<DIV align=left> 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 Education. The anonymous double-blind peer review by the two independent reviewers is applied to all the papers. The purposes of Biometrical Letters are: <UL> <LI>publishing papers dealing with various aspects of the analysis and interpretation of results from biometrical experiments, using mathematical and statistical methods; </LI> <LI>promoting and extending the use of statistical and mathematical methods in the principal disciplines of life sciences by reporting on the development and application of these methods; </LI> <LI>presenting statistical and mathematical tools useful in biometry. Methodological developments should be motivated by interesting problems from life sciences, applied or applicable; </LI> <LI>publishing review papers and papers presenting practical use of various methods of data analysis and statistical inference. </LI></UL> The core of most Biometrical Letters articles is statistical inference that sets scientific or policy objectives, motivates methodological development and demonstrates the operation of new methods. The paper should include a description of the biometrical problem and a section detailing the application of the new methodology. The Journal welcomes the submission of manuscripts from bioscience, mathematical and statistical theory, biology, genetics, medical statistics, agriculture, forestry, ecology, environmental sciences, biometrics and clinical trials. Case studies and articles on the use and development of statistical software are also welcome. Rejection Rate <UL> <LI>20% </LI></UL> Archiving Sciendo archives the contents of this journal in <A href="https://www.portico.org/">Portico</A> - digital long-term preservation service of scholarly books, journals and collections. Plagiarism Policy The editorial board is participating in a growing community of <A href="https://www.crossref.org/services/similarity-check/">Similarity Check System's</A> users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. </DIV>

The Journal of Polish Biometric Society

Biometrical Letters

<abstract><title style='display:none'>Summary</title>Inspired by the <bold>MaCzek</bold> Visual Basic program we pprovide an R package, <bold>RMaCzek</bold>, that produces Czekanowski’s diagrams. Our package permits any seriation and distance method the user provides. In this paper we focus on the “OLO” and “QAP_2SUM” methods from the <bold>seriation</bold> package. We illustrate the possibilities of our package with three anthropological studies, one socioeconomic study and a phylogenetically motivated simulation study.</abstract>

Summary

Department of Computer and Information Science

Keywords

<article-title>“Old Techniques for New Times”: the RMaCzek package for producing Czekanowski’s diagrams</article-title>

“Old Techniques for New Times”: the RMaCzek package for producing Czekanowski’s diagrams

<abstract><title style='display:none'>Summary</title>The aim of this paper is to study the association between two random vectors related to two groups of characteristics. To analyze the multivariate association, the <italic>ρV</italic> coefficient and distance correlation are used. Two methods (classical and recent) are compared and illustrated with real data.</abstract>

Department of Mathematical and Statistical Methods

<article-title>Application of the <italic>ρV</italic> coefficient and distance correlation to the analysis of multivariate association</article-title>

Application of the  coefficient and distance correlation to the analysis of multivariate association

<abstract><title style='display:none'>Summary</title>The Cobb angle is calculated in the coronal plane, irrespective of vertebral rotation, lordokyphosis and local wedge properties of individual verte-brae other than the end plates used for the measurement. Rigorous three-dimensional generalizations of the Cobb angle are complicated for at least two reasons. Firstly, the vertebral column is segmented, not continuous, making the choice of rigorous model ambiguous. Secondly, there exists an inherent curvature (in terms of thoracic kyphosis and lumbar lordosis) that may be considered physiologically healthy or ’normal’. When attempting to find a three-dimensional deviation measure, such normal sagittal curvature must be compensated for.In this paper we introduce a three-dimensional local deformation parameter (which we call the <italic>local effective deformation</italic>) motivated by both biomechanics and the basic theory of spatial curves, and simultaneously introduce a technical procedure to estimate the parameter from CT scans using MPR (multi-phase reconstruction) in PACS (IDS-7). A detailed description of the proposed modelling of vertebral column deformation is given, together with a stepwise procedure to estimate the three-dimensional deformation (in terms of local effective deformation). As a <italic>deformation measure</italic> it requires knowledge about the natural healthy kypholordosis. A method is described by which such knowledge may be incorporated in future work.</abstract>

Department of Mathematics and Mathematical Statistics

Department of Biomedical and Clinical Sciences, Division of Surgery, Orthopaedics and Oncology

<article-title>Defining the effective deformation of the vertebral column</article-title>

Defining the effective deformation of the vertebral column

{"article-title":"Defining the effective deformation of the vertebral column"}

<abstract><title style='display:none'>Summary</title>This paper provides estimation and hypothesis testing procedures for experiments in split-plot designs. These experiments have been shown to have a convenient orthogonal block structure when properly randomized. Due to this property, the analysis of experimental data can be carried out in a relatively simple manner. Relevant simplification procedures are indicated. According to the adopted approach, the analysis of variance and hypothesis testing procedures can be performed directly, rather than by combining the results of analyses based on some stratum submodels. The practical application of the presented theory is illustrated by examples of real experiments in appropriate split-plot designs. The present paper is the fourth in the planned series of publications on the analysis of experiments with orthogonal block structure.</abstract>

