rss_2.0Biometrical Letters FeedSciendo RSS Feed for Biometrical Letters Letters 's Cover decomposition of the sum-symmetry model using the two-parameters sum-symmetry model for ordinal square contingency tables<abstract> <title style='display:none'>Summary</title> <p>Studies 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.</p> </abstract>ARTICLE2021-12-30T00:00:00.000+00:00Facing sampling techniques as an optimal design problem<abstract> <title style='display:none'>Summary</title> <p>The 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.</p> </abstract>ARTICLE2021-12-30T00:00:00.000+00:00On sample size calculation in testing treatment efficacy in clinical trials<abstract> <title style='display:none'>Summary</title> <p>Sample 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.</p> </abstract>ARTICLE2021-12-30T00:00:00.000+00:00Cochran’s Q-Test on Soil Helminth Prevalence<abstract> <title style='display:none'>Summary</title> <p>A 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.</p> </abstract>ARTICLE2021-12-30T00:00:00.000+00:00Pupil changes in persons aged 8 to 79 during text reading – an eye-tracking study<abstract> <title style='display:none'>Summary</title> <p>The Eye <italic>Tribe</italic> 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.</p> </abstract>ARTICLE2021-12-30T00:00:00.000+00:00Influence of different sowing density in two varieties of maize. Part II. Relation to agricultural morphological features<abstract> <title style='display:none'>Summary</title> <p>In 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 m<sup>2</sup>. 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<sup>−2</sup> 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.</p> </abstract>ARTICLE2021-12-30T00:00:00.000+00:00Orthogonal decomposition of the sum-symmetry model for square contingency tables with ordinal categories: Use of the exponential sum-symmetry model<abstract> <title style='display:none'>Summary</title> <p>In 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.</p> </abstract>ARTICLE2021-12-30T00:00:00.000+00:00Catalogue of selected experimental plans<abstract> <title style='display:none'>Summary</title> <p>There 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.</p> </abstract>ARTICLE2021-12-30T00:00:00.000+00:00Influence of different sowing density in two varieties of maize. Part I. Relation to yielding<abstract> <title style='display:none'>Summary</title> <p>A 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 m<sup>2</sup>. 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<sup>−2</sup>, and the highest for 10 plants m<sup>−2</sup>. 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.</p> </abstract>ARTICLE2021-12-30T00:00:00.000+00:00Some notes on planning plant protection research in block designs with nested rows and columns<abstract> <title style='display:none'>Summary</title> <p>Factorial 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.</p> </abstract>ARTICLE2021-12-30T00:00:00.000+00:00An anti-sum-symmetry model and its orthogonal decomposition for ordinal square contingency tables with an application to grip strength test data<abstract> <title style='display:none'>Summary</title> <p>For the analysis of <italic>R × R</italic> 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 <italic>t</italic>, for <italic>t</italic> = 2, . . ., <italic>R</italic>, and the probability with which the sum of row and column variables is 2(<italic>R</italic> + 1) <italic>− t</italic>. 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.</p> </abstract>ARTICLE2021-06-24T00:00:00.000+00:00Stability Analysis of a Mathematical Model for the Use of Wolbachia to Stop the Spread of Zika Virus Disease<abstract> <title style='display:none'>Summary</title> <p>The 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.</p> </abstract>ARTICLE2021-06-24T00:00:00.000+00:00The Pearson Bayes factor: An analytic formula for computing evidential value from minimal summary statistics<abstract> <title style='display:none'>Summary</title> <p>In 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 <italic>t</italic> or <italic>F</italic> 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.</p> </abstract>ARTICLE2021-06-24T00:00:00.000+00:00Properties of an MLE algorithm for the multivariate linear model with a separable covariance matrix structure<abstract> <title style='display:none'>Summary</title> <p>In 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.</p> </abstract>ARTICLE2021-06-24T00:00:00.000+00:00Measure of departure from average marginal homogeneity for the analysis of collapsed ordinal square contingency tables<abstract> <title style='display:none'>Summary</title> <p>In clinical research, collected data are often classified into ordered categories using a set threshold to evaluate efficacy and safety of treatment. Data can be summarized as a shift table, which displays the change in the frequency of subjects across specified categories from the baseline to post-baseline. Although ordered categories are sometimes recombined into three categories, the combined patterns vary. To consider various collapsed patterns comprehensively, this paper proposes a new measure that represents the degree of departure from average marginal homogeneity, and can distinguish between two kinds of marginal inhomogeneity. Additionally, applications of the proposed measure to clinical data are discussed.