Abstract: The classical measurement error theory postulates that the measured (observed) value is a random variable while the true value is a constant. In contrast, a new-concept measurement theory postulates that the measured value is a constant while the true value is a random variable. After reviewing concepts in the probability theory, this paper makes a comparative analysis of the above-mentioned theories in respect of the different interpretations of the constant and the random variable. It is pointed out that the traditional measurement theory misinterprets basic mathematical concepts, leading to conceptual or logical trouble. The basic concepts and logic and principles of error evaluation are explained in the new measurement theory.