Measuring Growth with Vertical Scales

A vertical score scale is needed to measure growth across multiple tests in terms of absolute changes in magnitude. Since the warrant for subsequent growth interpretations depends upon the assumption that the scale has interval properties, the validation of a vertical scale would seem to require methods for distinguishing interval from ordinal. In taking up this issue, two different perspectives on educational measurement are contrasted, a metaphorical perspective and a classical perspective. Although the metaphorical perspective is more predominant, at present it provides no objective methods whereby the properties of a vertical scale can be validated. In contast, when taking a classical perspective, the axioms of additive conjoint measurement can be used to test the hypothesis that the latent variable underlying a vertical scale is quantitative (supporting ratio or interval properties) rather than merely qualitative (supporting ordinal or nominal properties). The application of such an approach is illustrated with both a hypothetical example and by drawing upon recent research that has been conducted on the Lexile scale for reading comprehension. Pre-print, forthcoming in Journal of Educational Measurement Acknowledgements: This work is the culmination of research initially supported by a National Academy of Education Postdoctoral Fellowship funded by the Spencer Foundation, and then continued under the auspices of a grant funded by the Carnegie Corporation. I would like to thank the reviewers of this manuscript for the constructive comments that led to improvements in the underlying argument.