Unequal Sizes Research Articles

Dynamic content layout optimization for news website front pages

Purpose The home page design of a digital news website is a key factor in determining its attractiveness to readers. This study aims to propose an approach to manage the frequent adjustment of the dynamic layout of the news content on the website home page in a real-time environment to increase its attractiveness to readers. Design/methodology/approach This paper shows that this news website layout design problem can be modeled as an optimization problem based on the information of news contents that change within a multiple-period planning horizon similar to the dynamic facility layout problem. A hybrid genetic algorithm-based approach integrated with local search heuristic methods is also proposed to improve the solution. Findings This paper finds that the DPLP model is effective in modeling the changing layout of a digital news website. The problem can solved in a timely manner using the proposed hybrid genetic algorithm. Research limitations/implications This paper was based on hypothetical data and on the assumption of equal section size. Actual data would help fine-tune the application of the dynamic facility layout model. As well the algorithm could be enhanced for unequal size sections. Practical implications The model should help online newspapers apply sophisticated algorithms to optimize the layout of news websites dynamically in a timely manner. Social implications News websites are increasingly the desired medium to consume news. So it has an important role in educating society. Thus optimizing and improving the process will help in this regard. Originality/value To the best of the authors’ knowledge, this paper is the first one to apply the DPLP model to the digital newspaper website dynamic design problem.

Sample size and power calculation for testing treatment effect heterogeneity in cluster randomized crossover designs.

The cluster randomized crossover design has been proposed to improve efficiency over the traditional parallel-arm cluster randomized design. While statistical methods have been developed for designing cluster randomized crossover trials, they have exclusively focused on testing the overall average treatment effect, with little attention to differential treatment effects across subpopulations. Recently, interest has grown in understanding whether treatment effects may vary across pre-specified patient subpopulations, such as those defined by demographic or clinical characteristics. In this article, we consider the two-treatment two-period cluster randomized crossover design under either a cross-sectional or closed-cohort sampling scheme, where it is of interest to detect the heterogeneity of treatment effect via an interaction test. Assuming a patterned correlation structure for both the covariate and the outcome, we derive new sample size formulas for testing the heterogeneity of treatment effect with continuous outcomes based on linear mixed models. Our formulas also address unequal cluster sizes and therefore allow us to analytically assess the impact of unequal cluster sizes on the power of the interaction test in cluster randomized crossover designs. We conduct simulations to confirm the accuracy of the proposed methods, and illustrate their application in two real cluster randomized crossover trials.

An Evaluation of Racial and Ethnic Representation in Research Conducted with Young Adults Diagnosed with Cancer: Challenges and Considerations for Building More Equitable and Inclusive Research Practices.

The psychosocial outcomes of adolescents and young adults (AYAs) diagnosed with cancer are poorer compared to their peers without cancer. However, AYAs with cancer from diverse racial and ethnic groups have been under-represented in research, which contributes to an incomplete understanding of the psychosocial outcomes of all AYAs with cancer. This paper evaluated the racial and ethnic representation in research on AYAs diagnosed with cancer using observational, cross-sectional data from the large Young Adults with Cancer in Their Prime (YACPRIME) study. The purpose was to better understand the psychosocial outcomes for those from diverse racial and ethnic groups. A total of 622 participants with a mean age of 34.15 years completed an online survey, including measures of post-traumatic growth, quality of life, psychological distress, and social support. Of this sample, 2% (n = 13) of the participants self-identified as Indigenous, 3% (n = 21) as Asian, 3% (n = 20) as "other," 4% (n = 25) as multi-racial, and 87% (n = 543) as White. A one-way ANOVA indicated a statistically significant difference between racial and ethnic groups in relation to spiritual change, a subscale of post-traumatic growth, F(4,548) = 6.02, p < 0.001. Post hoc analyses showed that those under the "other" category endorsed greater levels of spiritual change than those who identified as multi-racial (p < 0.001, 95% CI = [2.49,7.09]) and those who identified as White (p < 0.001, 95% CI = [1.60,5.04]). Similarly, participants that identified as Indigenous endorsed greater levels of spiritual change than those that identified as White (p = 0.03, 95% CI = [1.16,4.08]) and those that identified as multi-racial (p = 0.005, 95% CI = [1.10,6.07]). We provided an extensive discussion on the challenges and limitations of interpreting these findings, given the unequal and small sample sizes across groups. We concluded by outlining key recommendations for researchers to move towards greater equity, inclusivity, and culturally responsiveness in future work.

