The publication is devoted to the development of a method for assessing the quality of wheat grain based on Harrington’s desirability function, which reflects the nonlinearity of the relationship between the quantitative values of quality indicators and the psychological perception of a person. As an empirical base, we used the results of studies on the protein content, gluten content and sedimentation index – Zeleny test of more than 40 varieties of winter wheat, zoned in the Oryol region, the main analysis tool was the factor analysis by the method of principal components. It is substantiated that the set of these wheat grain quality indicators can be described with one slight distortion by one main factor, along with particular desirability functions used to construct a generalized quality indicator with linguistic levels “very good”, “good”, “satisfactory”, “bad” and “very bad”. The calculation of the values of the main factor of wheat varieties, which are absent in the initial data array, is proposed using an approximate formula that takes into account the indicator that is most closely correlated with it - the protein content. The proposed methodology was tested on the example of assessing the influence of sowing dates on the productivity of winter wheat variety Moscow 39. Based on the results of the studies, it is recommended to use the Harrington’s transformation to evaluate particular indicators of the quality of wheat grain. It is also promising to use the method of principal components for the formation of a generalized function of desirability, when the weights of particular indicators are taken into account “automatically” by using the main component as a normalized variable, which comprehensively reflects the quality of wheat grain.
Рассмотрены основные этапы моделирования результатов сельскохозяйственных исследований с использованием процедуры обобщенной линейной модели, показаны ее преимущества и возможности при анализе данных полевых опытов. Приведены примеры использования процедуры для оценки статистической значимости влияния факторов агротехнических опытов, построения доверительных областей выборочных параметров и проверки гипотез. Показано, что моделью, адекватно отражающей влияние предшественников (кукурузы на зеленую массу, гороха на зерно и ячменя) и нормы удобрений (2 и 4 ц/га азофоски) на урожайность озимой пшеницы сорта Московская 39, является двухфакторная линейная модель дисперсионного анализа, причем влияние предшественника больше влияния нормы минеральных удобрений. Получены мнк-оценки параметров модели, доверительные интервалы эффектов предшественников и норм удобрений. Доказано, что оптимальными для повышения урожайности озимой пшеницы являются предшественник горох и норма азофоски 4 ц/га. Сформированы однородные группы предшественников по критерию множественного сравнения Тьюки, при этом предшественник горох образует самостоятельную подгруппу, обеспечивающую большую урожайность озимой пшеницы, а ячмень и кукуруза входят в общую подгруппу предшественников, обеспечивающих меньшую урожайность. Получены двухфакторные линейные модели дисперсионного анализа, которые также адекватно отражают влияние предшественников и нормы удобрений на показатели качества зерна озимой пшеницы сорта Московская 39 -содержание сырого белка и клейковины. Доказано, что, как и для урожайности, оптимальными являются предшественник горох и норма азофоски 4 ц/га. Предложено визуально оценивать качество моделирования путем сравнения диаграмм зависимости показателей продуктивности от уровней факторов, построенных по фактическим и расчетным данным. Существенным преимуществом использования процедуры обобщенной линейной модели для анализа результатов полевых опытов является возможность моделирования по средним данным, при отсутствии информации по повторностям, что позволяет строить модели по данным публикаций.Ключевые слова: озимая пшеница, предшественники, норма удобрений, обобщенная линейная модель, дисперсионный анализ, статистическая значимость, критерий Тьюки, различия средних
Introduction. The relevance of the article is determined by the lack of scientific substantiation of existing methods of quantitative analysis of mass student questionnaires that can lead to erroneous conclusions about the quality of educational services they receive. Authors first applied the in-house probabilistic approach to the preparation of data for mass questioning of students to develop regression and factor models that adequately reflect their subjective judgments about learning quality. Our goal was to estimate the efficiency and possibility of the practical application of the authors, approach to the analysis of student questionnaire results by means of multivariate statistics by the example of the development of the quantitative estimation model of education quality and subjective well-being of student s of Orel State Agrarian University. Materials and Methods. The suggested approach is based on the methods of parametrical multivariate statistics. The empiric basis of modeling consists of the results of questioning students of the 2nd-4th years of learning. The analytic software SPSS Base was used. Results. At the example of the development of correlation-regressive and factor models of the subjective well-being of the students, we proved the efficiency of the suggested approach to the quantitative modeling of questionnaire results by means of multivariate statistical methods. It is shown that all the obtained correlation-regression models have high statistical characteristics of quality and adequately reflect the simulated phenomena. Of particular interest is the model structure of factors of subjective well-being of students, reflecting the process of their professional and cultural development and adaptation to the current socio-political environment. Discussion and Conclusion. The completed study expanded the understanding of possibilities of quantitative analysis of the results of mass student questioning by simulating various aspects of their subjective wellbeing. The advantage of this method is that at modeling it allows considering the status features influence on the degree of the higher educational institution satisfaction and the obtainable education quality. The approach suggested by the authors will be useful in quality education monitoring at higher schools as well as in the educational sphere in general and for various social and economic studies.
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