Skill type: DISCIPLINE-ENFORCING. Before any hypothesis test consumes a scale, this gate checks that the scale measures what it claims, reliably, and comparably across groups. It does not fit factor models itself — it requires the right evidence and routes execution to the psychometrics skill.
The Core Rule
A RELIABLE MEASURE OF THE WRONG CONSTRUCT IS STILL WRONG. RELIABILITY ≠ VALIDITY.
High internal consistency only means the items move together; it says nothing about whether they capture the intended construct. Evidence for validity (content, criterion, construct) is separate and mandatory. And the usual reliability number — Cronbach alpha — rests on an assumption (tau-equivalence: equal item loadings) that real scales rarely meet, so alpha is a lower bound that can under- or (with correlated errors) over-state reliability.
When to Use This Skill
- "Is my scale / survey instrument valid?"
- "My Cronbach alpha is 0.78 — is the scale good to use?" (← alpha alone is not enough)
- "I built a new 6-item measure of burnout; how do I show it works?"
- "I want to compare a latent trait (e.g. trust) across countries/groups."
Does NOT Trigger
| The request is really about… | Route to | Why not this skill |
|---|---|---|
| Writing / wording the questionnaire items, response scales | alterlab-survey-design |
Instrument construction, upstream of validation. |
| Running the CFA / SEM / IRT / invariance model | alterlab-sem-psychometrics |
This gate requires CFA; that skill fits it. |
| Basic descriptive/inferential stats execution | alterlab-statistical-analysis |
Computation, not measurement discipline. |
| Which statistical test to run on a measured outcome | alterlab-test-selection-guard |
Test choice, not measurement quality. |
| Sampling frame / how many respondents | alterlab-ssci-sampling-gate |
Sampling, not measurement. |
Reliability: report alpha AND omega
Cronbach's alpha assumes tau-equivalence (all items load equally on one factor) and is a lower bound on reliability under that model. McDonald's omega relaxes tau-equivalence by weighting items by their factor loadings and should be reported alongside alpha (McNeish, 2018, Psychological Methods, "Thanks coefficient alpha, we'll take it from here"). In practice the alpha-vs-omega gap for well-constructed unidimensional scales is often small (in one cognitive test battery, omega exceeded alpha by 4.5% on average — Warne, 2025, blog analysis), so the discipline is: report both, plus item-total correlations and a dimensionality check — not to fetishize a single number, but to show the estimate is not resting on an unexamined assumption.
Rules this gate enforces:
- Alpha alone is insufficient. Ask for omega; if only alpha is available, state the tau-equivalence caveat explicitly.
- Reliability presupposes dimensionality. A high alpha on a multidimensional set is
meaningless — check the factor structure (CFA,
alterlab-sem-psychometrics) first. - Item diagnostics. Item-total correlations and (for two halves) Spearman-Brown; drop or revise items that do not cohere — but pre-specify such decisions, do not fish.
Validity: four kinds, none optional
| Validity | Question | Evidence |
|---|---|---|
| Content | Do items cover the construct's domain? | expert review, blueprint against the definition |
| Criterion | Does it predict/correlate with a gold standard? | concurrent & predictive correlations |
| Convergent | Does it correlate with related measures? | AVE, correlations with kindred scales |
| Discriminant | Is it distinct from other constructs? | heterotrait-monotrait ratio, cross-loadings |
Construct validity is established with a confirmatory factor analysis — route the fit to
alterlab-sem-psychometrics (CFI/TLI, RMSEA, SRMR against Hu & Bentler cutoffs).
Measurement invariance before group comparison
Comparing a latent construct across groups (countries, waves, conditions) is only valid if the
measure means the same thing in each group. Require a multi-group CFA invariance sequence —
configural → metric → scalar — before interpreting group differences in means. Without at least
metric/scalar invariance, a "difference" may be a measurement artifact, not a real effect.
Route the test to alterlab-sem-psychometrics.
The Design Passport (hand-off)
Append to each construct in the Passport: reliability (alpha + omega + caveat),
validity_evidence (which of the four kinds are shown), dimensionality (CFA fit), and
invariance (level established) before any group comparison downstream.
Self-Check Before Advancing
- Is each construct explicitly defined and operationalized to its items?
- Is reliability shown with omega (or alpha with the tau-equivalence caveat stated)?
- Is at least one form of validity evidence present — not just reliability?
- Was dimensionality confirmed (CFA) before trusting a single reliability coefficient?
- Is measurement invariance established before comparing the construct across groups?
References
references/reliability_and_validity.md— alpha vs omega math, the four validities, the invariance sequence, and reporting templates. Loaded on demand.
Part of the AlterLab Academic Skills suite.