Fluid structure interaction problem for flow past three unequal sized square cylinders at different Reynolds numbers

The flow past three square cylinders of unequal size placed in an inline arrangement is studied using the lattice Boltzmann method at different Reynolds numbers [Re = (u∞ d)/ν] within the range of Re = 120, 150, 160, 175, and 200 for various gap spacings (g = s/d), ranging from 1 to 6. This study focused on the symmetric examination of flow behavior for various gap spacing within the three unequal-sized square cylinders. The main objective of this study was to investigate the effects of Reynolds numbers and gap spacing for flow structure mechanism and vortex shedding suppression in between the gap and down-stream position of all three cylinders. Results are obtained in terms of vorticity contours visualization, drag and lift coefficients, Strouhal number, and physical parameters. In vorticity contour visualization, different flow behaviors are observed, known as flow regimes, and are named according to their characteristics, and they are (i) steady flow regime, (ii) shear layer reattachment flow regime (SLR), (iii) fully developed vortex shedding flow regime, (iv) two-row fully developed vortex shedding flow regime, and (v) fully developed irregular vortex shedding flow regime. The present study also includes a discussion on aerodynamic forces, namely the mean drag coefficient (Cdmean), root mean square of the lift coefficient (Clrms), and Strouhal numbers (St) for three cylinders with sizes d = 20, d1 = 15, and d2 = 10, respectively. The maximum value of Cdmean for the first cylinder (C1) is obtained at (Re, g) = (200, 3) that is, 1.5156, where the existing flow regime is the SLR flow regime, while for C2 and C3, the maximum Cdmean values are examined at critical flow behaviors, where the existing flow regime is a fully developed irregular vortex shedding flow regime. Negative values of Cdmean are also examined for cylinders C2 and C3 at some combinations of (Re, g), attributed to the effect of thrust. Furthermore, it is noticed that the values of Strouhal number are increased with an increment in values of gap spacing. The highest value of the Strouhal number for all three cylinders is observed for C1 at (Re, g) = (120, 5), reaching 0.1556 along with a two-row fully developed flow regime. Furthermore, it is investigated from the present problem that the position of unequal sized square cylinders strongly influenced the flow structure mechanism. The information found and discussed in this study could be effective for structure designing arrangement in the case of three square cylinders of unequal size placed in a horizontal arrangement.

Mathematical simulation of transverse cut in the fiber of a composite reinforced with unidirectional fibers with linear cohesion cracks

In the reviewed paper, the case of a transverse displacement plane with two pairs of biperiodic (corresponding to the X and Y axes) cohesive cracks of unequal size, weakened by biperiodic circular holes, is considered. The circular holes are filled with reinforcing fibers and the surface is covered with a thin homogeneous non-metallic material of the same thickness. In this case, boundary issues between filler and coating, coating and matrix, and boundary issues along cohesion cracks are determined. For both cases, the solution to the problem is sought in the form of an analytical function with complex variables. According to the boundary conditions of the case, a system of unequal algebraic equations is found along the holes, and singular integral equations are constructed along the cohesion cracks. Currently, the singular integral equations are brought to the system of finite linear algebraic equations with the help of mathematical transformations. Both systems are solved together using the Gaussian method and the crack growth is determined using the stress intensity factor formulas at the crack tips. During the solution of the problem, the stress intensity coefficients at the end are found by the variation of the length of the cracks based on the radius of the circular holes.

Hierarchical Principal Components for Data-Driven Multiresolution fMRI Analyses.

Understanding the organization of neural processing is a fundamental goal of neuroscience. Recent work suggests that these systems are organized as a multiscale hierarchy, with increasingly specialized subsystems nested inside general processing systems. Current neuroimaging methods, such as independent component analysis (ICA), cannot fully capture this hierarchy since they are limited to a single spatial scale. In this manuscript, we introduce multiresolution hierarchical principal components analysis (hPCA) and compare it to ICA using simulated fMRI datasets. Furthermore, we describe a parametric statistical filtering method developed to focus analyses on biologically relevant features. Lastly, we apply hPCA to the Human Connectome Project (HCP) to demonstrate its ability to estimate a hierarchy from real fMRI data. hPCA accurately estimated spatial maps and time series from networks with diverse hierarchical structures. Simulated hierarchies varied in the degree of branching, such as two-way or three-way subdivisions, and the total number of levels, with varying equal or unequal subdivision sizes at each branch. In each case, as well as in the HCP, hPCA was able to reconstruct a known hierarchy of networks. Our results suggest that hPCA can facilitate more detailed and comprehensive analyses of the brain's network of networks and the multiscale regional specializations underlying neural processing and cognition.

