The correlation coefficient is a commonly used criterion to measure the strength of a linear relationship between the two quantitative variables. For a bivariate normal distribution, numerous procedures have been proposed for testing a precise null hypothesis of the correlation coefficient, whereas the construction of flexible procedures for testing a set of (multiple) precise and/or interval hypotheses has received less attention. This paper fills the gap by proposing an objective Bayesian testing procedure using the divergence-based priors. The proposed Bayes factors can be used for testing any combination of precise and interval hypotheses and also allow a researcher to quantify evidence in the data in favor of the null or any other hypothesis under consideration. An extensive simulation study is conducted to compare the performances between the proposed Bayesian methods and some existing ones in the literature. Finally, a real-data example is provided for illustrative purposes.

The dataset used in the paper is a bivariate Gaussian likelihood example with uncorrelated priors.

*Weighted percentages by country are not showed since data were not adjusted for country size.

This supplemental file contains (1) the warpage values of 201 sample points that were used to construct the Bivariate Cut-HDMR metamodel; (2) the warpage values of 1,045 sample points that were used to construct the CCD metamodel; and (3) the Monte Carlo simulation sample points that used for validation.

This article compares distribution functions among pairs of locations in their domains, in contrast to the typical approach of univariate comparison across individual locations. This bivariate approach is studied in the presence of sampling bias, which has been gaining attention in COVID-19 studies that over-represent more symptomatic people. In cases with either known or unknown sampling bias, we introduce Anderson–Darling-type tests based on both the univariate and bivariate formulation. A simulation study shows the superior performance of the bivariate approach over the univariate one. We illustrate the proposed methods using real data on the distribution of the number of symptoms suggestive of COVID-19.

This paper investigates estimating the association parameter of Morgenstern type bivariate distribution using a modified maximum likelihood method where the regular maximum likelihood methods failed to achieve estimation. The simple random sampling, concomitant of ordered statistics and bivariate ranked set sampling methods are used and compared. Efficiency and bias of the produced estimators are compared for two specific examples, Morgenstern type bivariate uniform and exponential distributions.

We have conducted bivariate and multivariate statistical analysis of data measuring the integrated luminosity, shape, and potential depth of the Einstein sample of early-type galaxies (presented by Fabbiano et al. 1992, ApJS, 80, 531). We find significant correlations between the X-ray properties and the axial ratios (a/b) of our sample, such that the roundest systems tend to have the highest L_X and L_X/L_B. The most radio-loud objects are also the roundest. We confirm the assertion of Bender et al. (1989, A&A, 217, 35) that galaxies with high L_X are boxy (have negative a_4). Both a/b and a_4 are correlated with L_B, but not with IRAS 12 um and 100 um luminosities. There are strong correlations between L_X, Mg_2 and sigma_v in the sense that those systems with the deepest potential wells have the highest L_X and Mg_2. Thus the depth of the potential well appears to govern both the ability to retain an ISM at the present epoch and to retain the enriched ejecta of early star formation bursts. Both L_X/L_B and L_6 (the 6 cm radio luminosity) show threshold effects with sigma_v, exhibiting sharp increases at log(sigma_v) ~ 2.2. Finally, there is clearly an interrelationship between the various stellar and structural parameters: The scatter in the bivariate relationships between the shape parameters (a/b and a_4) and the depth parameter (sigma_v) is a function of abundance in the sense that, for a given a_4 or a/b, the systems with the highest sigma_v also have the highest Mg_2. Furthermore, for a constant sigma_v, disky galaxies tend to have higher Mg_2 than boxy ones. Alternatively, for a given abundance, boxy ellipticals tend to be more massive than disky ellipticals. One possibility is that early-type galaxies of a given mass, originating from mergers (boxy ellipticals), have lower abundances than "primordial" (disky) early-type galaxies. Another is that disky inner isophotes are due not to primordial dissipational collapse, but to either the self-gravitating inner disks of captured spirals or the dissipational collapse of new disk structures from the premerger ISM. The high measured nuclear Mg_2 values would thus be due to enrichment from secondary bursts of star formation triggered by the merging event., We have conducted bivariate and multivariate statistical analysis of data measuring the integrated luminosity, shape, and potential depth of the Einstein sample of early-type galaxies (presented by Fabbiano et al. 1992, ApJS, 80, 531). We find significant correlations between the X-ray properties and the axial ratios (a/b) of our sample, such that the roundest systems tend to have the highest L_X and L_X/L_B. The most radio-loud objects are also the roundest. We confirm the assertion of Bender et al. (1989, A&A, 217, 35) that galaxies with high L_X are boxy (have negative a_4). Both a/b and a_4 are correlated with L_B, but not with IRAS 12 um and 100 um luminosities. There are strong correlations between L_X, Mg_2 and sigma_v in the sense that those systems with the deepest potential wells have the highest L_X and Mg_2. Thus the depth of the potential well appears to govern both the ability to retain an ISM at the present epoch and to retain the enriched ejecta of early star formation bursts. Both L_X/L_B and L_6 (the 6 cm radio luminosity) show threshold effects with sigma_v, exhibiting sharp increases at log(sigma_v) ~ 2.2. Finally, there is clearly an interrelationship between the various stellar and structural parameters: The scatter in the bivariate relationships between the shape parameters (a/b and a_4) and the depth parameter (sigma_v) is a function of abundance in the sense that, for a given a_4 or a/b, the systems with the highest sigma_v also have the highest Mg_2. Furthermore, for a constant sigma_v, disky galaxies tend to have higher Mg_2 than boxy ones. Alternatively, for a given abundance, boxy ellipticals tend to be more massive than disky ellipticals. One possibility is that early-type galaxies of a given mass, originating from mergers (boxy ellipticals), have lower abundances than "primordial" (disky) early-type galaxies. Another is that disky inner isophotes are due not to primordial dissipational collapse, but to either the self-gravitating inner disks of captured spirals or the dissipational collapse of new disk structures from the premerger ISM. The high measured nuclear Mg_2 values would thus be due to enrichment from secondary bursts of star formation triggered by the merging event.

