Understanding Advanced Statistical Methods

Westfall, Peter H.; Henning, Kevin S. S.

doi:10.1201/b14398

Cited by 121 publications

(84 citation statements)

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“…However, because of the small number of observations available for this study ( n = 23), some deviation from uniformity is expected. To gage the severity of this deviation, 93% confidence bands [ Härdle et al ., ] for bin frequency are developed through simulation‐based approximation [ Westfall and Henning , ]. Here 5000 histograms are generated from random uniformly distributed data, and the maximum and minimum frequency (i.e., bin count) of each histogram is recorded.…”

Section: Methodsmentioning

confidence: 99%

Using a Bayesian hierarchical model to improve Lake Erie cyanobacteria bloom forecasts

Obenour

Gronewold

Stow

et al. 2014

Water Resources Research

153

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The last decade has seen a dramatic increase in the size of western Lake Erie cyanobacteria blooms, renewing concerns over phosphorus loading, a common driver of freshwater productivity. However, there is considerable uncertainty in the phosphorus load-bloom relationship, because of other biophysical factors that influence bloom size, and because the observed bloom size is not necessarily the true bloom size, owing to measurement error. In this study, we address these uncertainties by relating latesummer bloom observations to spring phosphorus load within a Bayesian modeling framework. This flexible framework allows us to evaluate three different forms of the load-bloom relationship, each with a particular combination of statistical error distribution and response transformation. We find that a novel implementation of a gamma error distribution, along with an untransformed response, results in a model with relatively high predictive skill and realistic uncertainty characterization, when compared to models based on more common statistical formulations. Our results also underscore the benefits of a hierarchical approach that enables assimilation of multiple sets of bloom observations within the calibration processes, allowing for more thorough uncertainty quantification and explicit differentiation between measurement and model error. Finally, in addition to phosphorus loading, the model includes a temporal trend component indicating that Lake Erie has become increasingly susceptible to large cyanobacteria blooms over the study period (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013). Results suggest that current phosphorus loading targets will be insufficient for reducing the intensity of cyanobacteria blooms to desired levels, so long as the lake remains in a heightened state of bloom susceptibility.

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Section: Methodsmentioning

confidence: 99%

Using a Bayesian hierarchical model to improve Lake Erie cyanobacteria bloom forecasts

Obenour

Gronewold

Stow

et al. 2014

Water Resources Research

153

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“…Researchers indicate variance (r 2 ) in social sciences models generally range from .15 to .40. This range of variance might not indicate the goodness of models in some fields; however, when examining human behaviors is considered appropriate (Aneshensel, 2012), especially when taking into consideration human behaviors are highly unpredictable (Westfall & Henning, 2013).…”

Section: Conclusion Recommendations Andmentioning

confidence: 99%

United States and Latin American Undergraduate Students’ Knowledge, Attitudes and Perception of Global Agricultural Issues

Morales

Brashears

Akers

et al. 2017

JIAEE

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Global trends are demanding agricultural students have a broader perspective of agriculture and competitiveness and they become responsible global citizens. This study compared United States and Latin American undergraduate students' knowledge, attitudes, and beliefs regarding international agricultural issues, as well as their attitudes about global citizenship. Overall, students' results indicated a lack of knowledge regarding international agricultural issues, with only 3.6% obtaining a score above 60%. Students' recorded positive attitudes and beliefs about international agricultural issues but had mixed feelings regarding global citizenship attitudes. Scores on all constructs were found to be significantly different between the studied academic institutions (p < .05). The stepwise multiple linear regression indicated the predictors of university of enrollment and students' attitudes and beliefs about international agricultural issues were significantly related to their global citizenship attitudes: F (3, 1194) = 83.04, p = .01, explaining 17% of the variance in the model. The obtained results suggest students hold positive and open-minded attitudes and beliefs regarding international agricultural issues. These attitudes should be balanced by academic institutions with the knowledge needed by students to meet the demands of the agricultural industry. A global understanding can potentially enable future professionals to succeed in both local and global settings, and furthermore, help them become global citizens.

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“…Consider two independent random variables, Z which is standard normal random in distribution and 2 k X , which has a chisquare distributed random variable with k degrees of freedom. Pillai (2016) and Westfall (2013) showed that the random variable t defined in Equation (5) below, has a t-distribution with k degrees of freedom, where:…”

Section: Construction Of a Hypothesis Test For Vmentioning

confidence: 99%

Construction and Application of a Statistical Test for Coefficient of Variation on Normal Distributions

Seeletse¹,

Miyambu²

2017

American Journal of Applied Sciences

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In this study a novel statistical test is derived for the Coefficient of Variation (CV) under normal distributions. This is a newly derived test with value to engineering sciences in aspects of production of accurate items. The CV can measure the precision of a measuring instrument, among other applications. In order to determine instrument reliability, start by generating measures using the instrument. The CV is then calculated to determine if the measures generated by the instrument are concentrated around a central point. In use of normal distribution presumption, or approximation, applicable properties of the normal distributions lead to involvement of the chi-square and t-distributions. A CV test is then constructed, and two illustrative examples conclude the discussion.

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Understanding Advanced Statistical Methods

Cited by 121 publications

References 0 publications

Using a Bayesian hierarchical model to improve Lake Erie cyanobacteria bloom forecasts

Using a Bayesian hierarchical model to improve Lake Erie cyanobacteria bloom forecasts

United States and Latin American Undergraduate Students’ Knowledge, Attitudes and Perception of Global Agricultural Issues

Construction and Application of a Statistical Test for Coefficient of Variation on Normal Distributions

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