Proportions, Pitfalls and Pendulums

The use of proportions to transform raw scores into standardized, dimensionless units creates measurement problems. Such transformations alter the relationships among scale points in a way that impedes accurate comparisons among values. The loge of proportional values can be used to alleviate this problem. A second, related problem arises in the use of fractional (percentage) uncertainties for physical or any other measurements. Where possible, such uncertainties are better related to tolerance limits than to the absolute magnitude of the characteristic being measured. Problems of standardization are shown to be present across scientific fields.