###### Computing Bayes factors to measure evidence from experiments: An extension of the BIC approximation

## Summary

Bayesian inference affords scientists powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of the hesitance to adopt this approach may stem from an unfamiliarity with the computational tools necessary for computing Bayes factors. Previous work has shown that closed-form approximations of Bayes factors are relatively easy to obtain for between-groups methods, such as an analysis of variance or t-test. In this paper, I extend this approximation to develop a formula for the Bayes factor that directly uses information that is typically reported for ANOVAs (e.g., the F ratio and degrees of freedom). After giving two examples of its use, I report the results of simulations which show that even with minimal input, this approximate Bayes factor produces similar results to existing software solutions.

###### Statistical analysis of yield trials by AMMI analysis of genotype × environment interaction

## Abstract

The genotype by environment interaction (GEI)) has an influence on the selection and recommendation of cultivars. The aim of this work is to study the effect of GEI and evaluate the adaptability and stability of productivity (kg/ha) of nine maize genotypes using AMMI model (Additive Main effects and Multiplicative Interaction). The AMMI model is one of the most widely used statistical tools in the analysis of multiple-environment trials. It has two purposes, namely understanding complex GEI and increasing accuracy. Nevertheless, the AMMI model is a widely used tool for the analysis of multiple-environment trials, where the data are represented by a two-way table of GEI means. In the complete tables, least squares estimation for the AMMI model is equivalent to fitting an additive two-way ANOVA model for the main effects and applying a singular value decomposition to the interaction residuals. It assumes equal weights for all GEI means implicitly. The experiments were conducted in twenty environments, and the experimental design was a randomized complete block design with four repetitions. The AMMI model identified the best combinations of genotypes and environments with respect to the response variable. This paper concerns a basic and a common application of AMMI: yield-trial analysis without consideration of special structure or additional data for either genotypes or environments.

###### Impact of cereal diseases on the qualitative traits of spring barley breeding lines

## Summary

The differences between individual breeding lines of spring barley and a control variety were tested in terms of several measured (continuous) and qualitative traits. The impact of the qualitative traits (diseases) on the quantitative traits, especially yield, was assessed on the basis of the significance of differences for both qualitative traits and yield. Depending on the type of trait, either a logistic model or analysis of variance was used as a statistical tool. The statistically significant differences between some breeding lines and the control variety were shown. It was observed that in fodder barley both infection by mildew and lodging influenced yield. The results of analyses obtained in the so-called pre-preliminary trials and preliminary trials were different. This fact confirmed the necessity of repeating trials over several years.

###### Application of multivariate statistical methods in the assessment of mountain organic soil transformation in the central Sudetes

## Summary

In studies of organic soil degradation and transformation, alongside the conventional methods used in soil science, an increase in the importance of advanced statistical methods can be observed. In this study some multivariate statistical methods were applied in an investigation of organic soil transformation in the central Sudetes. Andrews curves, linear and kernel discriminant variable analysis and cluster analysis were used. The similarities among peatland soils and their layers were determined. It can be stated that the application of statistical methods in soil science research related to organic soil transformation is a valuable tool. The use of various statistical methods (such as Andrews curves, linear and kernel discriminant variables and cluster analysis) can with high probability confirm earlier laboratory or field observations. This is particularly justified in the case of organic soils derived from varied geobotanical peat materials, different types of peatlands and water supply types, which impact the primary properties of the soil.

###### A Multidimensional Analysis of Socioeconomic Factors in Housing Policy in the Eurozone Countries (2010–2014)

## Summary

The latest global economic and financial crisis has had adverse social consequences in many areas, including income and the social situation of households and their living conditions, especially when the housing phenomenon is addressed. The reality of this uncertainty has made the study of the housing phenomenon even more relevant, in particular from the perspective of an analysis of its evolution. In this context, we revisit EUROSTAT’s databases. This analysis was done for twelve Euro Area countries over five years, using the HJ-BIPLOT method developed by Galindo (1986). This multidimensional approach identified and represented twelve Eurozone sample countries in latent constructs of reduced dimensionality related to the housing policy problem. The simultaneous factorial representation identified (a) the most relevant variables to characterize these countries, (b) their trajectories during the period in analysis, and (c) the relations between variables, between countries, and between variables and countries. This approach also identified the most significant factors contributing to the countries' performance. This methodological approach can be useful in housing research, when studying data of a multivariate nature, and is also, by its visual interpretation, a potential tool for producing richer information not only for academia but also for policy makers.

