Aim. Traditionally, prediction of breeding values of male small horned ruminants   (rams) by referring to levels of economically useful traits of their progeny is carried  out by methods of statistical analysis. However, at the same time, there is a forecasting method based on the use of a mixed biometric model. The solution of the system  of equations constituting a mixed biometric model is associated with certain difficulties caused by the peculiarity of the system matrix. It is proposed to use integrated  mathematical packages in the forecast, by which the system of equations can be  solved in several ways, followed by analysis of the results. The prediction of progeny  values is carried out by statistical methods using three statistical tests, as well as with  the use of a mixed biometric model. It is of interest to compare estimates obtained  by using statistical methods with estimates using a mixed biometric model. Material and Methods. The initial data set was the live weight of Qigai rams, the  progeny of a group of sixteen rams belonging to eight genetic groups.   Results. It was found that the forecast of breeding values of each animal using a  mixed biometric model substantially clarifies the rank of each animal in the group  being evaluated.   Conclusion. The refinement of the estimation of breeding value is related to the  effects of the genetic groups to which the animals belong in the mixed model, as well  as the degree of relationship between them. Also the mixed model also allows one to  isolate environmental effects from the overall assessment. Solving the system of  equations in several ways will improve the reliability of the forecast.

Приведена последовательность действий, которую необходимо выполнить селекционеру при проведении оценки племенной ценности животных. Оцениваемой группой животных являются бараны-производители. Оценка проводится по значению хозяйственно полезных признаков потомков этих производителей. В качестве таких признаков выступают живая масса потомков и их настриг шерсти. Собранные опытным путем исходные данные должны подвергнуться статистическому анализу, в ходе которого необходимо исключить аномальные измерения. Затем следует определить достоверность различий между значениями хозяйственно полезных признаков в различных генеалогических группах животных. Показано, что для определения достоверности различий необходимо провести последовательно три статистических теста. Если тест на сравнение разности двух средних с доверительными границами дает результат о случайности различий, то необходимо перейти ко второму тесту -сравнению по методу Стьюдента. Если и этот тест покажет случайный характер различий, то необходимо перейти к третьему тесту -проверке по критерию Фишера. Если хотя бы один статистический тест указывает на достоверность различий между средними показателями, то принимается гипотеза о значимом характере различий между средними значениями хозяйственно полезных признаков в исследуемых генеалогических группах. Проведен сравнительный анализ этих тестов. Показано, что наибольшей достоверностью обладает проверка статистической значимости различий по критерию Фишера. Обладая данными о неслучайности различий, можно приступить к определению гарантированного минимума превосходства одной генеалогической группы животных над другой.Ключевые слова: статистические тесты, доверительный интервал, нулевая гипотеза, альтернативная гипотеза.The article presents the sequence of actions that must be performed by the breeder when assessing the breeding value of animals. The estimated groups of animals are the tupping rams. The evaluation made on the value of the economically useful traits of the descendants from these stud rams. As economically useful traits are the live weight of offspring and of their wool clip. The baseline data collected by the experiment should undergo statistical analysis, during which anomalous measurements should be excluded. Then it is necessary to define the reliability of the differences between the values of economically useful traits in various genealogical groups of animals. The article shows that in order to determine the accuracy of the differences, it is necessary to conduct three statistical tests sequentially. If the test for comparing the difference between two averages with confidence limits gives the result of about the randomness of the differences, then it is necessary to go to the second test -comparison according to the Student's t-test. If this test also shows the random nature of the differences, then you need to go to the third test -check by Fisher criterion. If at least one statistical test indicates the reliability of the differences between the average indices then the hypothesis about the ...

The use of a mixed biometric model for breeding evaluation of small cattle has been discussed in the article. This model of breeding evaluation involves a large number of matrix operations. At the same time, the volumes of the formed matrices are directly proportional to the number of animals in the evaluated sample as well as to the number of their off spring. An algorithm for generating matrices of estimated effects that have a large dimension has been presented in the paper. This task is the most time-consuming when using a mixed biometric model. Currently, there are the large number of mathematical packages that provide ample opportunities for performing calculations. A special place in this series is occupied by the integrated mathematical package MATLAB has been designed specifically for performing matrix operations. The authors rely on the use of this package in their work. At the same time the algorithm presented in this paper has the property of universality and can be applied by users in any other software product. Since the matrices of the estimated effects consist of zeros and ones we propose the two-step procedure for forming these matrices. At the first stage, a zero matrix of the required dimension is created. At the second stage, in accordance with the data on the number of evaluated animals, the number of herds for which off spring are distributed, the number and affiliation of evaluated animals to genetic groups, the elements of the matrix are determined, in which zeros are replaced by ones. The advantage of the proposed algorithm is its versatility, and the representation of the algorithm in the form of a block diagram will allow you to design it as a separate proceduresubroutine.