Many advanced metabolomics experiments currently lead to data where a large number of response variables were measured while one or several factors were changed. Often the number of response ...variables vastly exceeds the sample size and well-established techniques such as multivariate analysis of variance (MANOVA) cannot be used to analyze the data.
ANOVA simultaneous component analysis (ASCA) is an alternative to MANOVA for analysis of metabolomics data from an experimental design. In this paper, we show that ASCA assumes that none of the metabolites are correlated and that they all have the same variance. Because of these assumptions, ASCA may relate the wrong variables to a factor. This reduces the power of the method and hampers interpretation.
We propose an improved model that is essentially a weighted average of the ASCA and MANOVA models. The optimal weight is determined in a data-driven fashion. Compared to ASCA, this method assumes that variables can correlate, leading to a more realistic view of the data. Compared to MANOVA, the model is also applicable when the number of samples is (much) smaller than the number of variables. These advantages are demonstrated by means of simulated and real data examples. The source code of the method is available from the first author upon request, and at the following github repository: https://github.com/JasperE/regularized-MANOVA.
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•MANOVA and ASCA have serious drawbacks for analysis of experimental designs.•We propose regularized MANOVA (rMANOVA) for analysis of such data.•rMANOVA is a weighted average of the ASCA and MANOVA models.•Thus the best properties of both models are combined and their pitfalls avoided.•rMANOVA is used to analyze data of a metabolomics nutritional intervention study.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Let A and B be independent, central Wishart matrices in p variables with common covariance and having m and n degrees of freedom, respectively. The distribution of the largest eigenvalue of (A + B)⁻¹ ...B has numerous applications in multivariate statistics, but is difficult to calculate exactly. Suppose that m and n grow in proportion to p. We show that after centering and scaling, the distribution is approximated to second-order, $O(p^{-2/3})$, by the Tracy-Widom law. The results are obtained for both complex and then real-valued data by using methods of random matrix theory to study the largest eigenvalue of the Jacobi unitary and orthogonal ensembles. Asymptotic approximations of Jacobi polynomials near the largest zero play a central role.
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•Fcirc statistic shows how to compare means of multiple groups of Fourier estimates.•Fcirc statistic derives from Welch’s test but for multiple comparisons.•Unlike MANOVA, Fcirc statistic does not ...need equal variances across multiple means.•Fcirc statistic is used for multiple intra/inter-group comparisons of brain response.•Fcirc is primarily for Fourier samples extracted from steady-state evoked potentials.
Steady-state evoked potentials (ssEP) provide objective tools for studying brain function in different experimental conditions. Frequency components of brain response to repetitive stimuli have been analyzed using Tcirc2 statistic; however, Tcirc2 statistic is limited to comparisons between two means. Here, we present a generalized version of Tcirc2 statistic which enables us to compare multiple means of Fourier estimates corresponding to multiple conditions within participant(s) or multiple groups of participants.
Frequency components of brain response are extracted from ssEP data using Fourier transform. Discrete Fourier measurements at frequency of interest are represented on the complex plane for statistical analyses. We present a new statistic called Fcirc statistic to compare three or more clusters of Fourier estimates whether they have equal or unequal variances or/and numbers of samples. Fcirc statistic derives from Welch’s test but for multiple comparisons.
We demonstrate the validity of Fcirc statistic using simulated and empirical clusters of Fourier estimates with equal and unequal variances and numbers of samples. Type-I error remains 0.05 for all the conditions. Furthermore, we illustrate that the probability of achieving a significant difference among multiple means when the true means are unequal depends on the total length of ssEP data but is independent of the duration chosen for performing Fourier transform on a fixed length of ssEP data.
Fcirc statistic is useful for multiple intra- and inter-participant and group comparisons of brain response at any frequency component extracted from ssEP data whether the group means have equal or unequal variances.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Present parametric study shows that the flowrate, number of channels, hydrodynamic resistances and phase ratio significantly affect the maldistribution in parallel microfluidic reactors (i.e., ...numbering-up). Especially the effect of flow rate and phase ratio has not been reported before. However, these findings are of a qualitative nature due to a high degree of variability between experiments. Additional experiments show that the stable point of operation easily shifts in the considered set-ups, explaining this variability. Therefore, a Multivariate Analysis of Variance (MANOVA) in SPSS is introduced to partially compensate for this variance and, also, manage the large data set that results from a parametric study. It is shown that introducing advanced statistical methods can provide additional insights and can further push the field of numbering-up.
•Geometry, flowrate and phase ratio were varied in manifolds and bifurcations.•The effect on the maldistribution of two-phase flow was investigated.•MANOVA was performed with SPSS to analyze the large data set.•Most novel is the effect of flowrate and phase ratio, as well as the use of MANOVA.•The stable point of operation randomly shifts with time.
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GEOZS, IJS, IMTLJ, IZUM, KILJ, KISLJ, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Islamic boarding schools are institutions where students live who are not accompanied by their parents in their daily lives. The aim of this research is to determine the influence of parental ...education on the learning abilities of students living in Islamic boarding schools. This research uses a quantitative approach with the research subjects being Islamic boarding school-based junior high school students in Garut, Tasikmalaya Regency and City, West Java, Indonesia. The sample used was 161 students consisting of 63 students from class 1, 57 people from class 2 and 41 people from class 3 MTs (Junior High schools). Data analysis used the Multivariate Analysis of Variance (Manova). The results of the analysis show that there is a significant effect between parents' educational background on the ability to learn Mathematics, Indonesian and Arabic. Meanwhile, for English and science subjects, parents' educational background does not have a significant effect. Even though there is no effect, in general the educational background of bachelor’s parents has a better comparison across all subjects. Differences appear in the subjects of English, Science, Mathematics and Indonesian, where the junior high school education background is much better than the high school education. Meanwhile, for Arabic subjects, the results of the analysis show that the educational background of elementary school parents is better than high school.
