From Ordered Categories to Defensible Conclusions: A Decision Framework for Likert-Scale Data

Likert-type responses are often summarized, modeled, and converted into verbal conclusions as though these were one statistical operation. This article separates the response category, response distribution, composite score, and inferential estimand from the subsequent verbal label. Established ordinal-measurement and decision-theoretic results provide the foundation; the methodological contribution is an integrated audit of scoring, verbal-band choice, and interval stability. On a five-point scale, nearest-anchor and equal-range rules disagree on 20% of the numerical range, a geometric quantity rather than an empirical reclassification rate. A factorial Monte Carlo study crosses three latent distributions, two threshold structures, three category counts, five sample sizes, and 13 locations, with additional floor, ceiling, midpoint, uniform, polarized, and upper-tilted response patterns. Across 6.30 million replicated samples, disagreement may increase, decrease, or disappear with sample size, depending on the population mean and boundaries. A secondary analysis of a public five-point personality dataset finds different labels for 3 of 50 item means (6%); worked item, composite, and group examples demonstrate how retaining distributions and checking assumptions changes reporting. Ordinal recoding reverses a small empirical coded-mean contrast, while a proportional-odds diagnostic rejects a common-odds summary. These demonstrations support a six-step reporting framework, but do not constitute external validation of its effectiveness. Means remain usable for explicitly defined scores; ordinal models and distribution-based summaries address different estimands.