A New Theoretical Interpretation of Measurement Error and Its Uncertainty

TL;DR

This paper reinterprets measurement error variance as a probability interval rather than dispersion, challenging traditional views and clarifying conceptual and methodological implications.

Contribution

It introduces a new theoretical perspective that redefines measurement error variance as a probability interval, correcting a fundamental misconception.

Findings

Variance is a probability interval of error, not dispersion.

Traditional interpretation of variance as dispersion is incorrect.

New interpretation clarifies measurement error analysis.

Abstract

The traditional measurement theory interprets the variance as the dispersion of a measured value, which is actually contrary to a general mathematical concept that the variance of a constant is 0. This paper will fully demonstrate that the variance in measurement theory is actually the evaluation of probability interval of an error instead of the dispersion of a measured value, point out the key point of mistake in the traditional interpretation, and fully interpret a series of changes in conceptual logic and processing method brought about by this new concept.