The analysis of measurement uncertainty is fundamentally based on several laws and principles, including the law of error, the law of propagation of uncertainty, the principle of propagation of distributions, the Central Limit Theorem, and the -1/2 power law. Statistical inference approaches are tools for estimating the parameter(s) in these laws or principles. We argue that these laws and ... [Show full abstract] principles must be followed regardless of whether statistical inference approaches are used in uncertainty analysis. We propose a rule of conformity to these laws and principles as a uniform standard for judging the validity of statistical inference approaches. We provide an in-depth review of three competing statistical inference approaches: confidence interval-based, objective Bayesian, and probability interval-based. We focus on an important problem in practice: computing the combined standard uncertainty and expanded uncertainty of indirect measurements, where the measurand is related to multiple influence (input) quantities through a measurement model. These three statistical inference approaches are virtually incommensurable because they are established based on different philosophies and methodologies, and there is no common rule for uncertainty evaluation. We examine and evaluate these three approaches according to the proposed rule of conformity. Any limitations or counterinstances of a statistical inference approach are actually due to the fact that the approach does not conform to all (or some of) the laws or principles related to uncertainty analysis. An example is presented to demonstrate that, if there is only Type B information about influence quantities, the uncertainty analysis can be solely based on the law of propagation of uncertainty; it does not require any statistical inference approach.