rss_2.0Sciendo RSS Feed for Biometrical Lettershttps://sciendo.com/journal/BILEhttps://www.sciendo.comhttps://sciendo-parsed.s3.eu-central-1.amazonaws.com/6470d51071e4585e08aa6aac/cover-image.jpghttps://sciendo.com/journal/BILE140216https://sciendo.com/article/10.2478/bile-2024-0011<abstract><title style='display:none'>Abstract</title> <p>The differentiation between age classes of Scots pine (<italic>Pinus sylvestris </italic>L.) was analyzed with regard to the five-year increment of seven traits: height growth (zh5), diameter growth at breast height (zd5), cross-sectional area growth at breast height (zg5), volume growth (zv5), volume growth intensity coefficient (i5), and slenderness (s). Measurements were made in five periods for 24-year-old trees and six periods for 33-year-old trees, all growing in fresh mixed coniferous forest sites. Repeated measures data analysis was conducted separately for all traits. Multivariable functional data analysis (FDA) was proposed to compare age classes of trees. The functional variables which resulted from this analysis can be used, as data, in many analyses (designate functions representing each of trees, FPCA – functional principal component analysis, FLDC – discriminant analysis, permutation analysis of variance). The results of the above analyses revealed significant differences between age groups. Furthermore the functions and FPCA were used to detect outliers. This procedure had not previously been used for such a purpose. FPCA explained 55% of the total variance, with the first two components clearly separating the groups. The study showed that 33-year-old trees exhibit stable growth, while 24-year-old trees show greater variability, highlighting the impact of age on growth dynamics. Permutation analysis of variance confirmed significant growth differences between the groups. The findings highlight the importance of age as a factor influencing tree growth and demonstrate the effectiveness of the multivariable FDA approach for analyzing such data.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2024-00112025-01-09T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2024-0010<abstract><title style='display:none'>Abstract</title> <p>One classic definition of ecology is that it is the science that studies the distribution and abundance of biotic components and their relationship with abiotic components. The use of statistical tools is very important for understanding ecology, especially the distribution and abundance of biotic components. The classic statistical viewpoint was that an ecological community (an interaction of different species in defined time and space) has a determined structure due to biotic and abiotic interactions. Nevertheless, this classic viewpoint has the risk of proneness to type I errors or “false positives”. In this situation, null models were proposed that have the premise that community ecology is random, meaning the absence of structure, and the null hypothesis for these models is the absence of regular structured patterns. The present study is a review of null models and their application to aquatic environments. These null models include three main models: for species co-occurrence, asserting that species associations are random; for size overlap, asserting that the size structure of species in the community is random, as a strategy for use of ecological niche; and for niche overlap, asserting that species in a community can share a defined ecological niche with consequent interspecific competition.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2024-00102025-01-09T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2024-0012<abstract><title style='display:none'>Abstract</title> <p>This study investigates age-related changes in visuomotor functions by analyzing gaze path velocity (pixels per second). The research included 50 participants aged 7 to 83 years, divided into four groups: children (7–14 years), young adults (19–39 years), middle-aged adults (45–58 years), and older adults (62–83 years). Eye movements were tracked during a visual scanning task. Statistical analyses, including one-way ANOVA, post-hoc Tukey HSD tests, and effect size calculations (η&amp;sup2;), evaluated group differences.</p> <p>Significant differences in gaze path velocity were found across groups. Children had an average velocity of 150.44 px/s, serving as a baseline. Young adults showed a substantial increase (365.97 px/s), and middle-aged adults reached the highest velocities (423.48 px/s), indicating peak visuomotor function. Older adults demonstrated a decline (256.15 px/s), reflecting age-related neuroplasticity reductions.</p> <p>A nonlinear trajectory, modeled by a second-degree polynomial equation (R&amp;sup2; = 0.89), peaked at age 46.3 years (Vmax = 406.03 px/s). This pattern reflects rapid growth in childhood, stabilization in middle age, and decline in later life.</p> <p>The findings underscore the importance of age-specific interventions, optimized user interfaces, and neurodegenerative diagnostics. Future studies should expand on sample size and consider health and lifestyle factors to enhance understanding of visuomotor variability.