is about has_specified_input has_specified_output achieves_planned_objective is denoted by data set population study design dependent variable data transformation false positive rate Hotelling T2 distribution one sample Hotelling T2 test 2 1 Alejandra Gonzalez-Beltran Orlaith Burke Philippe Rocca-Serra The one-sample Hotelling’s T2 is the multivariate extension of the common one-sample or paired Student’s t-test. In a one-sample t-test, the mean response is compared against a specific value. Hotelling’s one-sample T2 is used when the number of response variables is two or more, although it can be used when there is only one response variable. T2 makes the usual assumption that the data are approximately multivariate normal. Randomization tests are provided that do not rely on this assumption. These randomization tests should be used whenever you want exact results that do not rely on several assumptions. adapted from: https://ncss-wpengine.netdna-ssl.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Hotellings_One-Sample_T2.pdf http://arxiv.org/pdf/1007.1094.pdf http://svitsrv25.epfl.ch/R-doc/library/rrcov/html/T2.test.html goodness of fit statistical test goodness of fit testing objective p-value ready for release