A sufficient criterion for reliability analysis on statistical results of vector datasets

In traditional vector data statistics, the reliability of the vector mean can not be quantified. This is because at least three independent variables are involved in each vector. In this paper, a quantified method is proposed to analyse the reliability of the statistical result of a set of vectors. This method is based on the combination of the conventional vector statistics and the error analysis theory. The paper firstly outlines the processes of the vector statistics and the theory of reliability analysis on the statistical result of a set of vectors using this new method. This new method is then applied to the vector statistics and reliability analysis of the statistical results of three vector datasets of remanent magnetisation carried in rocks. The case studies show that this reliability analysis is coincident with the natural judgment, and can be used as a sufficient criterion to judge if the statistical mean of a set of vectors is reliable.