For square contingency tables with ordered categories, Iki, Tahata and Tomizawa (2012) considered a measure to represent the degree of departure from marginal homogeneity. However, the maximum value of this measure cannot distinguish two kinds of marginal inhomogeneity. The present paper proposes a measure which can distinguish two kinds of marginal inhomogeneity. In particular, the proposed measure is useful for representing the degree of departure from marginal homogeneity when the marginal cumulative logistic model holds.
The effective dose of six herbicidal ionic liquids containing glyphosate [N-(phosphonomethyl)glycine] was investigated. Varied biological activity of the tested compounds was observed depending on the type of cation and targeted plant species. In the case of common lambsquarters, the lowest effective dose was obtained for compounds containing didecyldimethylammonium and di(hydrogenated tallow)dimethylammonium cations. In the case of white mustard, the lowest ED50 and ED90 values were obtained for the reference compound, which contained glyphosate isopropylamine salt. These parameters were determined using dose efficiency curves based on log-logistic models with three or four parameters. The study indicates that ionic liquids with glyphosate may be used as a new form of this herbicide in the future.
In the statistical literature there are proposed many test measures to determine the independence of two qualitative variables in contingency tables, in particular in two-way contingency tables larger than 2×2. For statistical analysis, three of the so-called “chi-squared tests”—the T3 test, BP test and |χ| test—were selected. These tests were compared with a logarithmic minimum test, which is the author’s proposal. Critical values for the tests were determined with the Monte Carlo method. To compare the tests, an appropriate measure of untruthfulness of H0 was used and the power of the tests was calculated.
Results of ecological studies that involve the use of multivariate analysis of variance techniques for testing various hypotheses, interesting from the point of view of comparing the linear functions of parameters, were considered. For testing the most interesting hypotheses on a variety of interaction effects and on contrasts of class means, the application of a multivariate test statistic is recommended. Canonical variate analysis is used for graphical presentation of the results of multidimensional experiments. In this paper it is shown how a generalized form of canonical variate analysis can be useful to reveal which parametric functions of a multivariate analysis of variance model are responsible for rejecting the linear hypothesis. As an example, an analysis was made of an ecological study of trace element accumulation in plants of Italian ryegrass as a method of biomonitoring of air pollution.
Iwona Mejza, Katarzyna Ambroży-Deręgowska, Jan Bocianowski, Józef Błażewicz, Marek Liszewski, Kamila Nowosad and Dariusz Zalewski
The main purpose of this study was the model fitting of data deriving from a three-year experiment with barley malt. Two linear models were considered: a fixed linear model with fixed effects of years and other factors, and a mixed linear model with random effects of years and fixed effects of other factors. Two cultivars of brewing barley, Sebastian and Mauritia, six methods of nitrogen fertilization and four germination times were analyzed. Three quantitative traits were observed: practical extractivity of the malt, malting productivity, and a quality coefficient Q. The starting point for the statistical analyses was the available experimental material, which consisted of barley grain samples destined for malting. The analyses were performed over a series of years with respect to fixed or random effects of years. Due to the strong differentiation of the years of the study and some significant interactions of factors with years, annual analyses were also carried out.
Delwyn G. Cooke, Leonard F. Blackwell and Simon Brown
It has been suggested that it is possible to monitor the menstrual cycle by measuring the concentration of urinary reproductive steroids. This neglects the variation in void volume and in urine production rate. In neither case has any systematic analysis been reported previously. Overnight urine samples were collected each day for one complete cycle by 24 women and the void volumes and intervoid times were recorded. The void volume and urine production rate were approximately lognormally distributed and the intervoid time was approximately normally distributed. Using these distributions we consider the implications of the variation in void volume and urine production rate for the comparison of the concentrations of a urinary analyte in two samples.
We develop a simple method that completely eliminates the specification error and spurious relationships in regression. Furthermore, we introduce a stronger test of causality. We apply our method to oil prices.
Bogna Zawieja, Sylwia Lewandowska, Tomasz Mikulski and Wiesław Pilarczyk
An analysis is made of results from early stages of testing of promising hybrids. The data consist of single-replicate trials performed by Norddeutsche Pflanzenzucht in 6 locations (5 in Poland and one in Germany). In total 165 hybrids were tested with 3 standard varieties. The subject of the analysis was the seed yield. Three measures of stability were used. The yield of tested hybrids is expressed as percentage of that of standard varieties. Wricke’s ecovalence expressed as a contribution to G x E interaction was used as a measure of stability. Additional characterization of the tested hybrids was performed by regressing hybrid yield on the mean yields of the experiment, as described by Finlay and Wilkinson and by Eberhart and Russel. The methods applied enabled selection of the most promising hybrids for further yield testing.
The usefulness of combining methods is examined using the example of microarray cancer data sets, where expression levels of huge numbers of genes are reported. Problems of discrimination into two groups are examined on three data sets relating to the expression of huge numbers of genes. For the three examined microarray data sets, the cross-validation errors evaluated on the remaining half of the whole data set, not used earlier for the selection of genes, were used as measures of classifier performance. Common single procedures for the selection of genes—Prediction Analysis of Microarrays (PAM) and Significance Analysis of Microarrays (SAM)—were compared with the fusion of eight selection procedures, or of a smaller subset of five of them, excluding SAM or PAM. Merging five or eight selection methods gave similar results. Based on the misclassification rates for the three examined microarray data sets, for any examined ensemble of classifiers, the combining of gene selection methods was not superior to single PAM or SAM selection for two of the examined data sets. Additionally, the procedure of heterogeneous combining of five base classifiers—k-nearest neighbors, SVM linear and SVM radial with parameter c=1, shrunken centroids regularized classifier (SCRDA) and nearest mean classifier—proved to significantly outperform resampling classifiers such as bagging decision trees. Heterogeneously combined classifiers also outperformed double bagging for some ranges of gene numbers and data sets, but merging is generally not superior to random forests. The preliminary step of combining gene rankings was generally not essential for the performance for either heterogeneously or homogeneously combined classifiers.
Mirosława Wesołowska-Janczarek and Monika Różańska-Boczula
This paper presents an application of Hellwig’s method for selecting concomitant variables under a growth curve model, where the values of the concomitant variables change over time and are the same for all experimental units. The authors present a simple adaptation of the growth curve model to the multiple regression model for which Hellwig’s method applies. The theoretical considerations are applied to the selection of significant concomitant variables for raspberry fruiting.