Isomorphism of Biologic Ordinal Scale Measurements and Arithmetic of Parametric Statistical Methods
Ash, George M.
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In the biological sciences, especially medicine, dentistry, and psychology, measurements of experimental variables are often based. on nominal or ordinal scales. Since the properties of these scales or indices are not isomorphic to the numerical system known as arithmetic, the extensive use of parametric techniques of statistical inference with data based on ordinal scales appears to be unwarranted.. In effect an important assumption of the parametric statistical model has been violated,viz.,the variables involved must have been measured in at least an interval scale so that it is possible to use the operation of arithmetic (adding, dividing, finding means,etc) on the data generated by the mensuration. The subject of the present investigation is that of considering to what extent error may occur in using parametric statistical methods rather than theoretically. more appropriate nonparametric tests tor the analysis of biological data obtained by measurements based on ordinal scales. The objective of the present study was to determine to what extent probability statements may be in error as the result of analyzing biological ordinal data by parametric statistical tests.