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Fig. 4 | Applied Informatics

Fig. 4

From: A new multivariate test formulation: theory, implementation, and applications to genome-scale sequencing and expression

Fig. 4

Tests with different dimensions of rejection in two taxonomies. a Two cascaded taxonomies of all the possible combinations of three dimensions. The bottom three levels belong to the taxonomy of those combinations resulted from the operator OR, while the top three levels belong to the taxonomy of those combinations resulted from the operatorĀ &, i.e. AND. The bottom is the one considered by the existing method, featured by a rejection of the weakest collegiality. The collegiality gradually enhances from one level up to the next level, reaching the top featured by a rejection of the strongest collegiality. b Folding Figure (a) along the central horizontal line into two layers, one rejection with a strong collegiality featured by & on the 1st layer is paired with its counterpart rejection with a weak collegiality featured by OR on the 2nd layer. c The outcome of all the tests organised in this taxonomy. Listed on the right side of each combination are the resulted \(\underline{p}_j^{\omega }\) and \(\overline{p}_j^{\omega }\). As to be further explained in Fig. 6a, each of \(\underline{p}_j^{\omega }\) and \(\overline{p}_j^{\omega }\) is evidenced by two estimating values that are obtained with and without considering some higher order dependence among different dimensions. Listed in the left-most column are \(\underline{p}_j, \overline{p}_j\), i.e. the minimum values of each level given by Eq. (12)

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