A Huber Loss Minimization Approach to Byzantine Robust Federated Learning

Federated learning systems are susceptible to adversarial attacks. To combat this, we introduce a novel aggregator based on Huber loss minimization, and provide a comprehensive theoretical analysis. Under independent and identically distributed (i.i.d) assumption, our approach has several advantages compared to existing methods. Firstly, it has optimal dependence on epsilon, which stands for the ratio of attacked clients. Secondly, our approach does not need precise knowledge of epsilon. Thirdly, it allows different clients to have unequal data sizes. We then broaden our analysis to include non-i.i.d data, such that clients have slightly different distributions.

Prevalence of Lameness in Dairy Cows and Associated Risk Factors at Hawassa Town Dairy Farms, Ethiopia.

Lameness is one of the greatest constraints on the productivity, health, and welfare of dairy cattle. A cross-sectional study was carried out from March 2021 to September 2021 in Hawassa town with the aim of assessing the prevalence and identifying the associated risk factors of lameness in dairy farms. The study was conducted on 440 animals belonging to 19 randomly selected intensive dairy farms. Data regarding lameness and its possible risk factors were collected both at animal and farm level using a questionnaire. The results showed that the overall prevalence of lameness was 10.2% (n = 45/440). The association of lameness prevalence with various risk factors including milking status, exercise, age, parity, milk yield, and lactation stage was statistically tested using logistic regression model. There was a significant variation in the prevalence of lameness (P < 0.05) between cattle with different milking status, age, parity, milk yield, and stage of lactation by the univariable analysis result. According to the multivariable analysis, only milk yield and lactation stage were statistically associated with the occurrence of lameness. Milking animals (8%) had higher prevalence of lameness than nonmilking (2.2%). The occurrence of lameness increased with milk yield. The highest prevalence of lameness was recorded in the early stage of lactation. Lameness was more frequent in hind limbs (6.6%) than in forelimbs (3.6%). The main causes of lameness observed in this study were both claw overgrowth 10 (2.3%), unequal claw size 10 (2.3%), solar ulcer 8 (1.8%), interdigital necrobacillosis 2 (0.5%), interdigital hyperplasia 2 (0.5%), and digital dermatitis 1 (0.2%). There was no means of early lameness diagnosis in 94.7% of farms. Lameness was found to be an important disease in dairy cows at Hawassa town. Prevention and early diagnosis leading to prompt treatment of lameness in cows should be part of dairy farm management practice.

Welch’s t test is more sensitive to real world violations of distributional assumptions than student’s t test but logistic regression is more robust than either

AbstractIt has previously been pointed out that Student’s t test, which assumes that samples are drawn from populations with equal standard deviations, can have an inflated Type I error rate if this assumption is violated. Hence it has been recommended that Welch’s t test should be preferred. In the context of carrying out gene-wise weighted burden tests for detecting association of rare variants with psoriasis we observe that Welch’s test performs unsatisfactorily. We show that if the assumption of normality is violated and observations follow a Poisson distribution, then with unequal sample sizes Welch’s t test has an inflated Type I error rate, is systematically biased and is prone to produce extremely low p values. We argue that such data can arise in a variety of real world situations and believe that researchers should be aware of this issue. Student’s t test performs much better in this scenario but a likelihood ratio test based on logistic regression models performs better still and we suggest that this might generally be a preferable method to test for a difference in distributions between two samples.This research has been conducted using the UK Biobank Resource.

Towards improving online learning in physical education: Gender differences and determinants of motivation, psychological needs satisfaction, and academic achievement in Saudi students.