Background: Clean water is an essential part of human healthy life and wellbeing. More recently, rapid population growth, high illiteracy rate, lack of sustainable development, and climate change; faces a global challenge in developing countries. The discontinuity of drinking water supply forces households either to use unsafe water storage materials or to use water from unsafe sources. The present study aimed to identify the determinants of water source types, use, quality of water, and sanitation perception of physical parameters among urban households in North-West Ethiopia.

Methods: A community-based cross-sectional study was conducted among households from February to March 2019. An interview-based a pretested and structured questionnaire was used to collect the data. Data collection samples were selected randomly and proportional to each of the kebeles' households. MS Excel and R Version 3.6.2 were used to enter and analyze the data; respectively. Descriptive statistics using frequencies and percentages were used to explain the sample data concerning the predictor variable. Both bivariate and multivariate logistic regressions were used to assess the association between independent and response variables.

Results: Four hundred eighteen (418) households have participated. Based on the study undertaken,78.95% of households used improved and 21.05% of households used unimproved drinking water sources. Households drinking water sources were significantly associated with the age of the participant (x2 = 20.392, df=3), educational status(x2 = 19.358, df=4), source of income (x2 = 21.777, df=3), monthly income (x2 = 13.322, df=3), availability of additional facilities (x2 = 98.144, df=7), cleanness status (x2 =42.979, df=4), scarcity of water (x2 = 5.1388, df=1) and family size (x2 = 9.934, df=2). The logistic regression analysis also indicated that those factors are significantly determining the water source types used by the households. Factors such as availability of toilet facility, household member type, and sex of the head of the household were not significantly associated with drinking water sources.

Conclusion: The uses of drinking water from improved sources were determined by different demographic, socio-economic, sanitation, and hygiene-related factors. Therefore, ; the local, regional, and national governments and other supporting organizations shall improve the accessibility and adequacy of drinking water from improved sources in the area.

Notes: Three population structures are considered. The contributions of the causal site for both the traits range from 0.0025 to 0.01. Powers are estimated on 1,000 replicates. See notes in Table 1 for sample sizes.Abbreviations: T12, the proposed test for bivariate analysis; T1, the proposed test for only the first trait; T2, the proposed test for only the second trait.

Dataset for: Leipold, B. & Loepthien, T. (2021). Attentive and emotional listening to music: The role of positive and negative affect. Jahrbuch Musikpsychologie, 30. https://doi.org/10.5964/jbdgm.78 In a cross-sectional study associations of global affect with two ways of listening to music – attentive–analytical listening (AL) and emotional listening (EL) were examined. More specifically, the degrees to which AL and EL are differentially correlated with positive and negative affect were examined. In Study 1, a sample of 1,291 individuals responded to questionnaires on listening to music, positive affect (PA), and negative affect (NA). We used the PANAS that measures PA and NA as high arousal dimensions. AL was positively correlated with PA, EL with NA. Moderation analyses showed stronger associations between PA and AL when NA was low. Study 2 (499 participants) differentiated between three facets of affect and focused, in addition to PA and NA, on the role of relaxation. Similar to the findings of Study 1, AL was correlated with PA, EL with NA and PA. Moderation analyses indicated that the degree to which PA is associated with an individual´s tendency to listen to music attentively depends on their degree of relaxation. In addition, the correlation between pleasant activation and EL was stronger for individuals who were more relaxed; for individuals who were less relaxed the correlation between unpleasant activation and EL was stronger. In sum, the results demonstrate not only simple bivariate correlations, but also that the expected associations vary, depending on the different affective states. We argue that the results reflect a dual function of listening to music, which includes emotional regulation and information processing.: Dataset Study 1

A bivariate random sample of motor insurance claims that include material damage and bodily injury. The sample was provided by an insurer in Spain and corresponds to claims occurred during year 2014. The sample size is n = 1751 and it represents 10% of the total of the analyzed claims

This folder contains four examples of merging crystallographic intensities with a bivariate prior:

- time-resolved Laue crystallography of the photoactive yellow protein
- anomalous diffraction from serial XFEL crystallography of thermolysin
- anomalous diffraction from Laue crystallography of NaI-soaked lysozyme
- [fragment screening monochromatic data of Nsp3 Mac1

Every example includes scripts to run `careless` as well as to analyze the outputs in order to reproduce the figures in the double-Wilson manuscript. For every example, there is a `README.md` that describes the contents of each example folder.

