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Multivariate statistics on pavement condition indicators
Published in Maurizio Crispino, Pavement and Asset Management, 2019
In order to quantify the different degrees of influence of the chosen predictors, analyses of variance (ANOVA) can be used. ANOVA consists of several statistical models to test significant differences between means. It is a very popular statistical method in social sciences and humanities to determine differences between two or more classified groups. The ANOVA is a statistic tool to investigate whether values of a target variable in different subgroups of the sample vary significantly. The grouping is based on the forms of one or more categorical independent variables which are also known as factors. Depending on the number of dependent variables considered, it is distinguished between one way (ANOVA) and multivariate analysis of variance (MANOVA). Therefore, the variance of the chosen parameter can be divided and referred to several classified groups within one predictor. Additionally to main effects of each factor, interactions between the inspected predictors can be statistically tested. The main idea of ANOVA is to split the total variance of the dependent variable into the variance within groups and the variance between groups. If the differences between the groups are relatively big and the variances within the factor groups are quite small, it can reasonably be concluded that the factor has an influence on the dependent variable. The square sum between the groups is called SS(B) and the square sum within one group is known as SS(W). The sum of both gives the total square sum SS(TOT): SST(TOT)=SS(B)+SS(W)
Applied Statistics
Published in Vinayak Bairagi, Mousami V. Munot, Research Methodology, 2019
Varsha K. Harpale, Vinayak K. Bairagi
MANOVA is an extended concept of Univariate Analysis of Variance (ANOVA). In ANOVA the relation of one dependent variable is observed with respect to the group independent variables whereas in MANOVA multiple dependent variable metrics is analyzed on the basis of multiple independent variables. To address multiple dependent variables, MANOVA groups them together into a weighted linear combination or composite variable. These composite variables are known by eigenvalues, vectors, or discriminant functions.
Multivariate Analysis
Published in Shyama Prasad Mukherjee, A Guide to Research Methodology, 2019
A direct extension of univariate ANOVA, MANOVA is a useful and, in some cases, essential tool in multivariate analysis – both in data-analytic and also in inferential procedures. Like ANOVA, this also requires the assumption of multivariate normality and homoscedasticity (common variance-covariance matrix). The second assumption can be checked by using Box’s M-test conveniently.
Perceptions of web accessibility guidelines by student website and app developers
Published in Behaviour & Information Technology, 2022
MANOVA was performed on the three dependent variables–Disability Awareness, Accessibility Exposure, and Guideline Familiarity–to examine the relationships between education and WEB&APP developer knowledge. MANOVA is used for situations in which there are several dependent variables (Field, 2013; Meyers et al., 2016). Compared with analysis of variance (ANOVA), in addition to testing the relationship between independent variable(s) and a single dependent variable, MANOVA has greater power to detect whether groups differ along a combination of dependent variables because it takes account of the correlations between those variables (Field, 2013; Meyers et al., 2016). In the present study, MANOVA is useful and important to examine whether or not having taken WEB&APP development and design courses has different effects on students’ perceptions of accessibility guidelines—a combination of their perceptions across three dimensions (Disability Awareness, Accessibility Exposure, and Guideline Familiarity).
A Worker’s Fitness-for-Duty Status Identification Based on Biosignals to Reduce Human Error in Nuclear Power Plants
Published in Nuclear Technology, 2020
With the selected biosignal indicators for identifying a worker’s fitness status, the subjects participated in the experiments, and data were collected to test the hypotheses. Statistical analysis made to test the hypotheses was based on the Statistical Package for the Social Sciences (SPSS) version 24.0 for Windows (64 bits). MANOVA (Ref. 56) using SPSS 24.0 was performed to identify possible biosignal indicators for classifying the FFD status. MANOVA is a method to compare variations between groups with variations within groups. MANOVA is used when there are two or more dependent variables. In this study MANOVA was to compare the EEG, ECG, GSR, BVP, BPHEG, and respiration results between the normal status and the abnormal status (alcohol use, sleep deprivation, stress, depression, and anxiety). To perform MANOVA, we assumed normality of the probability distributions of dependent variables, linearity between the dependent and independent variables, and homogeneity of variances and covariance.57,58 The results from MANOVA can be evaluated using a probability value (p-value). The p-value is the probability for a given model that when the null hypothesis is true, the statistical summary (such as the sample mean difference between two compared groups) will be the same as or of greater magnitude than the actual observed results.59 Statistical significance (p-value) is something that can be measured to a given confidence level: P* = 0.05 and P** = 0.01.
Consumer tendency to regret, compulsive buying, gender, and fashion time-of-adoption groups
Published in International Journal of Fashion Design, Technology and Education, 2018
Seung-Hee Lee, Jane E. Workman
Before conducting MANOVA, assumptions were checked: absence of multivariate outliers, linearity, absence of multicollinearity, and equality of covariance matrices. Mahalanobis Distances procedure was used to assess absence of multivariate outliers among the participants. One participant, with a Mahalanobis Distance greater than 16.27, was removed. An inspection of a scatterplot matrix, conducted for each dependent variable separately, showed that the dependent variables met the assumption of linearity. Correlations among the three dependent variables were moderate (see above) indicating an absence of multicollinearity. Box’s M test, used to check for equality of covariance matrices, revealed an F of 1.06, p < .363, providing evidence that the covariance matrices are not significantly unequal.