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2024-00122025-01-09T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2024-0009<abstract><title style='display:none'>Abstract</title> <p>Conditional and marginal analyses are widely used in clinical studies. However, the results of these two methods may occasionally contradict each other. For instance, marginal analysis may show that the treatment group outperforms the control group, while conditional analysis may suggest the opposite. We examine the causes of this inconsistency and provide general sufficient conditions for ensuring consistency.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2024-00092025-01-09T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2024-0008<abstract><title style='display:none'>Abstract</title> <p>The Spearman rank correlation coefficient is a non-parametric (distribution-free) rank statistic proposed by Charles Spearman as a measure of the strength of the relationship between two variables. It is a measure of a monotonic relationship that is used when the distribution of the data makes Pearson’s correlation coefficient undesirable or misleading. The Spearman coefficient is not a measure of the linear relationship between two variables. It assesses how well an arbitrary monotonic function can describe the relationship between two variables, without making any assumptions about the frequency distribution of the variables. Unlike Pearson’s product-moment (linear) correlation coefficient, it does not require the assumption that the relationship between variables is linear, nor does it require that the variables be measured on interval scales; it can be applied to variables measured at the ordinal level. The purpose of this study is to compare the values of Pearson’s product-moment correlation coefficient and Spearman’s rank correlation coefficient and their statistical significance for six morpho-anatomical traits of <italic>Pinus sylvestris</italic> L. (original – for Pearson’s coefficient, and ranked – for Spearman’s coefficient) estimated from all observations, object means (for trees), and medians. The results show that the linear and rank correlation coefficients are consistent (as to direction and strength). In cases of divergence in the direction of correlation, the correlation coefficients were not statistically significant, which does not imply consistency in decision-making. Estimation of correlation coefficients based on medians is robust to outlier observations and factors that linear correlation is then very similar to rank correlation.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2024-00082025-01-09T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2024-0007<abstract><title style='display:none'>Abstract</title> <p>In the analysis of square contingency tables, which are two-way contingency tables in which the row and column variables consist of the same classification, statistical models regarding the symmetry of row and column variables are often used rather than the independence. This study proposes an index for measuring the degree of departure from the anti-sum-symmetry model. The proposed index is constructed using the Kullback–Leibler divergence. The anti-sum-symmetry model is useful to evaluate whether symmetric and asymmetric structures exist with respect to the anti-diagonal of the table. We derive the plug-in estimator and large-sample confidence interval for the proposed index. The usefulness of the proposed index is demonstrated by applying it to real data.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2024-00072025-01-09T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2024-0003<abstract> <title style='display:none'>Summary</title> <p>The choice of regression models can vary depending on a study’s objectives and the characteristics of the dataset. Yet it is crucial to recognize that the properties of conditional expectation impose a natural consistency requirement on the formulation of these models. This paper endeavors to demonstrate that, even under the most favorable assumptions concerning the covariates’ structure, inconsistent specifications can arise in generalized linear models, particularly when nonlinear link functions are employed.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2024-00032024-07-29T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2024-0005<abstract> <title style='display:none'>Summary</title> <p>In this research a closed system of testing and vaccination is considered using modified deterministic modeling of Covid-19 cases in Nigeria. A disease infection flow transmission diagram was constructed for a model with nine population compartments, represented as SNSVETeQIAISILR, and the assumptions governing the model were presented for the study. A set of nonlinear deterministic differential equations was obtained and tested for positive invariance, positivity of the system solution, boundedness of solution of the equation system, equilibrium point of system stability, endemic equilibrium point, and