Because of the ways studies are designed and the ways data are analyzed, research results in psychology and the social sciences often appear to be nonlinear, sample- and instrument-dependent, and incommensurable, even when they need not be. In contrast with what are common assumptions about the nature of the constructs involved, invariant relations may be more obscured than clarified by typically employed research designs and statistical methods.

To take a particularly salient example, the number of small factors with Eigenvalues greater than 1.0 identified via factor analysis increases as the number of modes in a multi-modal distribution also increases, and the interpretation of results is further complicated by the fact that the number of factors identified decreases as sample size increases (Smith, 1996).

Similarly, variation in employment test validity across settings was established as a basic assumption by the 1970s, after 50 years of studies observing the situational specificity of results. But then Schmidt and Hunter (1977) identified sampling error, measurement error, and range restriction as major sources of what was only the appearance of incommensurable variation in employment test validity. In other words, for most of the 20^{th} century, the identification of constructs and comparisons of results across studies were pointlessly confused by mixed populations, uncontrolled variation in reliability, and unnoted floor and/or ceiling effects. Though they do nothing to establish information systems deploying common languages structured by standard units of measurement (Feinstein, 1995), meta-analysis techniques are a step forward in equating effect sizes (Hunter & Schmidt, 2004).

Wright and Stone’s (1979) *Best Test Design*, in contrast, takes up each of these problems in an explicit way. Sampling error is addressed in that both the sample’s and the items’ representations of the same populations of persons and expressions of a construct are evaluated. The evaluation of reliability is foregrounded and clarified by taking advantage of the availability of individualized measurement uncertainty (error) estimates (following Andrich, 1982, presented at AERA in 1977). And range restriction becomes manageable in terms of equating and linking instruments measuring in different ranges of the same construct. As was demonstrated by Duncan (1985; Allerup, Bech, Loldrup, et al., 1994; Andrich & Styles, 1998), for instance, the restricted ranges of various studies assessing relationships between measures of attitudes and behaviors led to the mistaken conclusion that these were separate constructs. When the entire range of variation was explicitly modeled and studied, a consistent relationship was found.

Statistical and correlational methods have long histories of preventing the discovery, assessment, and practical application of invariant relations because they fail to test for invariant units of measurement, do not define standard metrics, never calibrate all instruments measuring the same thing in common units, and have no concept of formal measurement systems of interconnected instruments. Wider appreciation of the distinction between statistics and measurement (Duncan & Stenbeck, 1988; Fisher, 2010; Wilson, 2013a), and of the potential for metrological traceability we have within our reach (Fisher, 2009, 2012; Fisher & Stenner, 2013; Mari & Wilson, 2013; Pendrill, 2014; Pendrill & Fisher, 2015; Wilson, 2013b; Wilson, Mari, Maul, & Torres Irribarra, 2015), are demonstrably fundamental to the advancement of a wide range of fields.

References

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Duncan, O. D., & Stenbeck, M. (1988). Panels and cohorts: Design and model in the study of voting turnout. In C. C. Clogg (Ed.), Sociological Methodology 1988 (pp. 1-35). Washington, DC: American Sociological Association.

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