Since a measurement is no better than its uncertainty, specifying the uncertainty is a very important part of metrology. One is inclined to believe that the fundamental constants in physics are invariant with time and that they are the foundation upon which to build internationl system (SI) standards and metrology. Therefore clearly specifying uncertainties for these physical invariants at state-of-the-art levels should be one of the principal goals of metrology. However, by the very act of observing some physical quantity we may perturb the standard, thus introducing uncertainties. The random deviations in a series of observations may be caused by the measurement system, by environmental coupling or by intrinsic deviations in the standard. For these reasons and because correlated random noise is as commonly occurring in nature as uncorrelated random noise, the universal use of the classical variance, and the standard deviation of the mean may cloud rather than clarify questions regarding uncertainties; i.e., these measures are well behaved only for random uncorrelated deviations (white noise), and white noise is typically a subset of the spectrum of observed deviations. The assumption that each measurement in a series is independent because the measurements are taken at different times should be called into question if, in fact, the series is not random and uncorrelated, i.e., does not have a white spectrum. In this paper, studies of frequency standards, standard-volt cells, and gauge blocks provide examples of long-term random-correlated time series which indicate behavior that is not “white” (not random and uncorrelated). This paper outlines and illustrates a straightforward time-domain statistical approach, which for power-law spectra yields an alternative estimation method for most of the important random power-law processes encountered. Knowing the spectrum provides for clearer uncertainty assessment in the presence of correlated random deviations, the statistical approach outlined also provides a simple test for a white spectrum, thus allowing a metrologist to know whether use of the classical variance is suitable or whether to incorporate better uncertainty assessment procedures, e.g., as outlined in the paper.