existence of endemic global stability. The simulated results showed that the equilibrium stability point of the system exists at a basic reproduction number Ro of 0.0000295, and the model estimates show a positive contribution of population recruitment rate (Λ), transmission rate from infected (asymptomatic – β₁, symptomatic – β₂, undetected but exposed - ф) population, testing rate (βV), (σ), population exposure, exposed tested becoming infected (ρ), quarantine, and isolation to promoting the Covid-19 epidemic infection in Nigeria. Following the findings, the following are recommended: early closure of the country’s borders to check increasing recruitment rate, introduction of social distancing, wearing of nose &amp; mouth masks, early commencement of free testing for the disease (Covid-19), introduction of movement restrictions (close-down/lock-down), compulsory Covid-19 vaccination for every vulnerable person in the population, effective government quarantine and isolation (treatment) centers, and immediate engagement of both medical and non-medical researchers to find lasting solutions.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2024-00052024-07-29T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2024-0002<abstract> <title style='display:none'>Summary</title> <p>Metabolic syndrome is a complex of interrelated health conditions that pose a significant risk of developing cardiovascular disease, stroke, and type 2 diabetes. Resistance to insulin, genetic predisposition, high blood pressure, inflammation, and excess abdominal fat are the main stimuli of this syndrome. Metabolic syndrome is becoming more widespread due to fast and unplanned urbanization causing changes in lifestyle, such as poor dietary habits and sedentary behavior, that decrease the metabolic rate in the human body. A developing South Asian country like Bangladesh is most vulnerable to components of metabolic syndrome such as obesity, hypertension and diabetes. Consequently, it has become one of the major public health concerns. Prediction of disease status is a key component of community and health service policymaking. A nationally representative cross-sectional survey, the Bangladesh Demographic and Health Survey (BDHS), is used to find statistically significant variables for metabolic syndrome. BDHS datasets do not contain any direct data regarding metabolic syndrome. A binary variable is generated by utilizing the available data on blood pressure, blood glucose level, and body mass index (BMI). Overall, 34.33% of the population has metabolic syndrome. Primarily, bivariate analysis is performed using chi-square testing to find variables that are correlated with metabolic syndrome. Results of binary logistic analysis are presented in terms of coefficients and odds ratios (OR) with 95% confidence intervals (CI). Age, gender, education, division (province), occupation type, and wealth index are found to be important covariates for the syndrome. Age especially is seen as one of the most influential factors, since the prevalence of metabolic syndrome is only 12.17% for the age group younger than 18 years, while for the group older than 65 years it is 62.18%. Residents of Barishal have the highest rate of metabolic syndrome (38.58%). The rate in the country’s capital Dhaka is 34.48%. Individuals whose employment primarily involves manual labor are 11.1% less likely to suffer from metabolic syndrome than those doing non-manual work.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2024-00022024-07-29T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2024-0006<abstract> <title style='display:none'>Summary</title> <p>This study deals with square contingency tables, which are two-way contingency tables in which the row and column variables consist of the same classification. When the categorical variables are grouped into ordered categories from quantitative variables by cut points, a score that approximates the distance between the midpoints of the quantitative scale categories may be used to reflect the characteristics of the data. As an asymmetry model based on scores, this study proposes the cumulative ordinal quasi-symmetry model and ordinal marginal homogeneity model based on cumulative probabilities. The asymmetric parameter in the proposed models would be useful for making inferences such as that a row variable is stochastically less than a column variable or vice versa. This study also gives a separation of the cumulative ordinal quasi-symmetry model, that is, the cumulative ordinal quasi-symmetry model holds if and only if both the cumulative quasi-symmetry and ordinal marginal homogeneity models hold. The usefulness of the proposed models and the proposed separation is demonstrated through real data analysis.