An approximation to the F distribution using the chi-square distribution

Li, Baibing; Martin, E.B.

doi:10.1016/s0167-9473(01)00097-4

Cited by 61 publications

(51 citation statements)

References 3 publications

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“…Thereafter, terms were removed sequentially until only significant interactions and main effects (P , 0.05) remained in the minimal adequate model (MAM). For ease in tabulating degrees of freedom, the F statistics conventionally evaluated in the presence of overdispersion were replaced by accurate chi-square approximations (Li and Martin 2002). Having selected MAMs, we estimated bumble bee worker density and species density for a standardized amount of forage in order to illustrate differences in preference for sown vs. control patches over and above the influence of available forage.…”

Section: Bumble Bee Response To Sown Forage Patchesmentioning

confidence: 99%

Bumble bee species' responses to a targeted conservation measure depend on landscape context and habitat quality

Carvell

Osborne

Bourke

et al. 2011

Ecological Applications

140

122

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Abstract. The global decline of insect pollinators, especially bees, is cause for concern, and there is an urgent need for cost-effective conservation measures in agricultural landscapes. While landscape context and habitat quality are known to influence species richness and abundance of bees, there is a lack of evidence from manipulative field experiments on bees' responses to adaptive management across differently structured landscapes. We present the results of a large-scale study that investigated the effects of a targeted agri-environment scheme (AES) on bumble bees (Bombus spp.) over three years in the United Kingdom. Forage patches of different sizes were sown with a conservation flower mixture across eight sites covering a broad range of agricultural land use types. Species richness and worker densities (especially of the longer-tongued Bombus species for which the mixture was targeted) were significantly higher on sown forage patches than on existing non-crop control habitats throughout the three-year study, but the strength of this response depended on both the proportions of arable land and abundance of herbaceous forb species in the surrounding landscape. The size of sown patches also affected worker density, with smaller patches (0.25 ha) attracting higher densities of some species than larger patches (1.0 ha). Our models show that a targeted AES can deliver greater net benefits in more intensively farmed areas, in terms of the number and species richness of bumble bees supported, than in heterogeneous landscapes where other foraging habitats exist. These findings serve to strengthen the evidence base for extending agri-environment schemes to boost declining pollinator populations to a larger number of agricultural landscapes across the globe.

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Section: Bumble Bee Response To Sown Forage Patchesmentioning

confidence: 99%

Bumble bee species' responses to a targeted conservation measure depend on landscape context and habitat quality

Carvell

Osborne

Bourke

et al. 2011

Ecological Applications

140

122

View full text Add to dashboard Cite

show abstract

“…In this paper, the Fisher-Snedecor F function used for the test was calculated 186 with the approximation of Li and Martin (2002) using the Fortran code of 187 the Lahey Fortran library for the χ 2 function, owned by E.J. Szondi, whose 188 source was Bargmann and Gosh (1963).…”

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confidence: 99%

Comparison of statistical algorithms for detecting homogeneous river reaches along a longitudinal continuum

et al. 2012

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International audienceSeven methods designed to delineate homogeneous river segments, belonging to four families, namely -- tests of homogeneity, contrast enhancing, spatially constrained classification, and hidden Markov models -- are compared, firstly on their principles, then on a case study, and on theoretical templates. These templates contain patterns found in the case study but not considered in the standard assumptions of statistical methods, such as gradients and curvilinear structures. The influence of data resolution, noise and weak satisfaction of the assumptions underlying the methods is investigated. The control of the number of reaches obtained in order to achieve meaningful comparisons is discussed. No method is found that outperforms all the others on all trials. However, the methods with sequential algorithms (keeping at order n + 1 all breakpoints found at order n) fail more often than those running complete optimisation at any order. The Hubert-Kehagias method and Hidden Markov Models are the most successful at identifying subpatterns encapsulated within the templates. Ergodic Hidden Markov Models are, moreover, liable to exhibit transition areas

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“…Heterogeneity for the Wald ratios was tested with the Cochran’s Q and quantified with the I 2 index (24). The strength of the association between the exposure and the outcome was estimated by calculation of the F-statistic (25).…”

Section: Methodsmentioning

confidence: 99%

Mendelian Randomization analyses reveal a causal effect of thyroid function on stroke via atrial fibrillation

Marouli

Kuś

Greco

et al. 2019

Preprint

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49Background 50 Several observational studies suggest that variations in thyroid function, even within the normal 51 range, are a risk factor for cardiovascular diseases, but it remains to be determined if these 52 associations are causal or not. This study investigates whether the relationship between variation 53 in normal range thyroid function, as well as hypothyroidism and hyperthyroidism, and the risk of 54 stroke and Coronary Artery Disease (CAD) are causal and via which pathways these relations are 55 mediated. 56 Methods and Findings 57We performed Mendelian Randomization (MR) analyses for stroke and CAD using genetic 58 instruments associated with TSH and FT4 levels respectively within either the normal range, 59 hypothyroidism or hyperthyroidism. In detected associations, the potential mediatory role of 60 known stroke and CAD risk factors was also examined. A one standard deviation increase in TSH 61 was associated with a 5% decrease in the risk of stroke (OR=0.95, 95% CI= 0.91 to 0.99). 62Multivariable MR analyses indicated that this effect is mediated through atrial fibrillation (AF). 63Hashimoto's Disease (HD) was associated with a 7% increased risk of CAD (OR=1.07, 95% CI= 64 1.01 to 1.13). The effect of Hashimoto's Disease (HD) on CAD risk appears to be mediated via 65 body mass index (BMI). 66 Conclusions 67These results provide important new insights into the causal relationships and mediating pathways 68 between thyroid function, stroke and CAD. Specifically, we identify normal range TSH levels and 69 HD as potential modifiable risk factors for stroke and CAD, respectively. 70 71

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An approximation to the F distribution using the chi-square distribution

Cited by 61 publications

References 3 publications

Bumble bee species' responses to a targeted conservation measure depend on landscape context and habitat quality

Bumble bee species' responses to a targeted conservation measure depend on landscape context and habitat quality

Comparison of statistical algorithms for detecting homogeneous river reaches along a longitudinal continuum

Mendelian Randomization analyses reveal a causal effect of thyroid function on stroke via atrial fibrillation

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