An explication is offered for the notion of dimensionality both for tests and items. A set ofntests or ofnbinary items is unidimensional if and only if the tests or the items fit a common factor model, generally non‐linear, with one common factor, that is, one latent trait. Both test scores and item responses in general contain stable specific factors as well as errors of retest measurement. The two‐parameter normal ogive model can be obtained from a joint space which in general is ofn+ 1 dimensions. One of these is the latent trait continuum while the remainingnare dimensions of unique (specific and error) variation. If and only if the items fit the perfect scale then+ 1 dimensions collapse into one dimension. Proposals to regard coefficient alpha as a coefficient measuring homogeneity, internal consistency, or generalizability, do not appear to be well foun