</p> </abstract>ARTICLE2021-06-24T00:00:00.000+00:00Asymmetry models based on ordered score and separations of symmetry model for square contingency tables<abstract> <title style='display:none'>Summary</title> <p>This study proposes two original asymmetry models based on ordered scores for square contingency tables with the same row and column ordinal classifications. The proposed models can be applied to cases in which the scores of all categories are known or unknown. In the proposed models, the log odds for an observation falling in the (<italic>i, j</italic>)th cell instead of the (<italic>j, i</italic>)th cell are inversely proportional to the difference of the ordered scores corresponding to categories <italic>i</italic> and <italic>j</italic>. The asymmetry parameter of the proposed model can be useful for inferring whether the row variable is stochastically greater than the column variable or vice versa. The proposed models constantly hold when the symmetry model holds, but the converse is not necessarily true. This study also examines what is necessary for a model, in addition to the proposed models, to satisfy the symmetry model, and gives separations of the symmetry model using the proposed and marginal mean equality models. We apply real data to show the utility of the proposed models. The proposed models provide a better fit than that of the existing models.</p> </abstract>ARTICLE2021-06-24T00:00:00.000+00:00Measuring change in longitudinal research on pragmatic competence: A multinomial logistic model<abstract><title style='display:none'>Summary</title><p>This paper focuses on pragmatic competence development in second or foreign language learners. In particular, it attempts to fill the significant research gap in measuring change in pragmatic competence and capturing pragmalinguistic and sociopragmatic development over time. The paper proposes an innovative approach by applying a logistic model with multinomial distribution for measuring change in InterLanguage Pragmatics Research (ILP). Applied in the field of pragmatics, this statistical tool offers a comprehensive and flexible approach to modelling relations between independent and dependent variables in ILP research. The model is tested in a longitudinal study of Polish undergraduate students learning English, and specifically in the way they formulate requests by means of requestive directness strategies. The paper concludes that, regardless of time elapsing, the factors <italic>P</italic> (power distance) and <italic>D</italic> (social distance) have a highly significant influence on the use of requestive directness strategies by Poles learning EFL. Furthermore, the analysis indicates that the pragmatic output of Poles learning EFL is dependent on one more independent variable: the estimation of future social distance (<italic>F</italic>).</p></abstract>ARTICLE2020-12-31T00:00:00.000+00:00A meta-analysis of genotype × environment interaction on sugar beet performance<abstract><title style='display:none'>Summary</title><p>The evaluation of sugar beet genotypes under different climate conditions is a principal goal of breeding programs. In most studies, environment has a high influence on the qualitative and quantitative traits of sugar beet. Therefore, data collected from different environments may contribute to more accurate genotype selection. In this study, the effect of different environments on sugar beet genotypes’ performance was evaluated using a meta-analysis method based on Hedges’ technique. Data were collected from 149 trials conducted in twelve regions in Iran over 15 years (2003–18). For all trials, the value of the traits was weighted, and subsequently the effect size, reaction ratio and confidence interval were estimated. Among the studied environments, Khoy had a positive effect on root yield, sugar content, sugar yield and white sugar yield. As could be expected, the effect of environment on final yield formation was high, so that the Shiraz environment had a negative effect on root yield and sugar yield. Overall, the ranking of environments based on the meta-analysis results was quite different from that obtained by comparison of mean results.</p></abstract>ARTICLE2020-12-31T00:00:00.000+00:00Assessment of the impact of NP fertilizer application depth on the rate of initial dry matter accumulation of maize ( L.)<abstract><title style='display:none'>Summary</title><p>A field study was conducted at the Department of Agronomy of Poznań University of Life Sciences to determine the effect of the depth of NP fertilizer application in maize cultivation on the dynamics of initial maize growth, expressed in dry matter of a single plant at two juvenile maize stages. The adopted assumptions were verified on the basis of a four-year field experiment using four depths of NP fertilizer application, two nitrogen fertilizers and two nitrogen dose application dates. Thermal conditions in the early maize growing season had a significant effect on maize response to the depth of application of a phosphorus starting dose. Row fertilization (regardless of the depth of fertilizer application) was more effective than broadcast fertilization at both studied developmental stages.</p></abstract>ARTICLE2020-12-31T00:00:00.000+00:00On a new approach to the analysis of variance for experiments with orthogonal block structure. IV. Experiments in split-plot designs<abstract><title style='display:none'>Summary</title><p>This paper provides estimation and hypothesis testing procedures for experiments in split-plot designs. These experiments have been shown to have a convenient orthogonal block structure when properly randomized. Due to this property, the analysis of experimental data can be carried out in a relatively simple manner. Relevant simplification procedures are indicated. According to the adopted approach, the analysis of variance and hypothesis testing procedures can be performed directly, rather than by combining the results of analyses based on some stratum submodels. The practical application of the presented theory is illustrated by examples of real experiments in appropriate split-plot designs. The present paper is the fourth in the planned series of publications on the analysis of experiments with orthogonal block structure.</p></abstract>ARTICLE2020-12-31T00:00:00.000+00:00en-us-1