<abstract xmlns="http://www.w3.org/1999/xhtml">

This study proposes a new exponential sum-symmetry model for square contingency tables with same row and column ordinal classifications. In the existing exponential sum-symmetry (ESS) model, the probability that the sum of row and column levels is <italic>t</italic>, where the row level is less than the column level, is ∆<italic>t−</italic>2 times higher than the probability that the sum of row and column levels is <italic>t</italic>, where the row level is greater than the column level. On the other hand, in the proposed ESS model, the ratio of these two probabilities is ∆<italic>t/</italic>3. In other words, in the existing ESS model, the ratio of the two probabilities varies exponentially depending on the absolute gap between <italic>t</italic> and 2, while in the proposed ESS model, the ratio of the two probabilities varies exponentially depending on the relative gap between <italic>t</italic> and 3, although in both ESS models, the ratio of the two probabilities is ∆ when <italic>t</italic> is the minimum value (i.e., <italic>t</italic> = 3). Moreover, this study introduces a new decomposition theorem for the sum-symmetry model using the proposed ESS. The proposed decomposition theorem satisfies asymptotic equivalence for the test statistic.
</abstract>

Relative exponential sum-symmetry model and orthogonal decomposition of the sum-symmetry model for ordinal square contingency tables

<abstract xmlns="http://www.w3.org/1999/xhtml">

In general, varieties of any cultivated species can differ in many aspects. One of the desirable traits in breeding new varieties is high yield, which can be significantly reduced by plant diseases. This study is an extension of previous research about the resistance of seed pea lines to downy mildew, and provides an extended analysis of this type of experiment. The probability of a degree of infection is determined based on a logistic model with a multinomial distribution. In the analysis the impact of a fixed effect of variety and random environmental effects is considered. It is shown that the environmental effects (combinations of years and location – macro-environments) significantly influence the resistance to diseases, and the differences among environments are larger than the variability of differences among genotypes over all environments. For two types of soils (light and rich) the most resistant varieties, which are significantly different from the control variety, are indicated.
</abstract>

Department of Mathematical and Statistical Methods

Environmental impact on downy mildew infection for different pea varieties

<abstract xmlns="http://www.w3.org/1999/xhtml">

This paper describes an iterative analysis of incomplete genotype × environment data. <italic>L</italic><italic>2 environmental indices</italic> were introduced to enable the use of Joint Regression Analysis (JRA) in analyzing experiments with incomplete blocks. We now show how, once normality of yields is assumed, the introduction of L2 environmental indices provides a theoretical framework for Joint Regression Analysis. Using this framework, maximum likelihood estimators are obtained and likelihood ratio tests are derived. It is noted that the technique allows unequal weighting of data, and the special case of complete blocks is discussed.
</abstract>

Maximum Likelihood and L2 Environmental Indices in Joint Regression Analysis

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we present some new results regarding spring balance weighing designs. We consider issues with regard to conditions for the existence of optimal designs, and give examples of optimal designs.
</abstract>

Contribution to spring balance weighing designs

<abstract xmlns="http://www.w3.org/1999/xhtml">

The construction of incomplete split-block-plot (SBP) designs for three-factor experiments is investigated. A semi-Kronecker (Khatri–Rao) product of matrices is used in the construction procedure. With this method some generated designs are obtained where column treatments and subplot treatments are allocated in balanced square lattice designs, while row treatments are in a randomized complete block design. Experiments with an orthogonal block structure are considered. In this paper we consider designs which are generally balanced. This allows us to give the stratum efficiency factors for treatment combination contrasts in the proposed split-block-plot designs.
</abstract>

katarzyna.ambrozy.deregowska@up.poznan.pl

On a construction procedure for split-block-plot designs based on the Khatri–Rao product of incidence matrices

<abstract xmlns="http://www.w3.org/1999/xhtml">

The target of this paper is to offer a compact review of the so called distance methods in Statistics, which cover all the known estimation methods. Based on this fact we propose a new step, to adopt from Information Theory, the divergence measures, as distance methods, to compare two distributions, and not only to investigate if the means or the variances of the distributions are equal. Some useful results towards this line of thought are presented, adopting a compact form for all known divergence measures, and are appropriately analyzed for Biometrical, and not only, applications.
</abstract>

Department of Informatics and Computer Engineering

Department of Public and Community Health

Considering distance measures in Statistics

AHEAD OF PRINT

Volume 60 (2023): Issue 2 (December 2023)

Volume 60 (2023): Issue 1 (June 2023)

Volume 59 (2022): Issue 2 (December 2022)

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Volume 58 (2021): Issue 2 (December 2021)

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Volume 57 (2020): Issue 2 (December 2020)

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Volume 56 (2019): Issue 2 (December 2019)

Volume 56 (2019): Issue 1 (June 2019)

Volume 55 (2018): Issue 2 (December 2018)

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Volume 54 (2017): Issue 2 (December 2017)

Volume 54 (2017): Issue 1 (June 2017)

Volume 53 (2016): Issue 2 (December 2016)

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Volume 52 (2015): Issue 2 (December 2015)

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Volume 51 (2014): Issue 2 (December 2014)

Volume 51 (2014): Issue 1 (June 2014)

Volume 50 (2013): Issue 2 (December 2013)

Volume 50 (2013): Issue 1 (June 2013)

Volume 49 (2012): Issue 2 (December 2012)

Volume 49 (2012): Issue 1 (June 2012)

Biometrical Letters

 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:   publishing papers dealing with various aspects of the analysis and interpretation of results from biometrical experiments, using mathematical and statistical methods;  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;  presenting statistical and mathematical tools useful in biometry. Methodological developments should be motivated by interesting problems from life sciences, applied or applicable;  publishing review papers and papers presenting practical use of various methods of data analysis and statistical inference.   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   20%   Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's 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. 