<article-title>On a new approach to the analysis of variance for experiments with orthogonal block structure. IV. Experiments in split-plot designs</article-title>

On a new approach to the analysis of variance for experiments with orthogonal block structure. IV. Experiments in split-plot designs

<abstract><title style='display:none'>Summary</title>We consider a new method of constructing non-orthogonal (incomplete) split-split-plot designs (SSPDs) for three (<italic>A</italic>, <italic>B</italic>, <italic>C</italic>) factor experiments. The final design is generated by some resolvable incomplete block design (for the factor <italic>A</italic>) and by square lattice designs for factors <italic>B</italic> and <italic>C</italic> using a modified Kronecker product of those designs (incidence matrices). Statistical properties of the constructed designs are investigated under a randomized-derived linear model. This model is strictly connected with a four-step randomization of units (blocks, whole plots, subplots, sub-subplots inside each block). The final SSPD has orthogonal block structure (OBS) and satisfies the general balance (GB) property. The statistical analysis of experiments performed in the SSPD is based on the analysis of variance often used for multistratum experiments. We characterize the SSPD with respect to the stratum efficiency factors for the basic estimable treatment contrasts. The structures of the vectors defining treatment contrasts are also given.</abstract>

<article-title>Constructing non-orthogonal split-split-plot designs using some resolvable block designs</article-title>

Constructing non-orthogonal split-split-plot designs using some resolvable block designs

<abstract><title style='display:none'>Summary</title>This paper focuses on pragmatic competence development in second or foreign language learners. In particular, it attempts to fill the significant research gap in measuring change in pragmatic competence and capturing pragmalinguistic and sociopragmatic development over time. The paper proposes an innovative approach by applying a logistic model with multinomial distribution for measuring change in InterLanguage Pragmatics Research (ILP). Applied in the field of pragmatics, this statistical tool offers a comprehensive and flexible approach to modelling relations between independent and dependent variables in ILP research. The model is tested in a longitudinal study of Polish undergraduate students learning English, and specifically in the way they formulate requests by means of requestive directness strategies. The paper concludes that, regardless of time elapsing, the factors <italic>P</italic> (power distance) and <italic>D</italic> (social distance) have a highly significant influence on the use of requestive directness strategies by Poles learning EFL. Furthermore, the analysis indicates that the pragmatic output of Poles learning EFL is dependent on one more independent variable: the estimation of future social distance (<italic>F</italic>).</abstract>

Department of Languages and Intercultural Studies

<article-title>Measuring change in longitudinal research on pragmatic competence: A multinomial logistic model</article-title>

Measuring change in longitudinal research on pragmatic competence: A multinomial logistic model

<abstract><title style='display:none'>Summary</title>The evaluation of sugar beet genotypes under different climate conditions is a principal goal of breeding programs. In most studies, environment has a high influence on the qualitative and quantitative traits of sugar beet. Therefore, data collected from different environments may contribute to more accurate genotype selection. In this study, the effect of different environments on sugar beet genotypes’ performance was evaluated using a meta-analysis method based on Hedges’ technique. Data were collected from 149 trials conducted in twelve regions in Iran over 15 years (2003–18). For all trials, the value of the traits was weighted, and subsequently the effect size, reaction ratio and confidence interval were estimated. Among the studied environments, Khoy had a positive effect on root yield, sugar content, sugar yield and white sugar yield. As could be expected, the effect of environment on final yield formation was high, so that the Shiraz environment had a negative effect on root yield and sugar yield. Overall, the ranking of environments based on the meta-analysis results was quite different from that obtained by comparison of mean results.</abstract>

<article-title>A meta-analysis of genotype × environment interaction on sugar beet performance</article-title>

A meta-analysis of genotype × environment interaction on sugar beet performance

{"article-title":"A meta-analysis of genotype × environment interaction on sugar beet performance"}

<abstract><title style='display:none'>Summary</title>The normal distribution is considered to be one of the most important distributions, with numerous applications in various fields, including the field of agricultural sciences. The purpose of this study is to evaluate the most popular normality tests, comparing the performance in terms of the size (type I error) and the power against a large spectrum of distributions with simulations for various sample sizes and significance levels, as well as through empirical data from agricultural experiments. The simulation results show that the power of all normality tests is low for small sample size, but as the sample size increases, the power increases as well. Also, the results show that the Shapiro–Wilk test is powerful over a wide range of alternative distributions and sample sizes and especially in asymmetric distributions. Moreover the D’Agostino–Pearson Omnibus test is powerful for small sample sizes against symmetric alternative distributions, while the same is true for the Kurtosis test for moderate and large sample sizes.</abstract>

