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Multivariate Methods
Published in Shayne C. Gad, Carrol S. Weil, Statistics and Experimental Design for Toxicologists, 1988
MANOVA (multivariate analysis of variance) is the multidimensional extension of the ANOVA process we explored before. It can be shown to have grown out of Hotelling’s T2 (Hotelling, 1931), which provides a means of testing the overall null hypothesis that two groups do not differ in their means on any of p measures. MANOVA accomplishes its comparison of two (or more) groups by reducing the set of p measures on each group to a simple number applying the linear combining rule Wi = wjXij (where wj is a weighting factor) and then computing a univariate F-ratio on the combined variables. New sets of weights (wj) are selected in turn until that set which maximizes the F-ratio is found. The final resulting maximum F-ratio (based on the multiple discriminant functions) is then the basis of the significance test. As with ANOVA, MANOVA can be one-way or higher order, and MANOVA has as a basic assumption a multivariate normal distribution.
Development of alternative predictor equations for blast-induced ground vibrations considering stiffness ratio, blast dimension and free face conditions
Published in International Journal of Mining, Reclamation and Environment, 2021
Table 4 shows test of equality of group means. Wilks’ lambda is a test statistic used in multivariate analysis of variance (MANOVA) [26]. Wilks’ lambda test is the measure of variable’s potential. It helps to understand dominant variables which are responsible to creation of the two homogenous groups. Smaller values indicate that the variable is better at discriminating between groups [21]. For model D, Pf has the lowest Wilks’ Lambda value (Table 4). S/B ratio is the second lowest one. Clearly, B/D ratio and Pf have the lowest Wilks’ Lambda values for Model E. B/D and Pf play a dominant role in grouping process. The smallest Wilks’ Lambda value was obtained for H/B ratio for Model J. H/B is the most influential parameter by far. The lowest Wilks’ Lambda values are highlighted by green and yellow colour in Table 4.
Improving drainage water quality: Constructed wetlands-performance assessment using multivariate and cost analysis
Published in Water Science, 2018
Multivariate analysis of variance (MANOVA), an extension of the analysis of variance (ANOVA), aims at determining the effect of several independent variables on multiple dependent variables. MANOVA investigates the significant differences between means by dividing the total variance into: component due to true random error (i.e., within- groups) and components due to differences between means. There are three fundamental assumptions for using MANOVA: the dependent variable should be normally distributed within groups; the variances in the different groups are homogenous and the inter-correlations (covariances) for the multiple dependent variables are homogeneous (Field, 2009).
The dynamics of changes in PPP projects – a meta-case analysis approach
Published in Construction Management and Economics, 2022
Nannan Wang, Hongmei Wang, Kui Zhang
Furthermore, the multivariate analysis of variance (MANOVA) is used to assess the statistical significance of the effect of one or more independent variables on a set of two or more dependent variables (Weinfurt 1995). In this study, the MANOVA was used to analyse the relationship between the causes and results of negative change events, by using software SPSS (Version 22.0).