Controlling the multiplicity using weighted T-sum statistic.

We introduce a new test procedure for multiple hypothesis testing based on the permutation space of the sum of test-statistics (t-sum). The underlying combining function is shown to be an instance of a family to which it also belongs the well-known combining functions based on the maximum of test-statistics (t-max). After discussing the family-wise error rate and the false discovery rate, two common approaches to the control of the type I error in multiple testing, we consider two further error rates, the stochastic family error and the mean square error model fit estimator. By means of a two large set of simulations we shoe that besides controlling the family-wise error rate the weak sense, the t-sum procedure also controls the stochastic family error and could considerably outperform the t-max procedure in power and mean square error in experiments with low degrees of freedom. They are also shown several circumstances in which it fits the model better than a procedure controlling the false discovery rate and even better of simply performing a series of univariate tests, which do not control any errors. The t-sum procedure is suitable for pilot and exploratory studies in neuroimaging and in other experimental contexts in which the sample size/number of hypotheses ratio is low, the data correlation is moderate, and the proportion of false hypothesis is possibly large. We end the discussion outlining possible investigations of the more general form of combining function (weighted sum) with the aim of data-driven selection of an optimal poewer combining function.