Robustness of Multivariate Tests

Kariya, Takeaki

doi:10.1214/aos/1176345643

Cited by 56 publications

(26 citation statements)

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“…It is interesting to compare our results with those of Kariya (1981) and Kariya and Sinha (1985) who proved similar results under the fixed effects MANOVA model (i.e. M i , M 2 fixed matrices), Kariya (1981) requiring q e 0 to be convex for the UMPI property to hold when min(n 2 ,P) = 1, while Kariya and Sinha Moreover, our proof of the LBI property of the trace test for min(nl,p) > 1 is extremely simple due to the nature of the model (1.2). We refer to Schwartz (1967) and Kariya and Sinha (1985) for the LBI property of the trace test under fixed effects MANOVA model for normal q and el'iptically symmetric q respectively.…”

Section: Imentioning

confidence: 73%

Robust Optimum Invariant Tests for Random MANOVA Models.

Das¹,

Sinha²

1986

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Section: Imentioning

confidence: 73%

Robust Optimum Invariant Tests for Random MANOVA Models.

Das¹,

Sinha²

1986

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“…It is well known that the elliptical distribution in which the mean is zero and variance-covariance matrix is diagonal possesses orthant symmetry. Many authors have reported that a test statistic is robust when the distribution of observation is the elliptical distribution, e.g., Efron (1969), Eaton and Efron (1970), Dawid (1977), Kariya (1981aKariya ( , 1981b and Khatri (1988). Robustness to nonnormality, which is caused by Condition 2, corresponds to their results.…”

Section: Consequently the Location Of The Null Distribution Of T Doementioning

confidence: 90%

Conditions for Robustness to Nonnormality on Test Statistics in a GMANOVA Model

Yanagihara

2007

JJSS

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This paper presents the conditions for robustness to the nonnormality on three test statistics for a general multivariate linear hypothesis, which were proposed under the normal assumption in a generalized multivariate analysis of variance (GMANOVA) model. The proposed conditions require the cumulants of an unknown population's distribution to vanish in the second terms of the asymptotic expansions for both the mean and variance of the test statistics. With the proposed conditions, the test statistic can be investigated for robustness to nonnormality of the population's distribution. When the conditions are satisfied, the Bartlett correction and the modified Bartlett correction in the normal case improve the quality of the chi-square approximation even under nonnormality.

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“…The four chosen indicators (DMQ-Total, DMQ-Task, DMQ-Subject, and DMQ-Context) obtained values in the KolmogorovSmirnov test that lead to rejecting the null hypothesis of adaptation to the normal distribution. However, we considered the application of MANOVA to be adequate, given its robustness versus the deviations from normality in symmetrical distributions (Kariya & Sinha, 2014), as is the case of our study. On another hand, the contrast indicators of variance equality of the error term between the groups are satisfactory for all variables.…”

Section: Psychometric Properties and Initial Exploratory Analysismentioning

confidence: 99%

Relations between mental workload and decision-making in an organizational setting

Soria-Oliver

López

Torrano

2017

Psicol. Refl. Crít.

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AsbtractBackground: The complexity of current organizations implies a potential overload for workers. For this reason, it is of interest to study the effects that mental workload has on the performance of complex tasks in professional settings. Objective: The objective of this study is to empirically analyze the relation between the quality of decision-making, on the one hand, and the expected and real mental workload, on the other. Methods: The study uses an ex post facto prospective design with a sample of 176 professionals from a higher education organization. Expected mental workload (Pre-Task WL) and real mental workload (Post-Task WL) were measured with the unweighted NASA-Task Load Index (NASA-TLX) questionnaire; difference between real WL and expected WL (Differential WL) was also calculated; quality of decision-making was measured by means of the Decision-Making Questionnaire.Results: General quality of decision-making and Pre-Task WL relation is compatible with an inverted U pattern, with slight variations depending on the specific dimension of decision-making that is considered. There were no verifiable relations between Post-Task WL and decision-making. The subjects whose expected WL matched the real WL showed worse quality in decision-making than subjects with high or low Differential WL. Conclusions: The relations between mental workload and decision-making reveal a complex pattern, with evidence of nonlinear relations.

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Robustness of Multivariate Tests

Cited by 56 publications

References 0 publications

Robust Optimum Invariant Tests for Random MANOVA Models.

Robust Optimum Invariant Tests for Random MANOVA Models.

Conditions for Robustness to Nonnormality on Test Statistics in a GMANOVA Model

Relations between mental workload and decision-making in an organizational setting

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