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2024-00062024-07-29T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2024-0001<abstract> <title style='display:none'>Summary</title> <p>This study builds on previous research indicating that breast cancer survival time is influenced by several underlying factors. The study covered a period of 10 years from January 2012 to December 2022, and 140 cases were considered within the study cohort. The study considered breast cancer patients from North East Nigeria. The methodologies used are Cox hazard proportional regression and Kaplan–Meier analysis. The mean patient survival time is 592.2 days, with an average age of 44.61 years, average number of children of 5, and mean weight difference of 1.95 kg while on treatment. Kaplan-Meier analysis and the log rank test were used to investigate how the various covariates affect survival time, and it was found that age and family history have significant effects on the survival time in the studied population. The p-value of 0.04 for radiotherapy indicates statistical significance, in contrast to other treatment options such as surgery (p-value 0.7), targeted therapy (p-value 0.7), and chemotherapy (p-value 0.6). Residual diagnostic analysis with a component for assessment of Variance Inflation Factors (VIF) was used to detect multicollinearity among the independent variables. A total of 60 events (deaths) occurred within the study period with a concordance value of 0.73, which indicates a moderate level of agreement. This implies that the model’s predictions align reasonably well with the observed outcomes.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2024-00012024-07-29T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2023-0015<abstract> <title style='display:none'>Summary</title> <p>Starting from a simple Gauss–Markov model, this paper presents notes about criteria for the estimability of parametric functions of the vector of interest in linear models. The results obtained for the transformed models are compared with known results from the literature.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2023-00152023-12-29T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2023-0011<abstract> <title style='display:none'>Summary</title> <p>The theory of inequalities is an essential tool in all fields of the theoretical and practical sciences, especially in statistics and biometrics. Fujiwara’s inequality provides relationships between expected values of products of random variables. Special cases of this inequality include important classical inequalities such as the Cauchy–Schwarz and Chebyshev inequalities.</p> <p>The purpose of this article is to prove Fujiwara’s inequality in abstract probability spaces with more general assumptions for random variables than those associated with monotonicity as found in the literature. This newly introduced property of random variables will be called synchronicity. As a consequence, we obtain inequalities originated by Chebyshev, Hardy–Littlewood–Pólya and Jensen–Mercer under new conditions.</p> <p>The results are illustrated by some examples constructed for specific probability measures and specific random variables. In biometrics, the obtained inequalities can be used wherever there is a need to compare the characteristics of experimental data based on means or moments, and the data can be modeled using functions that are synchronous or convex.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2023-00112023-12-29T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2023-0009<abstract> <title style='display:none'>Summary</title> <p>Brain tumor is a very serious disease from which many people die every day. Appropriate early diagnosis is extremely important in treatment. In recent years, machine learning methods have come to the aid of doctors, allowing them to automate the process of brain tumor detection. It is a useful tool that can support doctors in their daily work. We consider here the use of machine learning methods to detect brain tumors based on magnetic resonance images. We use artificial neural networks to classify the images into those containing and those without a brain tumor. More specifically, we apply convolutional neural networks on appropriately transformed input data. The three proposed convolutional neural network models were created based on the pre-trained VGG19, DenseNet-121, and InceptionV3 networks, which achieved an accuracy of 92.59%, with areas under the ROC curve ranging from 0.95 to 0.96. The precision, sensitivity, and F1-score are also satisfactory and promising. These results are better than those for the models presented on the Kaggle platform.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2023-00092023-12-29T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2023-0014<abstract> <title style='display:none'>Summary</title> <p>Covariance matrices with a linear structure are widely used in multivariate analysis. The choice of covariance structure can be made from a set of possible linear structures. As a result, the most appropriate structure is determined by minimizing the discrepancy function. This paper is a continuation of previous work on identifying linear structures with an entropy loss function as a discrepancy function. We present extensive simulation studies on the correctness of identification with the assumed pentagonal banded Toeplitz structure.