Studies on students' perceptions and expectations during physical education (PE) online learning remain scarce. Centered on self-determination theory, the present cross-sectional study aims to identify gender differences and predictors affecting motivation, psychological needs satisfaction (PNS), and academic achievement during PE online learning. Data were collected from Saudi students' (N = 308, 161 females and 147 males) responses to the PE autonomy, relatedness, competence, and motivation questionnaires. Welch's t-test for unequal sample sizes, multiple linear regression, and binary logistic regression were used to compare means and to predict the relationships between the independent and dependent variables. The results showed higher autonomy and competence perceptions in female than in male students, but no differences were observed in relatedness. Female students presented higher intrinsic motivations, lower amotivation perceptions than males. However, no gender differences were recorded in extrinsic motivation. Students with less experience in online learning and weak grade point averages (GPAs) are more susceptible to having a high level of amotivation. Gender, GPA, and prior experience with online learning are the common predictors for all PNS and amotivation, while GPA and prior experience with online learning are the determinants of intrinsic motivation. GPA is affected by prior experience with online learning, autonomy, competence, intrinsic motivation, and amotivation. Therefore, teachers are encouraged to adapt their didactic-pedagogical behaviors during PE online learning according to students' motivation and autonomy perceptions. Structuring teaching activities with more individualized support for autonomy, competence, intrinsic motivation, and students' online skills/competencies ensures better learning efficiency and academic achievements.

Research on cavitation bubble behaviors between a dual-particle pair

The interactions between particle clusters and cavitation bubbles play an important role in several industrial applications, e.g., the abrasive erosion of hydraulic machinery, the efficiency improvement of ultrasonic cleaning, and the mineral flotation. This paper explores the influence of a dual-particle pair of unequal sizes on the bubble collapse dynamics based on a Kelvin impulse model and high-speed photography. The impact of the radius ratio of the dual-particle pair (ranging from 1.0 to 3.0), defined as the ratio of the large-particle radius to the small-particle radius, on the bubble interface deformation, collapse jet, and the translational movement of the bubble is analyzed. The main findings are as follows: (1) the Kelvin impulse based on the Weiss theorem can effectively predict the asymmetric bubble behaviors in terms of the moving distance and the direction of the bubble centroid during the bubble collapse; (2) the particle radius ratio is a key parameter affecting the intensity and direction of the Kelvin impulse, as well as the bubble centroid moving distance; and (3) the zero-Kelvin-impulse point is always biased toward the smaller particle in the dual-particle pair.

Control of successive unequal cell divisions by neural cell fate regulators determines embryonic neuroblast cell size.

Asymmetric cell divisions often generate daughter cells of unequal size in addition to different fates. In some contexts, daughter cell size asymmetry is thought to be a key input to specific binary cell fate decisions. An alternative possibility is that unequal division is a mechanism by which a variety of cells of different sizes are generated during embryonic development. We show here that two unequal cell divisions precede neuroblast formation in the C lineage of Caenorhabditis elegans. The equalisation of these divisions in a pig-1/MELK mutant background has little effect on neuroblast specification. Instead, we demonstrate that let-19/MDT13 is a regulator of the proneural basic helix-loop-helix transcription factor hlh-14/ASCL1 and find that both are required to concomitantly regulate the acquisition of neuroblast identity and neuroblast cell size. Thus, embryonic neuroblast cell size in this lineage is progressively regulated in parallel with identity by key neural cell fate regulators. We propose that key cell fate determinants have a previously unappreciated function in regulating unequal cleavage, and therefore cell size, of the progenitor cells whose daughter cell fates they then go on to specify.

Improving incomplete mixing modeling for junctions of water distribution networks

Abstract Most of the existing water quality models for water distribution networks assume complete mixing at junctions. Albeit few models offer the possibility to consider incomplete mixing (IM) at junctions, most of them were developed under laboratory conditions and for equal pipe size junctions. In real-world distribution networks, however, cross junctions of 150 × 100 × 150 × 100 mm or 100 × 150 × 150 × 150 mm are common, yet no model has been developed for these configurations. This paper presents a new equation to compute concentrations in cross junction outlets while considering IM for six cross junction configurations, including unequal pipe sizes and 150 mm pipes. For each cross junction configuration, mixing was studied under 25 flow scenarios in the laboratory and 40 simulated flow scenarios using OpenFOAM software. Two new flow rate ratios were selected as independent variables to compute different outlet concentrations. For two specific cross junctions with equal pipe sizes, the root-mean-squared error between the observed and simulated concentrations of the newly developed model was 0.02, while it was 0.05 and 0.07, respectively, for the AZRED IM model and the Shao et al. IM model.

