<abstract xmlns="http://www.w3.org/1999/xhtml">This paper considers block designs and row-column designs where the information matrix <bold>C</bold> has two different nonzero eigenvalues, one of multiplicity 1 and the other of multiplicity <italic>h</italic>−1, where <italic>h</italic> is the rank of the matrix <bold>C</bold>. It was found that for each such design there exists a diagonal positive definite matrix <bold>X</bold> such that the design is <bold>X</bold>
−1-balanced.</abstract>

X−1-balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

<abstract xmlns="http://www.w3.org/1999/xhtml">Determination of optimum plot size has been regarded as an important and useful area of study for agriculturists and statisticians since the first remarkable contribution on this problem came to light in a paper by Smith (1938). As we explore the scientific literature relating to this problem, we may note a number of contributions, including those of Modjeska and Rawlings (1983), Webster and Burgess (1984), Sethi (1985), Zhang et al. (1990, 1994), Bhatti et al.(1991), Fagroud and Meirvenne (2002), etc. In Pal et al. (2007), a general method was presented by means of which the optimum plot size can be determined through a systematic analytical procedure. The importance of the procedure stems from the fact that even with Fisherian blocking, the correlation among the residuals is not eliminated (as such the residuals remain correlated). The method is based on an application of an empirical variogram constructed on real-life data sets (obtained from uniformity trials) wherein the data are serially correlated. This paper presents a deep and extensive investigation (involving theoretical exploration of the effect of different plot sizes and shapes in discovering the point – actually the minimum radius of curvature of the variogram at that point – beyond which the theoretical variogram assumes stationary values with further increase in lags) in the case of the most commonly employed model (incorporating a correlation structure) assumed to represent real-life data situations (uniformity trial or designed experiments, RBD/LSD).</abstract>

Sampling and Official Statistics Unit, Indian Statistical Institute, Kolkata, 700108, India

Dean, Post Graduate Studies and Professor of Statistics, Bidhan Chandra Krishi Viswavidyalaya, W.B., Pin-741252, India

Guru Nanak Institute of Technology, Sodepur, West Bengal, Pin-700114, India

Determination of robust optimum plot size and shape – a model-based approach

<abstract xmlns="http://www.w3.org/1999/xhtml">Tropospheric ozone affects plant growth and the yield of main pasture species all around the world. Experiments are usually performed in fully controlled conditions; the number of investigations in ambient air conditions is still limited. Moreover, most investigations of the effect of ozone on white clover biomass production consider one series after the other, including a period without leaves. Hence, based on the recommendations, additional series are proposed and studied here. The responses of sensitive and resistant white clover clones are presented and compared using multivariate analysis of variance and profile analysis. The canonical variate analysis used here makes it possible to present the profile comparison of dry matter content of white clover graphically in Euclidean space. The investigations revealed a difference in response between clones and the necessity of using the additional series.</abstract>

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

Department of Ecology and Environmental Protection, Poznan University of Life Sciences, Piątkowska 94C, 60-649 Poznań, Poland

An application of canonical variate analysis in profile comparison of dry matter content of white clover between ozone-sensitive and ozone-resistant clones exposed in ambient air conditions

<abstract xmlns="http://www.w3.org/1999/xhtml">For over 2.5 million dairy cows subject to assessment in Poland in 2005–2010, gestation length was analyzed. This trait follows a normal distribution, and it was found that the acceptable upper limit of gestation length for the Montbéliard and Simental breeds was 306 days, this being significantly different from other breeds. For the remaining dairy cattle breeds the value was 298 days. For cows with gestation length exceeding these limiting values, parentage control would be advisable.</abstract>

Department of Genetics and Animal Breeding, Poznan University of Life Science, Wołyńska 33, 60-637 Poznań

Departament of Mathematical and Statistical Methods, Poznan University of Life Science, Wojska Polskiego 28, 60-637 Poznań

The evaluation of gestation length range for different breeds of Polish dairy cattle

<abstract xmlns="http://www.w3.org/1999/xhtml">It is investigated how a reduction in the number of measurements influences uniformity decisions in distinctness, uniformity and stability (DUS) testing. Using real data from DUS trials performed in Poland for several species, it is shown that when final decisions are taken after three years of testing, a reduction in the number of measurements by 50% of the numbers indicated in the Guidelines has very limited impact on decisions (rejection or approval of candidate variety). Decisions taken after one year (or two years) are more dependent on the numbers of measurements.</abstract>

The Research Centre for Cultivar Testing at Słupia Wielka, 63-022, Poland

Comparison of uniformity decisions in DUS testing for full and reduced numbers of measurements

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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. 

Biometrical Letters

Volume 52 (2015): Issue 1 (June 2015)

X⁻¹-balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

Determination of robust optimum plot size and shape – a model-based approach

An application of canonical variate analysis in profile comparison of dry matter content of white clover between ozone-sensitive and ozone-resistant clones exposed in ambient air conditions

The evaluation of gestation length range for different breeds of Polish dairy cattle

Comparison of uniformity decisions in DUS testing for full and reduced numbers of measurements

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