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PURPOSE: In vivo MRS is often characterized by a spectral signal-to-noise ratio (SNR) that varies highly between experiments. A common design for spectroscopic studies is to compare the ratio of two spectral peak amplitudes between groups, e.g. individual PCr/γ-ATP ratios in 31 P-MRS. The uncertainty on this ratio is often neglected. We wished to explore this assumption. THEORY: The canonical theory for the propagation of uncertainty on the ratio of two spectral peaks and its incorporation in the Frequentist hypothesis testing framework by weighted averaging is presented. METHODS: Two retrospective re-analyses of studies comparing spectral peak ratios and one prospective simulation were performed using both the weighted and unweighted methods. RESULTS: It was found that propagating uncertainty correctly improved statistical power in all cases considered, which could be used to reduce the number of subjects required to perform an MR study. CONCLUSION: The variability of in vivo spectroscopy data is often accounted for by requiring it to meet an SNR threshold. A theoretically sound propagation of the variable uncertainty caused by quantifying spectra of differing SNR is therefore likely to improve the power of in vivo spectroscopy studies. Magn Reson Med 78:2082-2094, 2017. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Original publication




Journal article


Magn Reson Med

Publication Date





2082 - 2094


13C spectroscopy, 31P spectroscopy, biostatistics, hyperpolarized 13C, magnetic resonance spectroscopy, phosphorus MRS, uncertainty analysis