<abstract><title style='display:none'>Abstract</title> Two very well-known tests for normality, the Kolmogorov-Smirnov and the Shapiro- Wilk tests, are considered. Both of them may be normalized using Johnson’s (1949) SB distribution. In this paper, functions for normalizing constants, dependent on the sample size, are given. These functions eliminate the need to use non-standard statistical tables with normalizing constants, and make it easy to obtain p-values for testing normality.</abstract>

Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality

<abstract><title style='display:none'>Summary</title> Economic threshold level (ETL) is an important component in pest management and control. Usually, it is determined by the grower/technologist utilizing his experience on a crop; however, for cereals the values of these indices are available. Knowledge of ETL helps reduce crop loss (and ensure less pesticide application), and as a consequence, profit is increased. Also substantial knowledge is required on the dynamics of the pest population, in order to determine the density at which the economic injury level (EIL) may be prevented (Weersink et al. 1991). This paper is devoted to the development of an analytical method (probabilistic) for determination of ETL, which is defined as the density at which control measures should be determined to prevent an increasing pest population from reaching the economic injury level. A method to model the dynamics of the pest population is also proposed. The above method is demonstrated on a real life data set on pest (whitefly) incidence on betelvine, obtained from an experiment designed for that purpose.</abstract>

Former Dean, Post Graduate Studies and Professor of Agricultural Statistics, Bidhan Chandra Krishi Viswavidyalaya, Faculty of Agriculture, Mohanpur, Nadia, West Bengal, 741252, India

Uttar Banga Krishi Viswavidyalaya, Department of Agricultural Statistics, Pundibari, Coochbehar, West Bengal, 736165, India

Uttar Banga Krishi Viswavidyalaya, Regional Research Sub Station, Malda, West Bengal, 732203, India Uttar Banga Krishi Viswavidyalaya, Regional Research Sub Station, Malda, West Bengal, 732203, India

On determination of ETL – a distributional approach

<abstract><title style='display:none'>Summary</title>We develop a simple method that completely eliminates the specification error and spurious relationships in regression. Furthermore, we introduce a stronger test of causality. We apply our method to oil prices.</abstract>

A simple solution to the specification error

<abstract><title style='display:none'>Summary</title> To model cross-sectional growth data the LMS method is widely applied. In this method the distribution is summarized by three parameters: the Box-Cox power that converts outcome to normality (L); the median (M); and the coeficient of variation (S).Here, we propose an alternative approach based on fitting finite mixture models with several components which may perform better than the LMS method in case the data show an unusual distribution. Further, we explore fixing the weights of the mixture components in contrast to the standard approach where weights are estimated. Having fixed weights improves the speed of computation and the stability of the solution. In addition, fixing the weights provides almost as good a fit as when the weights are estimated. Our methodology combines Gaussian mixture modelling and spline smoothing. The estimation of the parameters is based on the joint modelling of mean and dispersion.We illustrate the methodology on the Fourth Dutch Growth Study, which is a cross-sectional study that contains information on the growth of 7303 boys as a function of age. This information is used to construct centile curves, so-called growth curves, which describe the distribution of height as a smooth function of age. Further, we analyse simulated data showing a bimodal structure at some time point.In its full generality, this approach permits the replacement of the Gaussian components by any parametric density. Further, different components of the mixture can have a diferent probabilistic (multivariate) structure, allowing for censoring and truncation. </abstract>

Department of Biostatistics, Erasmus MC, P.O. Box 2040, 3000 CA Rotterdam, Netherlands

Catholic University of Leuven, L-Biostat, U.Z. St. Rafael, Kapucijnenvoer 35, 3000 Leuven, Belgium