Ensuring operational safety in an automated working environment is a crucial requirement. In this article, we propose a technique for automated fault diagnosis in unmanned aerial vehicle-based sensor ...networks (UAV-sensor networks) aimed explicitly at the composite nature of different faults. Our technique consists of 3-stages: (1) UAVs collecting data from sensors and running a modified Z-score statistics to diagnose faulty readings; (2) the UAV cluster head running a multivariate analysis of variance (MANOVA) to identify data faults in cluster members; and (3) utilizing a probabilistic neural network with correlation centroids at the ground control station for further diagnosis of collected UAV data. This approach is intended for progressive improvement in fault diagnosis at different stages of data collection in a UAV-sensor network for critical applications. We conduct an extensive evaluation of our 3-stage approach on the data collected in real-time from the sensors in a physically created UAV-sensor network. The performance of the proposed modified Z-score test improves fault detection accuracy of ∼20.8%, false alarm rate of ∼54.3%, and false positive rate of ∼67.2% with the traditional and existing sensor fault detection approach. The performance of MANOVA to identify the permanent UAV data fault shows fault detection accuracy of ∼10.9%, false alarm rate of ∼44.3%, and false positive rate of ∼48.7% superior to the intermittent and transient faults. Our preliminary results suggest that the proposed approach can handle multiple composite faults and outperforms existing research results.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Designing cold mix and cold-laid asphalt mixtures based on performance criteria holds significant promise for enhancing road surface quality. This study specifically targets the optimization of ...basalt fiber cement composite modified cold mix asphalt mixtures to elevate their performance characteristics. Employing the Box Behnken method within a response surface methodology framework, we orchestrated a meticulously designed three-factor, three-level experiment. Emulsified asphalt, basalt fiber, and cement content were delineated as key influencing factors, while performance metrics encompassing high-temperature performance (including irreparable creep flexibility and strain recovery rate), bonding performance (flying loss), and low-temperature performance (splitting tensile strength) were designated as response variables to scrutinize the effects of these factors on cold mix asphalt mixture performance. Utilizing the experimental response values, we constructed a response surface model and employed multiple regression equations to accurately capture the functional relationships. Subsequently, a multivariate analysis of variance was conducted to ascertain the selection conditions for each response variable, leading to the optimization of the dosage of various influencing factors. Finally, the predicted values were validated against measured data. Our findings underscore the effectiveness of the quadratic equation model in accurately capturing the interplay between the influencing factors and the high-temperature, bonding, and low-temperature performance of cold mix asphalt mixtures. Furthermore, the fitting models for each response variable exhibit a high degree of significance and goodness of fit across different grading conditions, underscoring the robustness of our approach.
•Study optimizes basalt fiber cement composite modified cold mix asphalt for improved road surface quality.•Box Behnken method and response surface methodology employed in a three-factor, three-level experiment.•High-temperature performance, bonding performance, and low-temperature performance evaluated as response values.•Quadratic equation model effectively fits performance aspects, demonstrating significance and goodness of fit.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Background: Headaches are a major focus of public health efforts. Because stress and emotional disturbances play a role in various forms of headaches, emotion regulation can be thought of as a factor ...in adaptation and successful control of this illness. The effectiveness of cognitive emotion management strategies in women and men with migraine headaches, tension headaches, and healthy people was investigated in this study. Method: In the first six months of 2020, 60 patients with migraine tension headaches were studied in the neurology clinic of the Abdi Waluyo Hospital in Jakarta. Positive techniques (vision formation, positive refocus, positive appraisal, and planning) and negative strategies (self-blame, blaming others, rumination, and catastrophic perception and acceptance) were obtained in emotion regulation using the Emotion Regulation Questionnaire. Results: According to the findings, persons with migraines employ fewer positive techniques in the cognitive management of their emotions than people without migraines. Meanwhile, the findings revealed that there is a substantial difference in the usage of positive methods by females and males in both groups, with females employing more positive tactics. Conclusion: In conclusion, the findings of this study suggest that self-regulation is one component that can cause headaches in patients.
Abstract The use of repeated measures analysis of variance (ANOVA) options for the analysis of in vitro ruminal fermentation gas production profiles is illustrated. Because of the different variances ...and covariance structures among profile observations, ordinary ANOVA for more than two-time points is not recommended. To mitigate this problem, the Greenhouse–Geisser epsilon correction can be applied to reduce the degrees of freedom, inflated by violation of the sphericity assumption, for F ratio probability calculations. After this correction, the Box–Greenhouse–Geisser ANOVA (modified ANOVA) layout appears similar to the layout of a split-plot design ANOVA with whole plots divided into subplots (incubation time). Any F tests in the main plot part are valid but F tests involving the time factor from the subplot part need modification because time factor, by its very nature, cannot be allocated at random. Application of multivariate ANOVA, distance multivariate ANOVA, ante-dependence and mixed model analysis are also considered. All these options lend themselves to wide application in the applied biological sciences.
Multivariate analysis-of-variance (MANOVA) is a well established tool to examine multivariate endpoints. While classical approaches depend on restrictive assumptions like normality and homogeneity, ...there is a recent trend to more general and flexible procedures. In this paper, we proceed on this path, but do not follow the typical mean-focused perspective. Instead we consider general quantiles, in particular the median, for a more robust multivariate analysis. The resulting methodology is applicable for all kind of factorial designs and shown to be asymptotically valid. Our theoretical results are complemented by an extensive simulation study for small and moderate sample sizes. An illustrative data analysis is also presented.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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