Abstract: SummaryIn general, varieties of any cultivated species can differ in many aspects. One of the desirable traits in breeding new varieties is high yield, which can be significantly reduced by plant diseases. This study is an extension of previous research about the resistance of seed pea lines to downy mildew, and provides an extended analysis of this type of experiment. The probability of a degree of infection is determined based on a logistic model with a multinomial distribution. In the analysis the impact of a fixed effect of variety and random environmental effects is considered. It is shown that the environmental effects (combinations of years and location – macro-environments) significantly influence the resistance to diseases, and the differences among environments are larger than the variability of differences among genotypes over all environments. For two types of soils (light and rich) the most resistant varieties, which are significantly different from the control variety, are indicated. PubDate: Fri, 01 Jul 2022 00:00:00 GMT

Abstract: SummaryThe construction of incomplete split-block-plot (SBP) designs for three-factor experiments is investigated. A semi-Kronecker (Khatri–Rao) product of matrices is used in the construction procedure. With this method some generated designs are obtained where column treatments and subplot treatments are allocated in balanced square lattice designs, while row treatments are in a randomized complete block design. Experiments with an orthogonal block structure are considered. In this paper we consider designs which are generally balanced. This allows us to give the stratum efficiency factors for treatment combination contrasts in the proposed split-block-plot designs. PubDate: Fri, 01 Jul 2022 00:00:00 GMT

Abstract: SummaryThe target of this paper is to offer a compact review of the so called distance methods in Statistics, which cover all the known estimation methods. Based on this fact we propose a new step, to adopt from Information Theory, the divergence measures, as distance methods, to compare two distributions, and not only to investigate if the means or the variances of the distributions are equal. Some useful results towards this line of thought are presented, adopting a compact form for all known divergence measures, and are appropriately analyzed for Biometrical, and not only, applications. PubDate: Fri, 01 Jul 2022 00:00:00 GMT

Abstract: SummaryThis paper describes an iterative analysis of incomplete genotype × environment data. L2 environmental indices were introduced to enable the use of Joint Regression Analysis (JRA) in analyzing experiments with incomplete blocks. We now show how, once normality of yields is assumed, the introduction of L2 environmental indices provides a theoretical framework for Joint Regression Analysis. Using this framework, maximum likelihood estimators are obtained and likelihood ratio tests are derived. It is noted that the technique allows unequal weighting of data, and the special case of complete blocks is discussed. PubDate: Fri, 01 Jul 2022 00:00:00 GMT

Abstract: SummaryThis study proposes a new exponential sum-symmetry model for square contingency tables with same row and column ordinal classifications. In the existing exponential sum-symmetry (ESS) model, the probability that the sum of row and column levels is t, where the row level is less than the column level, is ∆t−2 times higher than the probability that the sum of row and column levels is t, where the row level is greater than the column level. On the other hand, in the proposed ESS model, the ratio of these two probabilities is ∆t/3. In other words, in the existing ESS model, the ratio of the two probabilities varies exponentially depending on the absolute gap between t and 2, while in the proposed ESS model, the ratio of the two probabilities varies exponentially depending on the relative gap between t and 3, although in both ESS models, the ratio of the two probabilities is ∆ when t is the minimum value (i.e., t = 3). Moreover, this study introduces a new decomposition theorem for the sum-symmetry model using the proposed ESS. The proposed decomposition theorem satisfies asymptotic equivalence for the test statistic. PubDate: Fri, 01 Jul 2022 00:00:00 GMT

Abstract: SummaryIn this paper, we present some new results regarding spring balance weighing designs. We consider issues with regard to conditions for the existence of optimal designs, and give examples of optimal designs. PubDate: Fri, 01 Jul 2022 00:00:00 GMT

Abstract: SummarySample size calculation is an integral part of any clinical trial design, and determining the optimal sample size for a study ensures adequate power to detect statistical significance. It is a critical step in designing a planned research protocol, since using too many participants in a study is expensive, exposing more subjects to the procedure. If a study is underpowered, it will be statistically inconclusive and may cause the whole protocol to fail. Amidst the attempt to maximize power and the underlying effort to minimize the budget, the optimization of both has become a significant issue in the determination of sample size for clinical trials in recent decades. Although it is hard to generalize a single method for sample size calculation, this study is an attempt to offer something that might be a basis for finding a permanent answer to the contradictions of sample size determination, by the use of simulation studies under simple random and cluster sampling schemes, with different sizes of power and type I error. The effective sample size is much higher when the design effect of the sampling method is smaller, particularly less than 1. Sample size increases for cluster sampling when the number of clusters increases. PubDate: Thu, 30 Dec 2021 00:00:00 GMT

