n.1. the premise or supposition that something is factual or true; that is, the act of taking something for granted. 2. one or more conditions that need to be met in order for a statistical procedure to be fully justified from a theoretical perspective. For example, the analysis of variance assumes homogeneity of variance and independence of observations, among other criteria. If the assumptions were to be violated to an extreme extent, the results would be invalid. See also robustness.