Finite mixture models with fixed weights applied to growth data

<abstract><title style='display:none'>Summary</title> This paper deals with the problems of selection in the early stages of a breeding program. During the improvement process, it is not possible to use an experimental design that satisfies the requirement of replicating all the treatments, because of the large number of genotypes involved, the small amount of seed and the low availability of resources. Hence unreplicated designs are used. To control the real or potential heterogeneity of experimental units, control (check) plots are arranged in the trial. There are many methods of using the information resulting from check plots. All of the usually applied adjusting methods for unreplicated experiments are appropriate for some specific structure of soil fertility. Their disadvantage is the fact that, before and also after the experiment, we usually do not know what a kind of soil structure is present in the experiment. Hence we cannot say which of the existing methods is appropriate for a given experimental situation. The method of inference presented below avoids this disadvantage. It is always appropriate, because of the fact that a trend of soil variability is identified and estimated. In the paper the main tool used to explore this information will be based on a response surface methodology. To begin with we will try to identify a response surface characterizing the experimental environments. We assume that observed yield (or another trait) results directly from two components, one of them due to soil fertility and the other due to the genotype effect. This means that difference between observed yield and forecast can be treated as the estimate of a genotype effect. The obtained response surface will then be used to adjust the observations for genotypes. Finally, the data so adjusted are used for inferences concerning the next stage of the breeding program. The theoretical considerations are illustrated with an example involving yields of spring barley.</abstract>

Check plots in field breeding experiments

<abstract><title style='display:none'>Summary</title> Classical canonical correlation analysis seeks the associations between two data sets, i.e. it searches for linear combinations of the original variables having maximal correlation. Our task is to maximize this correlation, and is equivalent to solving a generalized eigenvalue problem. The maximal correlation coefficient (being a solution of this problem) is the first canonical correlation coefficient. In this paper we propose a new method of constructing canonical correlations and canonical variables for a pair of stochastic processes represented by a finite number of orthonormal basis functions. </abstract>

Canonical correlation analysis for functional data

<abstract>
<title style='display:none'>Summary</title>
In this paper we consider issues related to the determination of chemical balance weighing designs satisfying the criterion of D-optimality. This problem is considered under the assumption that the measurements are equally positively correlated and they have the same variances. We answer the question of how to add four runs to a regular D-optimal chemical balance weighing design in order to obtain a highly D-efficient design. The problem formulated in this way leads to an extension of results contained in a previous paper in <italic>Biometrical Letters</italic>.
</abstract>

D-optimal chemical balance weighing designs with positively correlated errors: part III

<abstract>
<title style='display:none'>Summary</title>
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.
</abstract>

Survival Analysis of Covariates Influencing Breast Cancer Treatment: A Case Study of North Eastern Nigeria

<abstract>
<title style='display:none'>Summary</title>
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.
</abstract>

Cumulative ordinal quasi-symmetry model and its separation for square contingency tables with ordered categories

<abstract>
<title style='display:none'>Summary</title>
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.
</abstract>

Identifying the Risk Factors for Metabolic Syndrome in Bangladesh: Documented from a Nationwide Survey

<abstract>
<title style='display:none'>Summary</title>
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.
</abstract>

Modified deterministic modeling of Covid-19 in Nigeria: a case of a closed system

<abstract>
<title style='display:none'>Summary</title>
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.
</abstract>

Incompatibility of Model Specifications in Generalized Linear Models

<abstract><title style='display:none'>Abstract</title> The genotype by environment interaction (GEI)) has an influence on the selection and recommendation of cultivars. The aim of this work is to study the effect of GEI and evaluate the adaptability and stability of productivity (kg/ha) of nine maize genotypes using AMMI model (Additive Main effects and Multiplicative Interaction). The AMMI model is one of the most widely used statistical tools in the analysis of multiple-environment trials. It has two purposes, namely understanding complex GEI and increasing accuracy. Nevertheless, the AMMI model is a widely used tool for the analysis of multiple-environment trials, where the data are represented by a two-way table of GEI means. In the complete tables, least squares estimation for the AMMI model is equivalent to fitting an additive two-way ANOVA model for the main effects and applying a singular value decomposition to the interaction residuals. It assumes equal weights for all GEI means implicitly. The experiments were conducted in twenty environments, and the experimental design was a randomized complete block design with four repetitions. The AMMI model identified the best combinations of genotypes and environments with respect to the response variable. This paper concerns a basic and a common application of AMMI: yield-trial analysis without consideration of special structure or additional data for either genotypes or environments.</abstract>

