According to the guide Vocabulary in Metrology (VIM3) (JCGM, 2008), the definition of the concepts of trueness and accuracy has been revised, which has an important impact on analytical chemistry. Additionally, Eurachem/CITAC has published a new edition of the guide to Quantifying Uncertainty in Analytical Measurement (QUAM) (CITAC and Eurachem, 2012). These two documents, together, form a new basis for the evaluation of data. Results of prominent technologies of inductively coupled plasma mass spectrometry (ICP-MS), for determination of chloride-isotope ratios (Cl-35/Cl-37) and inductively coupled plasma optical emission spectrometry (ICP-OES) for determination of sodium, were evaluated in terms of the true level of uncertainty and revealed a genuine problem for science that was not addressed in VIM3 and QUAM. Comparison of theory and experimentation definitely requires statistical tools, but in contemporary science two approaches to the implementation of statistics in decision making are used: 1. Short-term precision and 2. long-term precision. Both approaches are valid and both are described using the same methods of statistics. However, they lead to completely different conclusions and decisions. Despite good intentions and new concepts, as well as practices and procedures for quality assurance, it is shown by these two examples that these efforts may be inadequate or mislead scientists into making major mistakes in the decision-making process. A set of equations is supplied, which are based on the propagation of uncertainty, and the implication of results and conclusions for other fields of science is discussed.