Everything that quacks ain't a duck. What can we learn from phonetic distributions?

Phonetic studies sometimes infer how many categories a linguistic system contains using surface distributional diagnostics. This inference is examined by distinguishing four levels: distribution shape, labeled-group separation, statistical components, and linguistic categories. In an equal-proportion, equal-variance Gaussian mixture, two speech categories produce a unimodal pooled distribution when the distance between their means is less than two standard deviations. In many realistic contexts, unimodality of a pooled distribution alone does not establish the presence of a single linguistic category. Conversely, bimodality of a pooled distribution alone does not establish two linguistic categories. The standard mixture-variance decomposition also shows that a two-category mixture need not have greater variance than its more variable component. Simulations show mode-based diagnostics can correctly describe surface modality yet poorly recover the categories that generated the data. Empirical cases further illustrate that distribution shape, labeled-group separation, and component structure capture distinct properties of the data and need not converge on the same category analysis. These diagnostics should thus be interpreted at their own levels. Agreement among them can strengthen a description of surface structure, but they cannot determine categoryhood on their own. Category-level claims require converging linguistic evidence suited to the category under study.