Case report on Ipratropium Bromide induced Anisocoria

Anisocoria or unequal pupil size is an alarming sign of a neurologic emergency, especially when the patient is in a critical care setting. It is important to identify the aetiology of anisocoria and consider drug-induced anisocoria as a possible aetiology after ruling out underlying pathology if any. Ipratropium bromide, an anticholinergic drug, can cause anisocoria. This case report emphasises Ipratropium bromide-induced anisocoria.

New blocked all-pairs shortest paths algorithms operating on blocks of unequal sizes

In real-world networks, many problems imply finding the All-Pairs Shortest Paths (APSP) and their distances in a graph. Solving the large-scale APSP problem on modern muti-processor (multi-core) systems is the key for various application domains. The computational cost of solving the problem is high, therefore in many cases approximate solutions are considered as acceptable. The blocked APSP algorithms are a promising approach which can exploit many processors (cores) and their caches in parallel mode efficiently. At the same time, to our best knowledge, all blocked algorithms of the Floyd-Warshall family use blocks of equal sizes. This property limits application of the algorithms. In this paper we propose new blocked algorithms which divide the input graph into unequal subgraphs and divide the matrix of distances between pairs of vertices into blocks of unequal sizes. The algorithms describe the dense subgraphs by the adjacency matrix and describe sparse subgraphs and connections between them by the adjacency list. This approach allows the Floyd-Warshall family algorithms to be used together with Dijkstra family algorithms. It can be applied to large graphs decomposed into dense (clusters) and sparse subgraphs. A new heterogeneous algorithm can significantly reduce the computation time of blocks depending on the block type and size. The contribution of the pa-per is the development of a new family of blocked APSP algorithms which can handle blocks of unequal sizes, save and extend the advantages of the state-of-the-art algorithms operating on blocks of equal sizes. The proposed algorithms are implemented as single- and multiple-threaded parallel applications for multi-core systems.

Optical properties and behavior of whispering gallery mode resonators in complex microsphere configurations: Insights for sensing and information processing applications

AbstractThis paper delves into the intricate world of whispering gallery mode (WGM) resonators within complex microsphere configurations, exploring their optical properties and behavior. Integrated with optical sensing and processing technology, WGM resonators offer compact size, high sensitivity, rapid response, and tunability. The study investigates the impact of configuration, size, excitation, polarization, and coupling effects on WGM properties. Notable findings include enhanced sensitivity in single microsphere resonators, influence of unequal sphere sizes and excitation locations on WGM modes, and higher quality factors (Q‐factors) in triangular three‐microsphere resonator configurations. Circular polarization was found to elevate Q‐factors, while the nine‐microsphere resonator configuration exhibited increased intensity of dominant WGM peaks with higher laser power, suppressing other peaks. These insights guide the design and optimization of microsphere resonator systems, positioning them for applications in sensing and optical information processing.

Research on optimization of spray drying conditions, characteristics of anthocyanins extracted from Hibiscus sabdariffa L. flower, and application to marshmallows.

Anthocyanin, a main-colored bioactive compound found in Hibiscus sabdariffa L., is well-known for a varied range of applications as food additives in foodstuff, and natural colorants in food, pharmaceutical, and printing industries. The study aimed to find out the suitable conditions for the spray-drying process to obtain anthocyanin powder from the extract as well as characterized the powder. In addition, the obtained powder was applied to marshmallows and determined the acceptability of appearance, quality, and scavenging capacity of the candy. The carrier of maltodextrin and gum arabic was selected for spray-drying, which had optimal conditions at 144°C and 7 mL/min, resulting in 100.22 mg/g anthocyanin content with an encapsulation efficiency of 93.87%. The obtained anthocyanin has appropriate moisture of 5.14%, quite appropriate bulk density, and tapped density, it also was high solubility, and poor flowability but easy compression. The shape of the particle by SEM analysis was low particle size (2-10 μm), wrinkled, unequal spherical size, rough surfaces with indentations, and slight cracks. The X-ray diffraction (XRD) spectrum of the sample had very low crystallinity and diffuse wide peaks revealing that anthocyanin still exists inside maltodextrin particles. The FT-IR spectrum had oscillations of characteristic groups of anthocyanin structure. Marshmallow samples added 5% anthocyanin powder gained high acceptability of appearance and maintained the scavenging capacity (DPPH) with an IC50 value of 7368.31 ppm after a month of storage.

