Maximum eccentricity as a union-intersection test statistic in multivariate analysis

This study used the multivariate analysis of variance (MANOVA) test statistic to examine the impact of three categories feed used in the production of pig in Delta State. The multivariate test statistic considered are the Pillai – Bartlett trace, Wilks’ Test Statistic, Roy’s Largest Root Test Statistic, and the Lawley- Hotelling (LH) Statistic. The objectives include to: evaluate the robustness of the four Multivariate Analysis of Variance test statistics to ensure that the best is employed in multivariate analysis to guarantee most useful result in pig production; determine the relatively efficient test statistic for pig production; and determine the test statistic that is consistent across the sample sizes. Secondary source of data collection was used to obtain the data required for the analysis. The outcome of the study showed that the obtained data was multivariate normally distributed based on the result of the asymmetry-based multivariate normality test and the multivariate normality test based on the kurtosis test which makes the data suitable parametric multivariate method such as multivariate analysis of variance (MANOVA). The results show that the Wilks and Roy tests found a significant difference for the intercept. While the Pillai and LH tests could not find any significance. The Roy test was also found to be significant for feed one, feed two, and feed three. The Wilks and Roy tests also turned out to be significant differences for the intercept. All test measures showed significance for feed one. The Wilks and Roy tests also showed a significant difference for feed two, while all test measures found a significance for feed one. Another result showed that none of the tests found significance for the interaction between feed one and two, while the Roy test found significance for the interaction between feed one and three, feed two and three and feed one, two and three. The performance of the test for evaluating the performance of feeds for pig production with/without considering interactions was found to be in the following order of magnitude: Roy, Wilks and Pilla = LH. This result implies that the Roy method, with or without consideration of the interaction, has a better performance of the test than the other methods considered in the study.

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On choosing a test statistic in multivariate analysis of variance.

Psychological Bulletin ◽

10.1037/0033-2909.83.4.579 ◽

1976 ◽

Vol 83 (4) ◽

pp. 579-586 ◽

Cited By ~ 331

Author(s):

Chester L. Olson

Keyword(s):

Multivariate Analysis ◽

Analysis Of Variance ◽

Multivariate Analysis Of Variance ◽

Test Statistic

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A note on testing hypotheses concerning interaction with special reference to a graphical presentation in the space of canonical variates

Biometrical Letters ◽

10.2478/bile-2019-0008 ◽

2019 ◽

Vol 56 (1) ◽

pp. 89-104 ◽

Cited By ~ 1

Author(s):

Dariusz Kayzer

Keyword(s):

Multivariate Analysis ◽

Analysis Of Variance ◽

Canonical Variate Analysis ◽

Italian Ryegrass ◽

Linear Functions ◽

Canonical Variate ◽

Multivariate Analysis Of Variance ◽

Test Statistic ◽

Variate Analysis ◽

Graphical Presentation

SummaryResults of ecological studies that involve the use of multivariate analysis of variance techniques for testing various hypotheses, interesting from the point of view of comparing the linear functions of parameters, were considered. For testing the most interesting hypotheses on a variety of interaction effects and on contrasts of class means, the application of a multivariate test statistic is recommended. Canonical variate analysis is used for graphical presentation of the results of multidimensional experiments. In this paper it is shown how a generalized form of canonical variate analysis can be useful to reveal which parametric functions of a multivariate analysis of variance model are responsible for rejecting the linear hypothesis. As an example, an analysis was made of an ecological study of trace element accumulation in plants of Italian ryegrass as a method of biomonitoring of air pollution.

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Comment on Olson: Choosing a test statistic in multivariate analysis of variance.

Psychological Bulletin ◽

10.1037/0033-2909.86.2.355 ◽

1979 ◽

Vol 86 (2) ◽

pp. 355-360 ◽

Cited By ~ 34

Author(s):

James Stevens

Keyword(s):

Multivariate Analysis ◽

Analysis Of Variance ◽

Multivariate Analysis Of Variance ◽

Test Statistic

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Statistical analysis of classification

Symposium - International Astronomical Union ◽

10.1017/s0074180900053420 ◽

1966 ◽

Vol 24 ◽

pp. 188-189

Author(s):

T. J. Deeming

Keyword(s):

Multivariate Analysis ◽

Statistical Analysis ◽

Classification Scheme ◽

Analytical Procedure ◽

Narrow Band ◽

Scientific Research ◽

Maximum Amount ◽

Amount Of Information

If we make a set of measurements, such as narrow-band or multicolour photo-electric measurements, which are designed to improve a scheme of classification, and in particular if they are designed to extend the number of dimensions of classification, i.e. the number of classification parameters, then some important problems of analytical procedure arise. First, it is important not to reproduce the errors of the classification scheme which we are trying to improve. Second, when trying to extend the number of dimensions of classification we have little or nothing with which to test the validity of the new parameters.Problems similar to these have occurred in other areas of scientific research (notably psychology and education) and the branch of Statistics called Multivariate Analysis has been developed to deal with them. The techniques of this subject are largely unknown to astronomers, but, if carefully applied, they should at the very least ensure that the astronomer gets the maximum amount of information out of his data and does not waste his time looking for information which is not there. More optimistically, these techniques are potentially capable of indicating the number of classification parameters necessary and giving specific formulas for computing them, as well as pinpointing those particular measurements which are most crucial for determining the classification parameters.

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