Robust and scale-free effect sizes for non-Normal two-sample comparisons, with applications in e-commerce

Wooff, David; Jamalzadeh, Amin

doi:10.1080/02664763.2013.818625

Cited by 5 publications

(3 citation statements)

References 35 publications

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“…To that aim we visited the topic of distribution comparisons. Employing the quantile comparison effect size, proposed in [42], we found a range of possible combinations of relative lipid volume fractions and water volume fractions for which the predicted RI distribution coincides with the measured one. However, for these inferred ranges, the MD varies significantly, resulting in large deviations.…”

Section: Discussion and Outlookmentioning

confidence: 69%

“…Hence, in an attempt to find the mean water volume fraction and the mean relative lipid volume fraction that resembles the experimental condition, we evaluated the quantile comparison effect size (QCES, see SI; Eq. (S11) [25]), as proposed in [42], denoted by Ξ, between predicted and measured RI distributions for a range of different and , shown in Fig. 4(a).…”

Section: Experimental Validation and Applicationmentioning

confidence: 99%

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Estimation of the mass density of biological matter from refractive index measurements

Möckel,

Beck,

Kaliman

et al. 2023

Preprint

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The quantification of physical properties of biological matter gives rise to novel ways of understanding functional mechanisms by utilizing models that explicitly depend on physical observables. One of the basic biophysical properties is the mass density (MD), which determines the degree of crowdedness. It impacts the dynamics in sub-cellular compartments and further plays a major role in defining the opto-acoustical properties of cells and tissues. As such, the MD can be connected to the refractive index (RI) via the well known Lorentz-Lorenz relation, which takes into account the polarizability of matter. However, computing the MD based on RI measurements poses a challenge as it requires detailed knowledge of the biochemical composition of the sample. Here we propose a methodology on how to account fora priorianda posterioriassumptions about the biochemical composition of the sample as well as respective RI measurements. To that aim, we employ the Biot mixing rule of RIs alongside the assumption of volume additivity to find an approximate relation of MD and RI. We use Monte-Carlo simulations as well as Gaussian propagation of uncertainty to obtain approximate analytical solutions for the respective uncertainties of MD and RI. We validate this approach by applying it to a set of well characterized complex mixtures given bybovinemilk and intralipid emulsion. Further, we employ it to estimate the mass density of trunk tissue of living zebrafish (Danio rerio) larvae. Our results enable quantifying changes of mass density estimates based on variations in thea prioriassumptions. This illustrates the importance of implementing this methodology not only for MD estimations but for many other related biophysical problems, such as mechanical measurements using Brillouin microscopy and transient optical coherence elastography.

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Section: Discussion and Outlookmentioning

confidence: 69%

Section: Experimental Validation and Applicationmentioning

confidence: 99%

Estimation of the mass density of biological matter from refractive index measurements

Möckel,

Beck,

Kaliman

et al. 2023

Preprint

View full text Add to dashboard Cite

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“…We might consider Cohen's d, that is, [the difference between the original spectrum width and the average surrogate spectrum width] divided by [the standard deviation of the average surrogate spectrum width]. However, the statistical validity of Cohen's d rests on the assumption of Normality (Wooff & Jamalzadeh, 2013), and, to our knowledge, no evidence exists that samples of spectrum widths should be Normally distributed. The use of average spectrum-width itself gives us access to a Normally distributed sampling distribution.…”

Section: Limitations To P-values Remain and Standardized Measures Of ...mentioning

confidence: 99%

Multifractal test for nonlinearity of interactions across scales in time series

Kelty-Stephen¹,

Lane²,

Bloomfield³

et al. 2022

Preprint

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The creativity and emergence of biological and psychological behavior tend to be nonlinear—biological and psychological measures contain degrees of irregularity. The linear model might fail to reduce these measurements to a sum of independent random factors (yielding a stable mean for the measurement), implying nonlinear changes over time. The present work reviews some of the concepts implicated in nonlinear changes over time and details the mathematical steps involved in their identification. It introduces multifractality as a mathematical framework helpful in determining whether and to what degree the measured series exhibits nonlinear changes over time. These mathematical steps include multifractal analysis and surrogate data production for resolving when multifractality entails nonlinear changes over time. Ultimately, when measurements fail to fit the structures of the traditional linear model, multifractal modeling allows making those nonlinear excursions explicit, that is, to come up with a quantitative estimate of how strongly events may interact across timescales. This estimate may serve some interests as merely a potentially statistically significant indicator, but we suspect that this estimate might serve more generally as a predictor of perceptuomotor or cognitive performance.

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