Abstract: SummaryStudies have been carried out on decomposing a model with symmetric structure using a model with asymmetric structure. In the existing decomposition theorem, the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and concordancediscordance models hold. However, this existing decomposition theorem does not satisfy the asymptotic equivalence for the test statistic, namely that the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the decomposed models. To address this issue, this study introduces a new decomposition theorem in which the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic—the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models. PubDate: Thu, 30 Dec 2021 00:00:00 GMT

Abstract: SummaryIn the existing decomposition theorem, the sum-symmetry model holds if and only if both the exponential sum-symmetry and global symmetry models hold. However, this decomposition theorem does not satisfy the asymptotic equivalence for the test statistic. To address the aforementioned gap, this study establishes a decomposition theorem in which the sum-symmetry model holds if and only if both the exponential sum-symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic. We demonstrate the advantages of the proposed decomposition theorem by applying it to datasets comprising real data and artificial data. PubDate: Thu, 30 Dec 2021 00:00:00 GMT

Abstract: SummaryA study was carried out to determine the effect of sowing density on the yield of maize of two different varieties. The field experiment was carried out in 2012–2014 at the Department of Agronomy of Poznań University of Life Sciences. The first-order factor was the variety: SY Cooky and Drim “stay-green”; the second-order factor was sowing density: 6, 7, 8, 9, 10 plants per m2. Weather conditions during the maize growing seasons significantly influenced the values of the studied traits. Significantly the lowest green mass yield of maize was obtained at the sowing density of 6 plants m−2, and the highest for 10 plants m−2. The “stay-green” variety significantly responded to an increase in sowing density with reduced fresh weight of leaf blades of a single plant compared with the conventional variety. This indicated highly effective photosynthesis with a lower plant density per unit area, which is also the basis for effective absorption of solar radiation for these maize varieties. PubDate: Thu, 30 Dec 2021 00:00:00 GMT

Abstract: SummaryIn this paper, we investigate the effect of seeding density on several morphological features such as plant height, height of the production ears, ear length, ear diameter, leaf area, and LAI (leaf area index). Inference is based on a series of three-year two-factor experiments with two hybrid maize varieties – SY Cooky and Drim “stay-green” type – and 5 sowing densities: 6, 7, 8, 9 and 10 plants per m2. The “stay-green” maize variety had production cobs significantly higher on the plant, and had a thicker cob and a larger leaf assimilation area than the conventional variety. Increasing maize sowing density from 6 to 10 plants m−2 resulted in a linear decrease in cob length and diameter, while it increased the LAI. Significantly higher chlorophyll content, expressed in SPAD units, was found in the “stay-green” hybrid at the BBCH 67 stage in a wet (2012) and drier year (2014), compared with the traditional variety. This may indicate that such a variety is more tolerant to stress conditions. PubDate: Thu, 30 Dec 2021 00:00:00 GMT

Abstract: SummaryThe Eye Tribe eye-tracker was used to capture pupil sizes and fixation times of 40 people aged 8 to 79 years during text reading. The dependence of the number of readable lines on the participants’ age was determined. A function describing the dependence of the eye surface area on age was also derived. Visual perception of the maximum number of consecutive lines with decreasing text font size is best for people aged 30–40. For the studied age group, the pupil area decreased with age by approximately 300%. An approximately two-fold increase in average fixation times was recorded. PubDate: Thu, 30 Dec 2021 00:00:00 GMT

Abstract: SummaryA study was made of the prevalence of nine geohelminth egg types in 184 soil samples from 16 recreational parks in Abuja metropolis, Nigeria. Cochran’s Q-test was applied to determine whether the difference in the proportions of the egg types found in the soil samples was significant. At a 5% significance level, it was found that the prevalence of the egg types was significantly different in the 184 soil samples from 16 parks. To identify which of the geohelminth eggs had a significantly larger mean proportional prevalence, a minimum required difference mean comparison technique was applied. The mean comparison test showed that Taenia and Coccocidia eggs were highly prevalent, with significantly larger mean proportions than the other analyzed geohelminth eggs in the 184 examined soil samples. PubDate: Thu, 30 Dec 2021 00:00:00 GMT

