Multivariate small sample tests for two-way designs with applications to industrial statistics

In this paper, we present a novel nonparametric approach for multivariate analysis of two-way crossed factorial design based on NonParametric Combination applied to Synchronized Permutation tests. This nonparametric hypothesis testing procedure not only allows to overcome the shortcomings of MANOVA test like violation of assumptions such as multivariate normality or covariance homogeneity, but, in an extensive simulation study, reveals to be a powerful instrument both in case of small sample size and many response variables. We contextualize its application in the field of industrial experiments and we assume a linear additive model for the data set analysis. Indeed, the linear additive model interpretation well adapts to the industrial production environment because of the way control of production machineries is implemented. The case of small sample size reflects the frequent needs of practitioners in the industrial environment where there are constraints or limited resources for the experimental design. Furthermore, an increase in rejection rate can be observed under alternative hypothesis when the number of response variables increases with fixed number of observed units. This could lead to a strategical benefit considering that in many real problems it could be easier to collect more information on a single experimental unit than adding a new unit to the experimental design. An application to industrial thermoforming processes is useful to illustrate and highlight the benefits of the adoption of the herein presented nonparametric approach

MATS: Inference for potentially Singular and Heteroscedastic MANOVA

In many experiments in the life sciences, several endpoints are recorded per subject. The analysis of such multivariate data is usually based on MANOVA models assuming multivariate normality and covariance homogeneity. These assumptions, however, are often not met in practice. Furthermore, test statistics should be invariant under scale transformations of the data, since the endpoints may be measured on different scales. In the context of high-dimensional data, Srivastava and Kubokawa (2013) proposed such a test statistic for a specific one-way model, which, however, relies on the assumption of a common non-singular covariance matrix. We modify and extend this test statistic to factorial MANOVA designs, incorporating general heteroscedastic models. In particular, our only distributional assumption is the existence of the group-wise covariance matrices, which may even be singular. We base inference on quantiles of resampling distributions, and derive confidence regions and ellipsoids based on these quantiles. In a simulation study, we extensively analyze the behavior of these procedures. Finally, the methods are applied to a data set containing information on the 2016 presidential elections in the USA with unequal and singular empirical covariance matrices

Identification of differentially expressed subnetworks based on multivariate ANOVA

<p>Abstract</p> <p>Background</p> <p>Since high-throughput protein-protein interaction (PPI) data has recently become available for humans, there has been a growing interest in combining PPI data with other genome-wide data. In particular, the identification of phenotype-related PPI subnetworks using gene expression data has been of great concern. Successful integration for the identification of significant subnetworks requires the use of a search algorithm with a proper scoring method. Here we propose a multivariate analysis of variance (MANOVA)-based scoring method with a greedy search for identifying differentially expressed PPI subnetworks.</p> <p>Results</p> <p>Given the MANOVA-based scoring method, we performed a greedy search to identify the subnetworks with the maximum scores in the PPI network. Our approach was successfully applied to human microarray datasets. Each identified subnetwork was annotated with the Gene Ontology (GO) term, resulting in the phenotype-related functional pathway or complex. We also compared these results with those of other scoring methods such as <it>t </it>statistic- and mutual information-based scoring methods. The MANOVA-based method produced subnetworks with a larger number of proteins than the other methods. Furthermore, the subnetworks identified by the MANOVA-based method tended to consist of highly correlated proteins.</p> <p>Conclusion</p> <p>This article proposes a MANOVA-based scoring method to combine PPI data with expression data using a greedy search. This method is recommended for the highly sensitive detection of large subnetworks.</p

Unraveling the influence of domain knowledge during simulation-based inquiry learning

This study investigated whether the mere knowledge of the meaning of variables can facilitate inquiry learning processes and outcomes. Fifty-seven college freshmen were randomly allocated to one of three inquiry tasks. The concrete task had familiar variables from which hypotheses about their underlying relations could be inferred. The intermediate task used familiar variables that did not invoke underlying relations, whereas the abstract task contained unfamiliar variables that did not allow for inference of hypotheses about relations. Results showed that concrete participants performed more successfully and efficiently than intermediate participants, who in turn were equally successful and efficient as abstract participants. From these findings it was concluded that students learning by inquiry benefit little from knowledge of the meaning of variables per se. Some additional understanding of the way these variables are interrelated seems required to enhance inquiry learning processes and outcomes

Changes in Hemodynamic Responses in Chronic Stroke Survivors Do Not Affect fMRI Signal Detection in a Block Experimental Design

The use of canonical functions to model BOLD-fMRI data in people post-stroke may lead to inaccurate descriptions of task-related brain activity. The purpose of this study was to determine whether the spatiotemporal profile of hemodynamic responses (HDRs) obtained from stroke survivors during an event-related experiment could be used to develop individualized HDR functions that would enhance BOLD-fMRI signal detection in block experiments. Our long term goal was to use this information to develop individualized HDR functions for stroke survivors that could be used to analyze brain activity associated with locomotor-like movements. We also aimed to examine the reproducibility of HDRs obtained across two scan sessions in order to determine whether data from a single event-related session could be used to analyze block data obtained in subsequent sessions. Results indicate that the spatiotemporal profile of HDRs measured with BOLD-fMRI in stroke survivors was not the same as that observed in individuals without stroke. We observed small between-group differences in the rates of rise and decline of HDRs that were more apparent in individuals with cortical as compared to subcortical stroke. There were no differences in the peak or time to peak of HDRs in people with and without stroke. Of interest, differences in HDRs were not as substantial as expected from previous reports and were not large enough to necessitate the use of individualized HDR functions to obtain valid measures of movement-related brain activity. We conclude that all strokes do not affect the spatiotemporal characteristics of HDRs in such a way as to produce inaccurate representations of brain activity as measured by BOLD-fMRI. However, care should be taken to identify individuals whose BOLD-fMRI data may not provide an accurate representation of underlying brain activation when canonical models are used. Examination of HDRs need not be done for each scan session, as our data suggest that the characteristics of HDRs in stroke survivors are reproducible across days