Department of Statistics and Actuarial-Financial Mathematics, Laboratory of Statistics and Data Analysis

Department of Crop Science, Laboratory of Plant Breeding and Biometry

<article-title>Comparative evaluation of goodness of fit tests for normal distribution using simulation and empirical data</article-title>

Comparative evaluation of goodness of fit tests for normal distribution using simulation and empirical data

<abstract><title style='display:none'>Summary</title>A field study was conducted at the Department of Agronomy of Poznań University of Life Sciences to determine the effect of the depth of NP fertilizer application in maize cultivation on the dynamics of initial maize growth, expressed in dry matter of a single plant at two juvenile maize stages. The adopted assumptions were verified on the basis of a four-year field experiment using four depths of NP fertilizer application, two nitrogen fertilizers and two nitrogen dose application dates. Thermal conditions in the early maize growing season had a significant effect on maize response to the depth of application of a phosphorus starting dose. Row fertilization (regardless of the depth of fertilizer application) was more effective than broadcast fertilization at both studied developmental stages.</abstract>

<article-title>Assessment of the impact of NP fertilizer application depth on the rate of initial dry matter accumulation of maize (<italic>Zea mays</italic> L.)</article-title>

Assessment of the impact of NP fertilizer application depth on the rate of initial dry matter accumulation of maize ( L.)

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Editor-in-Chief Stanisław Mejza, Poznan University of Life Sciences ul. Wojska Polskiego 28, PL-60-637 Poznań, Poland e-mail: <A href="mailto:smejza@up.poznan.pl">smejza@up.poznan.pl</A> Maria Kozłowska, Poznan University of Life Sciences ul. Wojska Polskiego 28, PL-60-637 Poznań, Poland e-mail: <A href="mailto:markoz@up.poznan.pl">markoz@up.poznan.pl</A> Co-Editors Jerzy Moczko, Poznan University of Medical Sciences ul. Dąbrowskiego 79, PL-60-529 Poznań, Poland e-mail: <A href="mailto:jmoczko@amp.edu.pl">jmoczko@amp.edu.pl</A> Wiesław Mądry, Warsaw University of Life Sciences ul. Nowoursynowska 159, PL-02-776 Warszawa, Poland e-mail: <A href="mailto:wieslaw.madry@omega.sggw.waw.pl">wieslaw.madry@omega.sggw.waw.pl</A> Paulo Canas Rodrigues, Federal University of Bahia, Av. Adhemar de Barros, 40.170-110 Salvador, BA, Brazil, email: <A href="mailto:paulocanas@gmail.com">paulocanas@gmail.com</A> Editorial Board Are Aastveit (Norwegian University of Life Sciences, Aas, Norway), Anthony C. Atkinson (London School of Economics, UK), Rosemary A. Bailey (University of St Andrews, Scotland) Tadeusz Caliński (Poznań University of Life Sciences, Poznań, Poland), Janusz Gołaszewski (University of Warmia and Mazury, Olsztyn, Poland), Zofia Hanusz (University of Life Sciences, Lublin, Poland), Chihiro Hirotsu (Meisei University, Tokyo, Japan), Christos Kitsos (Technological Educational Institute of Athens, Greece), Kristian M. Kristensen (Aarhus University, Aarhus, Denmark), Shinji Kuriki (Osaka Prefecture University, Osaka, Japan), Victor Leiva (Pontificia Universidad Católica de Valparaíso, Chile), Tadeusz Łuczkiewicz (Poznań University of Life Sciences, Poznań, Poland), Iwona Mejza (Poznań University of Life Sciences, Poznań, Poland), Joao T. Mexia (New University of Lisboa, Portugal), Amilcar Oliveira (Universidade Aberta, Lisboa, Portugal), Teresa A. Oliveira (Universidade Aberta, Lisboa, Portugal), Dulce G. Pereira (University of Evora, Evora, Portugal), Christel Richter (Humboldt-Universitat zu Berlin, Germany), Zbigniew Sobek (Poznań University of Life Sciences, Poznań, Poland), Milan Stehlik (Johannes Kepler University Linz, Austria). Language Editors John Catlow, Adam Mickiewicz University, Poznań, Poland /UK Publisher De Gruyter Poland Bogumiła Zuga 32A Str. 01-811 Warsaw, Poland T: +48 22 701 50 15

<DIV align=left> Please submit your manuscripts to Biometrical Letters via email to: <A href="mailto:biometrical.letters@up.poznan.pl">biometrical.letters@up.poznan.pl</A></DIV>

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