Abstract: SummaryFactorial experiments in block designs with nested rows and columns are described with suggestions about how they should be planned. In such experiments the importance of interaction and hidden replication are emphasized. Such experiments are carried out on heterogeneous experimental material. Thus, it is reasonable to seek a design that can withstand the loss of observations. The robustness of a block design with nested rows and columns against the loss of whole blocks is presented, along with examples of such designs. PubDate: Thu, 30 Dec 2021 00:00:00 GMT

Abstract: SummaryThere are many works in the literature on the construction of experimental plans based on weighing designs. Hence, it is useful to compile a catalogue of experimental designs with specific properties. In this work, we investigate the properties of experimental plans constructed using the matrices of spring balance weighing designs. Additionally, an even number of experimental objects is assumed. An overview of the construction methods of these designs and classes of design matrices with selected properties are given. The results make it possible to create a catalogue of experimental designs constructed on the basis of spring balance weighing designs. PubDate: Thu, 30 Dec 2021 00:00:00 GMT

Abstract: SummaryThe aim of this paper is to investigate and discuss the common points shared, in their line of development, by both Sampling Theory and Design of Experiments. In fact, Sampling Theory adopts the main optimality criterion of the Optimal Design of Experiments, the minimization of variance, i.e. D-optimality. There is also an approach based on c-optimality, as far as ratio estimates are concerned, in Design of Experiments, and the A-optimality involved in a proposed Sampling technique. It is pointed out that the L2 norm is mainly applied as a distance measure. PubDate: Thu, 30 Dec 2021 00:00:00 GMT

Abstract: SummaryIn this paper we present properties of an algorithm to determine the maximum likelihood estimators of the covariance matrix when two processes jointly affect the observations. Additionally, one process is partially modeled by a compound symmetry structure. We perform a simulation study of the properties of an iteratively determined estimator of the covariance matrix. PubDate: Thu, 24 Jun 2021 00:00:00 GMT

Abstract: SummaryThe use of wolbachia-infected mosquitoes to stop the spread of zika virus disease is modeled and analyzed. The model consists of a system of 10 ordinary differential equations which describes the dynamics of the disease in the human population, a wolbachia-free Aedes aegypti population, and a wolbachia-infected Aedes aegypti population used for disease control. A stability analysis of the disease-free equilibrium is conducted, which shows that it is both locally and globally asymptotically stable when the reproduction number is less than one. The result of the stability analysis shows that the spread of zika virus disease can be stopped, irrespective of the initial sizes of the infected human and mosquito populations, when wolbachia-infected Aedes aegypti are introduced in the area where the disease is endemic. PubDate: Thu, 24 Jun 2021 00:00:00 GMT

Abstract: SummaryFor the analysis of R × R square contingency tables, we need to estimate an unknown probability distribution with high confidence from obtained observations. For that purpose, we need to perform the analysis using a statistical model that fits the data well and has a simple interpretation. This study proposes two original models that have symmetric and asymmetric structures between the probability with which the sum of row and column variables is t, for t = 2, . . ., R, and the probability with which the sum of row and column variables is 2(R + 1) − t. The study also reveals that it is necessary to satisfy the anti-global symmetry model, in addition to the proposed asymmetry model, in order to satisfy the proposed symmetry model. This decomposition theorem is useful to explain why the proposed symmetry model does not hold. Moreover, we show that the value of the likelihood ratio chi-squared statistic of the proposed symmetry model is equal to the sum of those of the decomposed models. We evaluate the utility of the proposed models by applying them to real-world grip strength data. PubDate: Thu, 24 Jun 2021 00:00:00 GMT

Abstract: SummaryIn Bayesian hypothesis testing, evidence for a statistical model is quantified by the Bayes factor, which represents the relative likelihood of observed data under that model compared to another competing model. In general, computing Bayes factors is difficult, as computing the marginal likelihood of data under a given model requires integrating over a prior distribution of model parameters. In this paper, I capitalize on a particular choice of prior distribution that allows the Bayes factor to be expressed without integral representation, and I develop a simple formula – the Pearson Bayes factor – that requires only minimal summary statistics as commonly reported in scientific papers, such as the t or F score and the degrees of freedom. In addition to presenting this new result, I provide several examples of its use and report a simulation study validating its performance. Importantly, the Pearson Bayes factor gives applied researchers the ability to compute exact Bayes factors from minimal summary data, and thus easily assess the evidential value of any data for which these summary statistics are provided, even when the original data is not available. PubDate: Thu, 24 Jun 2021 00:00:00 GMT