<abstract><title style='display:none'>Summary</title> This paper discusses the problem of determining the number of observations necessary to apply the nonparametric Mann-Whitney test. We describe the method given by Noether (1987) for determining a sample size which guarantees that the Mann-Whitney test at a given significance level α has a predetermined power 1-β. The presented theory is tested by calculating the empirical power in computer simulations. The paper also raises the issue of the method of rounding the determined sample size to an even number when the sample is divided into two equinumerous subsamples.</abstract>

Sample size determination in the Mann–Whitney test

<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'>Abstract</title> In this study the Akaike information criterion for detecting outliers in a log-normal distribution is used. Theoretical results were applied to the identification of atypical varietal trials. This is an alternative to the tolerance interval method. Detection of outliers with the help of the Akaike information criterion represents an alternative to the method of testing hypotheses. This approach does not depend on the level of significance adopted by the investigator. It also does not lead to the masking effect of outliers.</abstract>

The use of outlier detection methods in the log-normal distribution for the identification of atypical varietal experiments

<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>
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>.
</abstract>

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

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

Existence, uniqueness, boundedness and stability of periodic solutions of a certain second-order nonlinear differential equation with damping and resonance effects

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

Zero-Inflated Poisson Regression Modeling of Plant Protein Consumption

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

Functional relationships between yield of maize (<italic>Zea mays</italic> L.) and its components

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

Estimation methods for a linearly structured covariance matrix

<abstract>
<title style='display:none'>Summary</title>
Oat is a grain in high demand, due to its physiological and nutritional attributes as a functional food. Oat is rich in <italic>β−</italic>glucans, and high in tocopherol and other dietary fibre components. It is also used for forage, fodder, chaff and as a major component of infant foods. In the present study, oat yields from six experimental stations in south-western Poland, obtained in 2019–2022, were analysed using three different linear mixed models that can be associated with three different stabilities. It is shown that the genotype Perun had the highest mean yield among the tested genotypes, while the genotype Armani was the most stable. Armani and Pablo had the lowest values of the GSI index, making them the most favourable genotypes for cultivation in that region.
</abstract>

Stability analysis of spring oat genotypes in south-west Poland

<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>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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