Several new and improved modalities, scanners, and protocols, together referred to as image-acquisition methods (IAMs), are being developed to provide reliable quantitative imaging. Objective evaluation of these IAMs on the clinically relevant quantitative tasks is highly desirable. Such evaluation is most reliable and clinically decisive when performed with patient data, but that requires the availability of a gold standard, which is often rare. While no-goldstandard (NGS) techniques have been developed to clinically evaluate quantitative imaging methods, these techniques require that each of the patients be scanned using all the IAMs, which is expensive, time consuming, and could lead to increased radiation dose. A more clinically practical scenario is where different set of patients are scanned using different IAMs. We have developed an NGS technique that uses patient data where different patient sets are imaged using different IAMs to compare the different IAMs. The technique posits a linear relationship, characterized by a slope, bias, and noise standard-deviation term, between the true and measured quantitative values. Under the assumption that the true quantitative values have been sampled from a unimodal distribution, a maximum-likelihood procedure was developed that estimates these linear relationship parameters for the different IAMs. Figures of merit can be estimated using these linear relationship parameters to evaluate the IAMs on the basis of accuracy, precision, and overall reliability. The proposed technique has several potential applications such as in protocol optimization, quantifying difference in system performance, and system harmonization using patient data.