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In the classic factor-analysis model, the total variance of an item is decomposed into common, specific, and random error components. Since with cross-sectional data it is not possible to estimate the specific variance component, specific and random error variance are summed to the item's uniqueness. This procedure imposes a downward bias to item reliability estimates, however, and results in correlated item uniqueness in longitudinal models. In this article, we describe a method for estimating common, specific, and random error variance with longitudinal data. An empirical example demonstrates the specification and testing of hypotheses regarding the temporal invariance of common, specific, and error components, and the practical utility of our approach. This example makes clear the limitations of combining specific and random error components. The assumption that all unique variance is random error is shown to be untenable.

The distinctions between nominal, ordinal, interval, and ratio measurement were popularized by S. S. Stevens. Unfortunately, positions taken by Stevens have often been disseminated without criticism. One problem is the common assumption that "ordinal" statistics are the best statistics to use for presumed noninterval continuous social variables, when, in fact, they use addition, subtraction, and division, which make the measurements interval by definition. Additionally, the relationship of the normal distribution to interval measurement is commonly misunderstood, the latter existing by definition if a normal distribution exists. Concern with levels of measurements may mislead persons into attending to issues other than maximizing (utility, given) the particular limits of the state of the measurement art in the social sciences.

The experimental model has severe limitations that often are ignored by experimenters. The limitations are likely to account for the low level of external validity of experiments. Placing the model in the context of requirements for measurement emphasizes the limitations and suggests alternatives for improvements in the future.

This article describes how following good measurement construction procedures result in normal variables, for which the use of nonparametric statistics would simply be inappropriate.