The author examined critically three beliefs of S.S. Stevens pertaining to his quadripartite system of scales of measurement: (1) There are four scales of measurement in common usage (2) These scales and the scientific disciplines that use them can be incrementally graded for levels of reliability and validity or accuracy such that: Nominal scale variables produce the lowest levels of reliability and accuracy; with successively improving levels for Ordinal, Equal Interval, and Equal Ratio scales; and (3) The scale upon which a variable is measured determines the type of statistical test that one is permitted to apply. It was shown that each of the three beliefs is fundamentally flawed.