A Federated Learning-Based Industrial Health Prognostics for Heterogeneous Edge Devices Using Matched Feature Extraction

Data-driven industrial health prognostics require rich training data to develop accurate and reliable predictive models. However, stringent data privacy laws and the abundance of edge industrial data necessitate decentralized data utilization. Thus, the industrial health prognostics field is well suited to significantly benefit from federated learning (FL), a decentralized and privacy-preserving learning technique. However, FL-based health prognostics tasks have hardly been investigated due to the complexities of meaningfully aggregating model parameters trained from heterogeneous data to form a high performing federated model. Specifically, data heterogeneity among edge devices, stemming from dissimilar degradation mechanisms and unequal dataset sizes, poses a critical statistical challenge for developing accurate federated models. We propose a pioneering FL-based health prognostic model with a feature similarity-matched parameter aggregation algorithm to discriminatingly learn from heterogeneous edge data. The algorithm searches across the heterogeneous locally trained models and matches neurons with probabilistically similar feature extraction functions first, before selectively averaging them to form the federated model parameters. As the algorithm only averages similar neurons, as opposed to conventional naive averaging of coordinate-wise neurons, the distinct feature extractors of local models are carried over with less dilution to the resultant federated model. Using both cyclic degradation data of Li-ion batteries and non-cyclic data of turbofan engines, we demonstrate that the proposed method yields accuracy improvements as high as 44.5\% and 39.3\% for state-of-health estimation and remaining useful life estimation, respectively.

On the sharpshooter genus Yunga Melichar, 1924 (Hemiptera: Cicadellidae: Cicadellinae): descriptions of a new species from Panama and of the internal female terminalia of Y. cartwrighti Young, 1968 and Y. coriacea Stl, 1864.

Yunga Melichar, 1924, is a little-known genus that currently includes three valid species distributed in North America (Mexico), Central America (Costa Rica, Panama), and northern South America (Colombia). A new species of this genus, Y. andresi sp. nov., is described and illustrated based on a single male specimen collected in Bocas del Toro province, Panama. This species can be distinguished from other species of the genus by the following combination of features: (1) apex of style curved inwards, hook-like; (2) aedeagal shaft with paired basal dorsolateral processes, spine-like and short, not extending beyond gonopore; (3) dorsoapical process robust, hook-shaped in lateral view, ending curved and acute; and 4) paraphyses paired, each robust and trifurcate with rami of unequal sizes and thickness. The female genitalia of Y. cartwrighti Young, 1968 and Y. coriacea Stl, 1864 are described and illustrated for the first time. Finally, a distribution map for the species of Yunga, as well as an updated key to species identification, are provided.

Evaluating the Efficiency of Restricted Pseudo Likelihood Estimation in Balanced and Unbalanced Clustered Binary Data Models

Clustered binary data analysis is a common task in various fields, such as social sciences and epidemiology. Restricted Pseudo Likelihood Estimation (PLE) is a widely used approach for analyzing clustered binary data, providing flexibility in handling complex dependencies within clusters. This study aims to evaluate the efficiency of Restricted Pseudo Likelihood Estimation in balanced and unbalanced clustered binary data models. Using simulated data, we compare the performance of PLE in balanced and unbalanced clustered binary data scenarios. We consider various factors such as the number of clusters, cluster sizes, and intra-cluster correlation. The preferred class of models for clustered binary data is the Hierarchical Generalized Linear Model (HGLM). This article compares the performance of a restricted pseudo-likelihood estimation method of the Hierarchical Generalized Linear Model (HGLM) with equal and unequal cluster sizes. Through comprehensive simulation experiments, we assess the accuracy and precision of PLE estimates in terms of parameter estimation, standard errors, and hypothesis testing. Our findings provide insights into the efficiency of Restricted Pseudo Likelihood Estimation (RPLE) in balanced and unbalanced clustered binary data models. The results highlight the advantages and limitations of PLE in different scenarios, aiding researchers in selecting appropriate modeling approaches for their specific data characteristics. The results can guide researchers in making informed decisions regarding the selection and application of PLE in their own studies, ultimately enhancing the validity and reliability of statistical analyses in the presence of clustered binary data.