Programa de Pos-graduação em Estatística e Experimentação Agronômica, Universidade de São Paulo, Brazil

Departamento de Estatística, Universidade Federal de Mato Grosso, Av. Fernando Corrêa da Costa, no 2367 - Bairro Boa Esperança. 78060-900, Cuiabá - MT - Brazil

Departamento de Estatística, Universidade Federal de Uberlândia, MG, Brazil

Departamento de Ciências Exatas, Universidade de São Paulo, Brazil

Statistical analysis of yield trials by AMMI analysis of genotype × environment interaction

<abstract><title style='display:none'>Summary</title>The presence of genotype-environment interaction (GEI) influences production making the selection of cultivars in a complex process. The two most used methods to analyze GEI and evaluate genotypes are AMMI and GGE Biplot, being used for the analysis of multi environment trials data (MET). Despite their different approaches, both models complement each other in order to strengthen decision making. However, both models are based on biplots, consequently, biplot-based interpretation doesn’t scale well beyond two-dimensional plots, which happens whenever the first two components don’t capture enough variation. This paper proposes an approach to such cases based on cluster analysis combined with the concept of medoids. It also applies AMMI and GGE Biplot to the adjusted data in order to compare both models. The data is provided by the International Maize and Wheat Improvement Center (CIMMYT) and comes from the 14th Semi-Arid Wheat Yield Trial (SAWYT), an experiment concerning 50 genotypes of spring bread wheat (Triticum aestivum) germplasm adapted to low rainfall. It was performed in 36 environments across 14 countries. The analysis provided 25 genotypes clusters and 6 environments clusters. Both models were equivalent for the data’s evaluation, permitting increased reliability in the selection of superior cultivars and test environments.</abstract>

AMMI and GGE Biplot for genotype <italic>×</italic> environment interaction: a medoid–based hierarchical cluster analysis approach for high–dimensional data

<abstract><title style='display:none'>Summary</title> Bayesian inference affords scientists powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of the hesitance to adopt this approach may stem from an unfamiliarity with the computational tools necessary for computing Bayes factors. Previous work has shown that closed-form approximations of Bayes factors are relatively easy to obtain for between-groups methods, such as an analysis of variance or t-test. In this paper, I extend this approximation to develop a formula for the Bayes factor that directly uses information that is typically reported for ANOVAs (e.g., the F ratio and degrees of freedom). After giving two examples of its use, I report the results of simulations which show that even with minimal input, this approximate Bayes factor produces similar results to existing software solutions.</abstract>

Computing Bayes factors to measure evidence from experiments: An extension of the BIC approximation

<abstract><title style='display:none'>SUMMARY</title> The purpose of this paper is to apply results on weighing designs to the setting of 2m factorial designs. Using weighing designs, we give some proposals for experimental plans. Relevant counterexamples are indicated. Also the results of a simulation study on the existence of weighing designs are presented.</abstract>

Some applications of weighing designs

<abstract><title style='display:none'>Summary</title> The Birnbaum-Saunders (BS) model is a life distribution that has been widely studied and applied. Recently, a new version of the BS distribution based on extreme value theory has been introduced, named the extreme value Birnbaum-Saunders (EVBS) distribution. In this article we provide some further details on the EVBS models that can be useful as a supplement to the existing results. We use these models to analyse real survival time data for patients treated with alkylating agents for multiple myeloma. This analysis allow us to show the adequacy of these new statistical distributions and identify them as models useful for medical practitioners in order to predict survival times for such patients and evaluate changes in their treatment dose.</abstract>

Universidade de Lisboa, DEIO, CEAUL and FCUL, Portugal

Departamento de Matemática, Universidade do Minho, Portugal

Departamento de Estadística, Universidad de Valparaíso, Chile

The extreme value Birnbaum-Saunders model, its moments and an application in biometry

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Biometrical Letters

The Journal of Polish Biometric Society

 Biometrical Letters is the official journal of the Polish Biometric Society, founded in 1964, now published with the financial support of the Ministry of Science and Higher...

MNiSW

 Biometrical Letters is the official journal of the Polish Biometric Society, founded in 1964, now published with the financial support of...