Certain Generalizations in the Analysis of Variance

Wilks, S. S.

doi:10.1093/biomet/24.3-4.471

Cited by 839 publications

(172 citation statements)

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“…In this procedure, each individual was allocated to the group with the nearest centroid (Ripley, 1996) and the proportion of correctly allocated individuals calculated. The discriminatory effectiveness of the analysis was also accessed using the Wilks' lambda (k) (Wilks, 1932) and the Cohen's Kappa (j) (Cohen, 1960), which according to Titus et al (1984) provide more reliable results.…”

Section: Methodsmentioning

confidence: 99%

Using body geometric morphometrics to identify bluemouth, Helicolenus dactylopterus (Delaroche, 1809) populations in the Northeastern Atlantic

et al. 2011

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In this study, landmark-based geometric morphometric methods were applied to evaluate the possible existence of different bluemouth, Helicolenus dactylopterus (Delaroche, 1809), populations in the NE Atlantic. Fish were obtained from commercial landings in Azores, Madeira, and Peniche (mainland Portugal). Samples from a research survey along the Galician coast (Spain) were also included in this study. A generalized procrustes analysis was done to remove non-shape variation. Then, the obtained shape variables were statistically adjusted to eliminate allometry and permit a comparative analysis of the samples. The discriminant analysis performed to test the homogeneity of the data set regarding sex revealed no shape differences between males and females within the four areas under study. The body shapes of bluemouth differed significantly among the four areas using Procrustes distances (P \ 0.01). In this study, a considerable morphological heterogeneity within the Azores group was observed, which could reflect a substructure of the bluemouth population within this area. According to our results, bluemouth from Galicia and Peniche seem to be relatively well separated from each other, despite both areas are relatively close geographically. Bluemouth from Madeira was well differentiated from the rest of locations and presented the highest correct classification rate in the discriminant analysis. In conclusion, morphological differences suggest that different bluemouth populations exist in the NE Atlantic, but an integrated approach, using different methods, would be needed to confirm the population structure of this species.

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Section: Methodsmentioning

confidence: 99%

Using body geometric morphometrics to identify bluemouth, Helicolenus dactylopterus (Delaroche, 1809) populations in the Northeastern Atlantic

et al. 2011

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“…. , m, Wilks [14] expressed the probability density function of the random variable Y = m k=1 Y k as the (m − 1)-fold integral…”

Section: Main Results and Discussionmentioning

confidence: 99%

On the Distribution of Sums of Independent Exponential Random Variables Via Wilks’ Integral Representation

Favaro

Walker

2008

Acta Appl Math

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In this note we consider an alternative approach to compute the distribution of the sum of independent exponential random variables. In particular, by considering the logarithmic relation between exponential and beta distribution functions and by considering the Wilks' integral representation for the product of independent beta random variables, we provide a closed-form expression for the distribution of the sum of independent exponential random variables. The expression we obtain is simpler than the ones previously obtained in the literature.

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“…The CA compared the relative abundance of different fi sh species among reef zones of each transect (56 sampling stations). To identify the fi sh communities on CA, Wilks' test (Wilks, 1932) was used. This statistical test compared variation between communities to variation within each community.…”

Section: Methodsmentioning

confidence: 99%

Spatiotemporal distribution of nocturnal coral reef fish juveniles in Moorea Island, French Polynesia

et al. 2007

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This study aimed to investigate the spatial structure of nocturnal fi sh communities at settlement on coral reefs in Moorea Island lagoon, French Polynesia; and the temporal consistency of habitat selection between winter (April to June 2001) and summer (November 2001). The Moorea lagoon was divided into 12 habitat zones (i.e., coral reef zones), which were distinct in terms of depth, wave exposure, and substratum composition. Nocturnal visual censuses among the 12 habitats found that the recently settled juveniles of 25 species recorded were dispatched among three communities spatially distributed according to the distance from the reef crest (reef crest, barrier reef, and fringing reef communities). This spatial communities structure of nocturnal juveniles was consistent in both winter and summer and would be explained primarily by a current gradient in Moorea lagoon (current speed was high near the reef crest and decreased towards the beach) and by the topographic characteristics of reef zones. Among the 25 species, 13 were recorded in both winter and summer. A comparison of the spatial distribution between summer and winter for 13 species that occurred during both seasons found that only 4 differed between the two seasons. For these species, habitat selection would be organized primarily by some stochastic processes such as inter-and intraspecifi c competition, predation, and food availability. Overall, the present study allowed us to highlight that most nocturnal coral reef fi sh juveniles at Moorea Island exhibited striking patterns in their distribution and current and topographic characteristics of reef zones might exert considerable infl uence on the distribution of fi shes.

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Certain Generalizations in the Analysis of Variance

Cited by 839 publications

References 0 publications

Using body geometric morphometrics to identify bluemouth, Helicolenus dactylopterus (Delaroche, 1809) populations in the Northeastern Atlantic

Using body geometric morphometrics to identify bluemouth, Helicolenus dactylopterus (Delaroche, 1809) populations in the Northeastern Atlantic

On the Distribution of Sums of Independent Exponential Random Variables Via Wilks’ Integral Representation

Spatiotemporal distribution of nocturnal coral reef fish juveniles in Moorea Island, French Polynesia

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