<abstract xmlns="http://www.w3.org/1999/xhtml"> Sometimes feature representations of measured individuals are better described by spherical coordinates than Cartesian ones. The author proposes to introduce a preprocessing step in LDA based on the arctangent transformation of spherical coordinates. This nonlinear transformation does not change the dimension of the data, but in combination with LDA it leads to a dimension reduction if the raw data are not linearly separated. The method is presented using various examples of real and artificial data.</abstract>

Directional representation of data in Linear Discriminant Analysis

<abstract xmlns="http://www.w3.org/1999/xhtml"> 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 xmlns="http://www.w3.org/1999/xhtml"> 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 xmlns="http://www.w3.org/1999/xhtml"> There are several statistics for testing hypotheses concerning the independence of the distributions represented by two rows in contingency tables. The most famous are Rao′s score, the Wald and the likelihood ratio tests. A comparison of the power of these tests indicates the Wald test as the most powerful. </abstract>

Power comparison of Rao′s score test, the Wald test and the likelihood ratio test in (2xc) contingency tables

<abstract xmlns="http://www.w3.org/1999/xhtml"> Variability among experimental plots may be a relevant problem in field genotype experiments, especially when a large number of entries are involved. Four field trials on 24 durum wheat genotypes were conducted in 2013/14 in order to evaluate the efficiency of Incomplete Block, Alpha and Augmented designs in comparison with the traditional Randomized Complete Block Design (RCBD). The results showed that the RCBD can be replaced by an Alpha design, which provides better control of variability among the experimental units when the number of treatments to be tested in an experiment exceeds twenty. The ranking of the genotypes across the four designs was not constant.</abstract>

Faculty of Crop Science, Laboratory of Plant Breeding and Biometry, Agricultural University of Athens, 11855, Athens, Greece

Department of Mathematics, National Technical University of Athens, Zografou 15773, Athens, Greece

Evaluation of experimental designs in durum wheat trials

<abstract xmlns="http://www.w3.org/1999/xhtml"> The usability of various single extractors in the chemical analysis of composts was evaluated using principal component analysis. Ten different single extractors were used to determine the contents of microelements obtained in the chemical extraction of four different composts. It was found that principal component analysis is a satisfactory statistical method enabling the comparison of different solutions in terms of efficiency of extraction of microelements from composts of different composition. The results showed that 1mol dm-3 HCL and 10% HNO3 solutions had the highest extraction strength, and 0.01mol dm-3 CaCl2 and 1mol dm-3 NH4NO3 the lowest.</abstract>

Department of Soil Science and Land Protection, Poznan University of Life Sciences Szydłowska 50, 60-656 Poznań, Poland

Department of Mathematical and Statistical Methods, Poznan University of Life Sciences Wojska Polskiego 28, 60-637 Poznań, Poland

Evaluation of the usability of single extractors in chemical analysis of composts using principal component analysis

<abstract xmlns="http://www.w3.org/1999/xhtml"> One of the main problems in plant breeding is the selection of the best genotypes. Most often the selection is made using yield as a main trait of continuous type, and ignoring the other traits of discrete type. Here, a simple procedure is proposed for dealing with the selection problem using not only the yield, but also an auxiliary discrete trait. The method is based on transforming the continuous variable into a discrete one and testing the dependence of variables with the use of contingency tables. The procedure is illustrated by a real unreplicated experiment with winter wheat.</abstract>

Institute of Mathematics, Poznan University of Technology, Piotrowo 3A, 60-965 Poznań, Poland

Malopolska Breeding Company Polanowice, Zbożowa 4, 30-002 Kraków, Poland

Department of Mathematical and Statistical Methods, Poznan University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, Poland

A remark on genotype selection in plant breeding projects

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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. 