An example of combining ANOVA terms for bivariate principle component data to create the ANODIS F-statistic where N is the total number of samples drawn and K, the number of assemblages compared.

The paper considers some of the issues emerging from the discrete wavelet analysis of popular bivariate spectral quantities such as the coherence and phase spectra and the frequency-dependent time delay. The approach utilised here is based on the maximal overlap discrete Hilbert wavelet transform (MODHWT). Firstly, via a broad set of simulation experiments, we examine the small and large sample properties of two wavelet estimators of the scale-dependent time delay. The estimators are the wavelet cross-correlator and the wavelet phase angle-based estimator. Our results provide some practical guidelines for the empirical examination of short- and medium-term lead-lag relations for octave frequency bands. Further, we point out a deficiency in the implementation of the MODHWT and suggest using a modified implementation scheme, which was proposed earlier in the context of the dual-tree complex wavelet transform. In addition, we show how MODHWT-based wavelet quantities can serve to approximate the Fourier bivariate spectra and discuss issues connected with building confidence intervals for them. The discrete wavelet analysis of coherence and phase angle is illustrated with a scale-dependent examination of business cycle synchronisation between 11 euro zone countries. The study is supplemented by a wavelet analysis of the variance and covariance of the euro zone business cycles. The empirical examination underlines the good localisation properties and high computational efficie ncy of the wavelet transformations applied and provides new arguments in favour of the endogeneity hypothesis of the optimum currency area criteria as well as the wavelet evidence on dating the Great Moderation in the euro zone.

Note: * Significant at 10%, **5%, ***1%

We consider the implications for forecast accuracy of imposing unit roots and cointegrating restrictions in linear systems of I(1) variables in levels, differences, and cointegrated combinations. Asymptotic formulae are obtained for multi-step forecast error variances for each representation. Alternative measures of forecast accuracy are discussed. Finite sample behaviour in a bivariate model is studied by Monte Carlo using control variables. We also analyse the interaction between unit roots and cointegrating restrictions and intercepts in the DGP. Some of the issues are illustrated with an empirical example of forecasting the demand for M1 in the UK.

In many clinical settings, improving patient survival is of interest but a practical surrogate, such as time to disease progression, is instead used as a clinical trial's primary endpoint. A time-to-first endpoint (e.g. death or disease progression) is commonly analyzed but may not be adequate to summarize patient outcomes if a subsequent event contains important additional information. We consider a surrogate outcome very generally, as one correlated with the true endpoint of interest. Settings of interest include those where the surrogate indicates a beneficial outcome so that the usual time-to-first endpoint of death or surrogate event is nonsensical. We present a new two-sample test for bivariate, interval-censored time-to-event data, where one endpoint is a surrogate for the second, less frequently observed endpoint of true interest. This test examines whether patient groups have equal clinical severity. If the true endpoint rarely occurs, the proposed test acts like a weighted logrank test on the surrogate; if it occurs for most individuals, then our test acts like a weighted logrank test on the true endpoint. If the surrogate is a useful statistical surrogate, our test can have better power than tests based on the surrogate that naively handle the true endpoint. In settings where the surrogate is not valid (treatment affects the surrogate but not the true endpoint), our test incorporates the information regarding the lack of treatment effect from the observed true endpoints and hence is expected to have a dampened treatment effect compared to tests based on the surrogate alone.

Analytical derivations FINALWolfram Mathematica notebook containing all analytical derivations from the article: mostly moment generating functions of the ditributions and their stochastic representations and moments.Simulation ChecksThis is a mathematica notebook containing the code for the simulation check of all results in the article, and generating figures disclosed in the article.Simulation_checks.nb

Note: * Significant at 10%, **5%, ***1%

1. In 1973 the statistician Francis Anscombe used a clever set of bivariate datasets (now known as Anscombe’s quartet) to illustrate the importance of graphing data as a component of statistical analyses. In his example, each of the four datasets yielded identical regression coefficients and model fits, and yet when visualized revealed strikingly different patterns of covariation between x and y. 2. Phylogenetic comparative methods are statistical methods too, yet visualizing the data and phylogeny in a sensible way that would permit us to detect unexpected patterns or unanticipated deviations from model assumptions is not a routine component of phylogenetic comparative analyses. 3. Here, we use a quartet of phylogenetic datasets to illustrate that the same estimated parameters and model fits can be obtained from data that were generated using markedly different procedures – including pure Brownian motion evolution and randomly selected data uncorrelated with the tree. Just as in the ca...