An empirical basis for the statement that measurement scale properties (and meaning) are irrelevant in statistical analyses

Abstract

A study was conducted to evaluate the notion that the relationship between a number and its referent determines the type of statistical analysis required (the measurement-statistics issue). A number of transformations of original data were performed in which the meaningfulness of this relationship was modified. No change in statistical analyses resulted, even when meaningfulness was at zero, or near zero, levels with random transformations.The controversy as to the independence, or the nonindependence, of measurement scale properties in a statistical analysis began with Stevens's (1946) thesis that the specific measurement scale involved with data (nominal, ordinal, interval, ratio) determines the specific operations of a statistical analysis. Recently, this thesis has been championed by Townsend and Ashby (1984) and rejected by Gaito (1980Gaito ( , 1986.Gaito's (1986) argument is that, for measurement purposes, numbers are important because they relate to some underlying referent. However, in a statistical analysis, these referents do not enter the picture; it is only the numbers (which have no uniqueness except as numbers) that are involved in the statistical operations in a manner prescribed by the mathematical properties of the method. These statistical operations allow an effective ordering of the sets of numbers so that empirical statements (and associated meaning) can be added in interpretation of the results.The purpose of this note is to provide an empirical basis for the statement that the meaning involved in the relationship between symbols (e.g., numbers) and their referents (although empirically important in measurement analyses) is irrelevant in a statistical analysis, because "The numbers do not know where they came from. " That is, the numbers behave in the same fashion in a statistical analysis, no matter what their origin or scale properties (as Lord showed in a humorous article in 1953; also see Burke, 1953). The only aspect in the statistical analysis that is important is the relationship between the numbers (Le., 1, 2, 3, 4, etc. are different from each other). METHODThe experimental data was taken from an experiment by Toukmanian and Rennie (1975). Before and after a training session. two advancedWe thank Shake Toukmanian and Dave Rennie for providing us with the empathy data. The authors' mailing address is: Department of Psychology, York University, 4700 Keele St., Downsview M3J IP3, Ontario, Canada. doctoral students in clinical psychology rated the empathy of a number of counseling trainees (on a scale from I to 5). For the purpose of this study, only the pre-and posttraining ratings by one doctoral student were used (Session I and Session 2). The statistical analysis was a 2 X 12 (sessions x subjects) design, using the original data and a number of transformations: reversing the scale, adding and subtracting a constant of2, multiplying and dividing by a constant of2, and randomizing the set of numbers separately within the pre-and posttraining sessions. Two separate randomizations were...

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