Reading focus
Syllabus: How Do We Describe and Measure Individual Differences?
Connect levels of measurement invariance with the comparisons they are intended to support. Distinguish comparing relationships from comparing averages.
Why you’re reading it. Understand why common questions, similar factor labels, or standardized scores alone cannot establish equivalence.
A question to consider. Two language groups give different answers to an item about speaking up in class. What would you investigate about the item's meaning and its relationship to the other items before interpreting the difference as a difference in the intended trait?
Why this reading
Using the same questions does not ensure comparable score meanings. This review explains why comparisons across groups or occasions require evidence about the relationship between a construct and its indicators.
Before you read
A factor loading connects an indicator to a modeled factor. An intercept represents its expected level when the factor is zero. Invariance asks whether specified measurement parameters can be treated as equal across groups or occasions.
Read for
- Distinguish configural, metric, scalar, and residual invariance by what each constrains.
- Connect each comparison of interest with the assumptions it needs.
- Notice disagreement about fit criteria and partial invariance rather than treating thresholds as universal guarantees.
Consider afterwards
- A programme changes how participants interpret one questionnaire item. How could that complicate a claim that its average score improvement represents psychological change?
Editorial context
This is a review of conventions and reporting at its publication date, centered on confirmatory factor analysis. It is not a timeless set of statistical cutoffs. Noninvariance calls for investigating which comparisons remain defensible; invariance within a model does not, by itself, establish fairness or complete construct validity.