The estimation of average molecular dimensions. 2. Hypothesis testing with weighted and unweighted means
Robin Taylor, Olga Kennard · Acta Crystallographica Section A Foundations of Crystallography · 1985
The average value (μ) of a molecular dimension may be estimated by a weighted (\bar xw) or unweighted (\bar xu) mean. Computer simulations show that \bar xu can be used in hypothesis tests, since the distribution of (\bar xu - μ)/σ(\bar xu) is closely approximated by Student's t distribution. In contrast, hypothesis tests based on the weighted mean are inexact and potentially misleading.