it. At three statements per ring, the measurement error alone is wider than the margin, so even a perfectly level set of four answers falls short. So instead of a verdict we show the bound: we did not detect a gradient, and can only rule out differences larger than X. When that number is large the result is telling you about the questionnaire rather than about you, and you should be able to see that for yourself. Closing the gap would take roughly twice the statements per ring — a change to the instrument, which we would rather state plainly than paper over with a looser threshold.

5.6  Below the facet: whether the statements agree

A facet’s ring curve is the mean of its three statement families, and a mean of things that disagree describes nobody. Someone whose embarrassment toward strangers is extreme while the facet’s other two statements stay level produces a gentle slope that looks unremarkable — the interesting part having been averaged away silently.

Every facet chart therefore draws the envelope of its three statements behind the mean, so agreement and disagreement are the same mark and no threshold has to be chosen. A callout is raised only under two gates, the same shape as the domain-coherence rule one level up: chi-square against “these share one slope”, and unusual scatter for this respondent. One gate is not enough — someone answering inconsistently has ten facets of real, significant, uninteresting disagreement, and a flag that fires on all ten has said nothing. Against random responders the two-gate rule fires on 1.9 facets of ten, down from all ten.

Statements that disagree in direction are treated as a separate finding rather than a larger version of the same one. The mean of a rise and a fall is a level line belonging to neither, so no average can represent them however precisely it is measured.

5.7  What the ordinal view is for

Every metric statement above treats the 1–7 gradient scale as an interval scale, and the per-facet comparison additionally lines it up against the 1–5 conventional scale. Putting both on 0–1 is a rescaling, not an equating: people do not use the ends of a seven-point scale as readily as the ends of a five-point one, so identical underlying trait levels land at systematically different proportions. Proper equipercentile equating needs a norming sample we do not have, so the cross-scale claim is made rarely and hedged where it is made.

Ranks need none of that. Ordering the four rings and summarising the agreement across facets with Kendall’s W assumes only that the respondent used the scale in a consistent direction — no equal intervals, no equating, no reference population. It is therefore the one figure on the results page that survives all of those assumptions failing, and it ships as a view rather than a footnote. Where the ordinal and metric pictures agree, the metric reading has support that does not come from its own assumptions; where they disagree, the assumptions are carrying the argument.

These are constraints on the instrument, not stylistic preferences. Violating any of them degrades the construct without producing a visible symptom.

1. Behavioural target, never comparison standard. The single distinction the instrument depends on.
2. Strict parallelism. Ring variants differ only in the target phrase. Enforced by generating all four from one template, so it holds by construction rather than by care.
3. Original IPIP items are never differenced against these.
4. Seven-point scale, for ceiling headroom.
5. Concrete distant anchors, to bound the abstraction confound.
6. Balanced keying within each facet, so acquiescence stays estimable.

Published in full. An instrument whose items are secret cannot be checked, and these in particular have not yet been reviewed by anyone but their author — if a stem reads to you as a comparison rather than as a behaviour toward someone, that is a defect and we would like to know.

⟨group⟩ is replaced by each of the four ring phrases in turn. Items marked − are reverse keyed.

Percentiles are computed against a named reference group, matched on age band and on the group the respondent chose. The reference sample is not a probability sample — internet volunteers seeking free personality feedback skew young, female and English-speaking.

The reference sample also records only a binary sex variable, which is coarser than many respondents are. We therefore ask sex assigned at birth and current gender identity separately, let the respondent choose which reference group to be compared against, and state the limitation on the results page rather than inventing a norm we do not have.

• Self-report of one’s own contingencies. The field’s position since Mischel is that people report these poorly. Convergence with informant reports or experience sampling has not been demonstrated, and that is the most serious limitation here.
• Abstraction confound. Distant targets are thought about more abstractly. The concrete middle ring bounds this but does not remove it.
• Ceiling effects. Prosocial facets sit near the top of the scale toward close others.
• Asymmetric social desirability. Admitting low concern for strangers is more permissible than admitting it for family, so an apparent gradient could partly be a desirability gradient.
• Confounding with adjustment. Every cross-target variability index in this literature is entangled with neuroticism.
• The items are unreviewed. Written by one person, not yet piloted, not yet checked by anyone else.

Ticknor, R. (2026). Concentric: A closeness-conditional measure of
Big Five trait expression (Version 1.0) [Measurement instrument].

Goldberg, L. R. (1999). A broad-bandwidth, public domain, personality
inventory measuring the lower-level facets of several five-factor models.

Goldberg, L. R., et al. (2006). The International Personality Item Pool
and the future of public-domain personality measures. Journal of
Research in Personality, 40, 84-96.

Johnson, J. A. (2014). Measuring thirty facets of the Five Factor Model
with a 120-item public domain inventory: Development of the IPIP-NEO-120.
Journal of Research in Personality, 51, 78-89.

IPIP items are public domain. Our novel items, scoring keys and data releases are dedicated to the public domain under CC0; this documentation is CC BY 4.0. Attribution is requested as an academic norm rather than enforced as a licence condition on the items — see the data page.