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2023-00142023-12-29T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2023-0013<abstract> <title style='display:none'>Summary</title> <p>A field experiment was carried out in the years 2017–2019 on the fields of the Experimental Station in Chrząstowo, belonging to the Research Centre for Cultivar Testing in Słupia Wielka. It was carried out for 3 years in the same split-plot design with 2 experimental factors in 3 field replicates. The following factors were studied: A – 1st order factor – maize variety: A1 – ES Bombastic (FAO 230-240) – single cross hybrid (SC), A2 – ES Abakus (FAO 230-240) – three-way cross hybrid (TC, stay-green), A3 – ES Metronom (FAO 240) – single cross hybrid (SC, stay-green + roots power). B – 2nd order factor – type of nitrogen fertilizer: B1 – control (without N application), B2 – ammonium nitrate, B3 – urea, B4 – ammonium nitrate + N-Lock, B5 – urea + N-Lock, B6 – Super N-46, B7 – UltraGran stabilo. In this study, we investigated whether there was a functional relationship between maize grain yield and ear number, TSW (thousand-seed weight), and seed number per ear. Additionally, we investigated whether there was a functional relationship between maize grain yield and ear number, TSW, and seed number per ear for each type of fertilization in a given study year, as well as for each type of fertilization regardless of year.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2023-00132023-12-29T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2023-0016<abstract> <title style='display:none'>Summary</title> <p>Covariance matrices with a linear structure are widely used in multivariate analysis. The choice of the most appropriate covariance structure can be made from a class of possible linear structures. Once we have made the choice, an important question is how we can estimate the covariance matrix for a given covariance structure. This article describes methods used to estimate the structured covariance matrix, and indicates the advantages and disadvantages of the selected methods.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2023-00162023-12-29T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2023-0010<abstract> <title style='display:none'>Summary</title> <p>This research fitted a discrete distribution for modeling count data. Specifically, Zero-Inflated Poisson (ZIP) regression was used to model plant protein consumption by 400 randomly sampled individuals in Wukari. The data was collected by questionnaire. The ZIP regression model was used based on its ability to model data with excess zeros present in the collected data. Variables considered and used for the analysis are Age, Body Mass Index, Blood Pressure, Occupation, Gender, Weight, Height, Body Reaction, and Consumption Class. The parameters of the ZIP model were estimated using the maximum likelihood estimation technique. The model was tested for Goodness of Fit (GoF) using deviance, scaled deviance, Pearson–<italic>χ</italic>² and scaled Pearson–<italic>χ</italic>² statistics. The results obtained showed that Age, Gender, and Reaction were significant at 5%, and the GoF tests revealed that the Zero-Inflated Poisson regression produces a good fit and is a good model for overcoming the overdispersion effect.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2023-00102023-12-29T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2023-0012<abstract> <title style='display:none'>Summary</title> <p>Some questions related to the problem of determining a chemical balance weighing design satisfying the criterion of D-optimality are considered. The theory is based on the assumption that the measurements are equally positively correlated and have the same variances. In this paper, we present a method of adding three measurements to a regular D-optimal chemical balance weighing designs to obtain a highly D-efficient chemical balance weighing design. The problem formulated in this way is an extension of results contained in a paper previously published in <italic>Biometrical Letters</italic>.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2023-00122023-12-29T00:00:00.000+00:00https://sciendo.com/article/10.2478/bile-2023-0008<abstract> <title style='display:none'>Summary</title> <p>In this paper, some qualitative behaviors of solutions for certain second-order nonlinear differential equation with damping and resonance effects are considered. By employing Lyapunov’s direct method, a complete Lyapunov function was used to investigate the stability of the system. Krasnoselskii’s fixed point theorem was used to establish sufficient conditions that guaranteed the existence and boundedness of a unique solution. The results show that the equilibrium point was asymptotically stable. Furthermore, a test for periodicity was conducted using the Bendixson criterion, and the results showed that the solution of the second-order nonlinear differential equation is aperiodic, which extends some results from the literature.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/bile-2023-00082023-12-29T00:00:00.000+00:00en-us-1