Abstract
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.
Highlights
The statistical power is the probability of rejecting a false null hypothesis
The aim of the study is to employ the multivariate analysis of variance (MANOVA) test statistic for the assessment of feed used in the production of pig in Delta State with the following specific objectives: i
From the outcome of the whole study, the following conclusions are drawn from both the preliminary results and the power analysis result it was found that; on the basis of the result of the asymmetry-based multivariate normality test and the multivariate normality test based on the kurtosis test that the data were multivariate normally distributed and meet the required assumption to apply a parametric multivariate method such as multivariate analysis of variance (MANOVA)
Summary
The statistical power is the probability of rejecting a false null hypothesis. The meaningfulness of a statistic reflects the accuracy and probability with which it checks Type 1 errors. Performance estimation is an important tool in the design of a study, but it is often ignored when designing multivariate studies because of the difficulties involved. There is not one meaningful statistic: Hotelling- Lawley trace ( U (s) ), Pillai-Bartlett trace ( (s) ), Wilk’s likelihood ratio ( ) and Roy’s Largest Root ( θ ), which are commonly used in multivariate analysis of variance (MANOVA). The performance fluctuates for a certain statistic and for the four statistics, depending on whether there is a violation of the homogeneity of the covariance matrices or the multivariate normality and/or whether the non-centrality is concentrated or diffuse. Performance is influenced by pvalue, sample size, and effect size
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