ILLUSTRATIVE EXAMPLE
Psychometric Validation for a
Translated Anxiety Scale
An ordinal factor model, invariance across groups, omega and convergent validity for a translated anxiety scale completed by about 500 adults, reported to COSMIN.
This example does not describe a real client or project. Every engagement is confidential, during the project and after it ends.
RESEARCH QUESTION
What the Study Set Out to Ask
This psychometric validation example follows a clinical psychology research team that has translated a seven-item anxiety scale into a new language and wants evidence that it measures anxiety in the same way as the original. The scale is meant for use in clinics and surveys, so the team needs its structure, reliability and relation to other measures reported in a form that a journal and later users can assess.
The questions are whether the structure published for the original scale holds in the translated version, whether scores are comparable across women and men and across age bands, and whether reliability and the relations with related measures are acceptable. No single analysis makes a scale valid, so the plan frames the study as evidence for named measurement properties, and fixes the planned model and its rivals before any fit is examined.
STUDY DESIGN AND DATA
One Sample of About 500 Adults
A cross-sectional study of about 500 adults recruited from community and outpatient settings, who complete the translated anxiety scale, a depression scale and a worry scale once. Each anxiety item has four ordered response categories, and the translation follows forward and back translation with a review by a panel of bilingual clinicians arranged by the research team. Responses are screened for careless patterns, missingness is described by item, and the planned one-factor structure is written into the plan with the rival models the data must be able to reject, such as a two-factor split of somatic and cognitive items.
- Design: cross-sectional validation of a translated scale
- Outcome: item responses in four ordered categories, with evidence for structure, invariance, reliability and convergent validity
- Software requested: Mplus, with input files and outputs
METHOD AND ASSUMPTIONS
Why an Ordinal Model, and What Must Hold
The items have four ordered categories and often show floor effects in non-clinical samples, so the factor model is estimated with an estimator for ordinal data that works from thresholds and polychoric correlations, not from item scores treated as continuous. Fit is judged from several indices, CFI, TLI, RMSEA with its confidence interval and SRMR, read together with the loadings and residuals, not against one cutoff. If two items with similar wording share a residual correlation, a translation effect is one explanation, so the plan allows a single residual covariance only on grounds of item content, labels it exploratory and reports the model with and without it, instead of freeing parameters from modification indices.
Comparability across groups is examined in a multi-group model whose constraints are added in steps, and for ordinal items the thresholds and loadings are constrained together. Group comparisons of mean anxiety are shown only at the level of invariance the data support, and partial invariance is reported with the freed items named. Reliability is reported as omega with its confidence interval, because coefficient alpha assumes equal loadings. Convergent validity is stated as hypotheses about the direction and rough size of the correlations with the depression and worry scales, written before the data are seen.
OUTPUT AND INTERPRETATION
How the Results Are Read
The output has a table of item loadings with 95% confidence intervals, thresholds in an appendix, fit indices for the planned model and each rival, and the invariance sequence with the change in fit at each step and the decision rule applied. Omega is reported with its interval, and the correlations with the convergent measures are tabulated against the hypotheses set in advance, each shown as supported or not supported.
Sensitivity analyses compare the ordinal estimator with a robust continuous alternative, and the model with and without the item pair that shares a residual correlation. The interpretation describes evidence for a structure and for comparability in this sample, not a conclusion that the scale is valid for every use. Test-retest reliability, responsiveness and performance in other samples need further studies, and the report lists what the data in hand cannot address.
REPORTING
What the Researcher Received
A written report structured to the COSMIN reporting guideline for studies on measurement properties, with statistical wording for the methods, matched to the output, for the team to check and incorporate. The research question, clinical interpretation and conclusions remain with the research team.