###### Canonical correlation analysis for functional data

References Krzyśko M. (2009): Podstawy wielowymiarowego wnioskowania statysty- cznego [Foundations of multidimensional statistical inference]. Wydawnictwo Naukowe UAM, Poznan. Leurgans S.E., Moyeed R.A., Silverman B.W. (1993): Canonical correlation analy- sis when the data are curves. Journal of the Royal Statistical Society B 55(3): 725{740. Ramsay J.O., Danzell C.J. (1991): Some tools for functional data analysis. Journal of the Royal Statistical Society B 53: 539-572. Ramsay J

###### Check plots in field breeding experiments

## Summary

This paper deals with the problems of selection in the early stages of a breeding program. During the improvement process, it is not possible to use an experimental design that satisfies the requirement of replicating all the treatments, because of the large number of genotypes involved, the small amount of seed and the low availability of resources. Hence unreplicated designs are used. To control the real or potential heterogeneity of experimental units, control (check) plots are arranged in the trial. There are many methods of using the information resulting from check plots. All of the usually applied adjusting methods for unreplicated experiments are appropriate for some specific structure of soil fertility. Their disadvantage is the fact that, before and also after the experiment, we usually do not know what a kind of soil structure is present in the experiment. Hence we cannot say which of the existing methods is appropriate for a given experimental situation. The method of inference presented below avoids this disadvantage. It is always appropriate, because of the fact that a trend of soil variability is identified and estimated. In the paper the main tool used to explore this information will be based on a response surface methodology. To begin with we will try to identify a response surface characterizing the experimental environments. We assume that observed yield (or another trait) results directly from two components, one of them due to soil fertility and the other due to the genotype effect. This means that difference between observed yield and forecast can be treated as the estimate of a genotype effect. The obtained response surface will then be used to adjust the observations for genotypes. Finally, the data so adjusted are used for inferences concerning the next stage of the breeding program. The theoretical considerations are illustrated with an example involving yields of spring barley.

###### Principal component analysis for functional data on grain yield of winter wheat cultivars

## Summary

The aim of this paper is to present a statistical methodology to assess patterns of cultivars' adaptive response to agricultural environments (agroecosystems) on the basis of complete Genotype x Crop Management x Location x Year (GxMxLxY) data obtained from 3-year multi-location twofactor trials conducted within the framework of the Polish post-registration trials (PDOiR), with an illustration of the application and usefulness of this methodology in analyzing winter wheat grain yield. Producing specific varieties for each subregion of a target region, from widely adapted varieties, may exploit positive genotype x location (GL) interactions to increase crop yields. Experiments designed to examine combinations of environment (E), management practices (M) and cultivars (G) also provide evidence of the relative importance of each of these factors for yield improvement. The evidence shows that variation due to E far outweighs the variation of grain yield that can be attributed to M or G, or the interactions between these factors, and between these factors and E (Anderson, 2010). This statistical method involves the use of functional PCA and cluster analysis. A total of 24 cultivars were evaluated over 3 years in 20 environments using randomized incomplete split-block designs with two replications per trial. The methodology proved an efficient tool for the reliable classification of 24 winter wheat cultivars, distinguishing cultivar groups that exhibited homogeneous adaptive response to environments. It enables the identification of cultivars displaying wide or specific adaptation. The remaining cultivars were locally adapted to some testing environments, or some of them were not relatively adapted to the environments because they always yielded substantially below the environmental means. Performing earlier specific selection, or adopting distinct genetic bases for each agro-ecosystem, may further increase the advantage of specific breeding.

###### Evaluation of the impact of fertilizers and seed quality on winter wheat yield

Policy 30: 206-213. Hosmer D., Lemeshow S. (2000): Applied Logistic Regression. John Wiley&Sons, New Jersey. Larose D.T. (2012): Metody i modele eksploracji danych. PWN Warszawa. Mańkowski D.R., Oleksiak T. (2007): Czynniki determinujące stosowanie kwalifikowanego materiału siewnego w gospodarstwach rolnych. Biul. IHAR 244: 5-9. Manso M.C., Cerqueira R.M., Fernandes C., Correia M. (2010): Logistic multivariate regression analysis as a tool to predict fibrosis in light-drinking chronic hepatitis C patients