Asymmetry models based on ordered score and separations of symmetry model for square contingency tables

Summary 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 (i, j)th cell instead of the (j, i)th cell are inversely proportional to the difference of the ordered scores corresponding to categories i and j. 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.

The Pearson Bayes factor: An analytic formula for computing evidential value from minimal summary statistics

Summary 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 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.

Comparative evaluation of goodness of fit tests for normal distribution using simulation and empirical data

SummaryThe normal distribution is considered to be one of the most important distributions, with numerous applications in various fields, including the field of agricultural sciences. The purpose of this study is to evaluate the most popular normality tests, comparing the performance in terms of the size (type I error) and the power against a large spectrum of distributions with simulations for various sample sizes and significance levels, as well as through empirical data from agricultural experiments. The simulation results show that the power of all normality tests is low for small sample size, but as the sample size increases, the power increases as well. Also, the results show that the Shapiro–Wilk test is powerful over a wide range of alternative distributions and sample sizes and especially in asymmetric distributions. Moreover the D’Agostino–Pearson Omnibus test is powerful for small sample sizes against symmetric alternative distributions, while the same is true for the Kurtosis test for moderate and large sample sizes.

On a new approach to the analysis of variance for experiments with orthogonal block structure. IV. Experiments in split-plot designs

SummaryThis 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.

Application of the ρV coefficient and distance correlation to the analysis of multivariate association

SummaryThe aim of this paper is to study the association between two random vectors related to two groups of characteristics. To analyze the multivariate association, the ρV coefficient and distance correlation are used. Two methods (classical and recent) are compared and illustrated with real data.

Measuring change in longitudinal research on pragmatic competence: A multinomial logistic model

SummaryThis 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 P (power distance) and D (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 (F).

“Old Techniques for New Times”: the RMaCzek package for producing Czekanowski’s diagrams

SummaryInspired by the MaCzek Visual Basic program we pprovide an R package, RMaCzek, that produces Czekanowski’s diagrams. Our package permits any seriation and distance method the user provides. In this paper we focus on the “OLO” and “QAP_2SUM” methods from the seriation package. We illustrate the possibilities of our package with three anthropological studies, one socioeconomic study and a phylogenetically motivated simulation study.

Constructing non-orthogonal split-split-plot designs using some resolvable block designs

SummaryWe consider a new method of constructing non-orthogonal (incomplete) split-split-plot designs (SSPDs) for three (A, B, C) factor experiments. The final design is generated by some resolvable incomplete block design (for the factor A) and by square lattice designs for factors B and C using a modified Kronecker product of those designs (incidence matrices). Statistical properties of the constructed designs are investigated under a randomized-derived linear model. This model is strictly connected with a four-step randomization of units (blocks, whole plots, subplots, sub-subplots inside each block). The final SSPD has orthogonal block structure (OBS) and satisfies the general balance (GB) property. The statistical analysis of experiments performed in the SSPD is based on the analysis of variance often used for multistratum experiments. We characterize the SSPD with respect to the stratum efficiency factors for the basic estimable treatment contrasts. The structures of the vectors defining treatment contrasts are also given.

A meta-analysis of genotype × environment interaction on sugar beet performance

SummaryThe 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.

Defining the effective deformation of the vertebral column

SummaryThe Cobb angle is calculated in the coronal plane, irrespective of vertebral rotation, lordokyphosis and local wedge properties of individual verte-brae other than the end plates used for the measurement. Rigorous three-dimensional generalizations of the Cobb angle are complicated for at least two reasons. Firstly, the vertebral column is segmented, not continuous, making the choice of rigorous model ambiguous. Secondly, there exists an inherent curvature (in terms of thoracic kyphosis and lumbar lordosis) that may be considered physiologically healthy or ’normal’. When attempting to find a three-dimensional deviation measure, such normal sagittal curvature must be compensated for.In this paper we introduce a three-dimensional local deformation parameter (which we call the local effective deformation) motivated by both biomechanics and the basic theory of spatial curves, and simultaneously introduce a technical procedure to estimate the parameter from CT scans using MPR (multi-phase reconstruction) in PACS (IDS-7). A detailed description of the proposed modelling of vertebral column deformation is given, together with a stepwise procedure to estimate the three-dimensional deformation (in terms of local effective deformation). As a deformation measure it requires knowledge about the natural healthy kypholordosis. A method is described by which such knowledge may be incorporated in future work.