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1
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Some applications of weighing designs

100%
Graczyk M.
Biometrical Letters
|
2013
|
tom 50
|
nr 1
15-26
EN
The purpose of this paper is to apply results on weighing designs to the setting of 2m factorial designs. Using weighing designs, we give some proposals for experimental plans. Relevant counterexamples are indicated. Also the results of a simulation study on the existence of weighing designs are presented.
2
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Relations between regular A-optimal chemical and spring balance weighing designs with diagonal covariance matrix of errors

64%
Ceranka B., Graczyk M.
Biometrical Letters
|
2013
|
tom 50
|
nr 2
127-136
EN
In this paper, we study the relationships between regular A-optimal spring balance weighing designs and regular A-optimal chemical balance weighing designs. We give the basic relation between these designs in the case where the errors are uncorrelated and they have different variances. We give some examples of methods of construction of such designs.
3
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Some D-optimal chemical balance weighing designs: theory and examples

64%
Ceranka B., Graczyk M.
Biometrical Letters
|
2017
|
tom 54
|
nr 2
137-154
EN
In this paper we study a certain kind of experimental designs called chemical balance weighing designs. We consider issues with regard to determining optimality conditions. We give new classes of designs in which we are able to determine an optimal design. Moreover, examples are given for the presented cases.
4
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Optimum chemical balance weighing designs with diagonal variance-covariance matrix of errors

64%
Ceranka B., Graczyk M.
Discussiones Mathematicae Probability and Statistics
|
2004
|
tom 24
|
nr 2
215-232
EN
In this paper we study the estimation problem of individual measurements (weights) of objects in a model of chemical balance weighing design with diagonal variance - covariance matrix of errors under the restriction k₁ + k₂ < p, where k₁ and k₂ represent the number of objects placed on the right and left pans, respectively. We want all variances of estimated measurments to be equal and attaining their lower bound. We give a necessary and sufficient condition under which this lower bound is attained by the variance of each of the estimated measurements. To construct the design matrix X of the considered optimum chemical balance weighing design we use the incidence matrices of balanced bipartite weighing designs.
5
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Optimum chemical balance weighing designs under the restriction on weighings

64%
Ceranka B., Graczyk M.
Discussiones Mathematicae Probability and Statistics
|
2001
|
tom 21
|
nr 2
111-120
EN
The paper deals with the problem of estimating individual weights of objects, using a chemical balance weighing design under the restriction on the number in which each object is weighed. A lower bound for the variance of each of the estimated weights from this chemical balance weighing design is obtained and a necessary and sufficient condition for this lower bound to be attained is given. The incidence matrix of ternary balanced block design is used to construct optimum chemical balance weighing design under the restriction on the number in which each object is weighed.
6
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Evaluation of the usability of single extractors in chemical analysis of composts using principal component analysis

64%
Jakubus M., Graczyk M.
Biometrical Letters
|
2015
|
tom 52
|
nr 2
115-130
EN
The usability of various single extractors in the chemical analysis of composts was evaluated using principal component analysis. Ten different single extractors were used to determine the contents of microelements obtained in the chemical extraction of four different composts. It was found that principal component analysis is a satisfactory statistical method enabling the comparison of different solutions in terms of efficiency of extraction of microelements from composts of different composition. The results showed that 1mol dm-3 HCL and 10% HNO3 solutions had the highest extraction strength, and 0.01mol dm-3 CaCl2 and 1mol dm-3 NH4NO3 the lowest.
7
Content available remote

The mineralization effect of wheat straw on soil properties described by MFPC analysis and other methods

51%
Jakubus M., Krzyśko M., Wołyński W., Graczyk M.
Biometrical Letters
|
2016
|
tom 53
|
nr 2
133-147
EN
Recycling of crop residues is essential to sustain soil fertility and crop production. Despite the positive effect of straw incorporation, the slow decomposition of that organic substance is a serious issue. The aim of the study was to assess the influence of winter wheat straws with different degrees of stem solidness on the rate of decomposition and soil properties. An incubation experiment lasting 425 days was carried out in controlled conditions. To perform analyses, soil samples were collected after 7, 14, 21, 28, 35, 49, 63, 77, 91, 119, 147, 175, 203, 231, 259, 313, 341, 369, 397 and 425 days of incubation. The addition of two types of winter wheat straw with different degree of stem solidness into the sandy soil differentiated the experimental treatments. The results demonstrate that straw mineralization was a relatively slow process and did not depend on the degree of filling of the stem by pith. Multivariate functional principal component analysis (MFPC) gave proof of significant variation between the control soil and the soil incubated with the straws. The first functional principal component describes 48.53% and the second 18.55%, of the variability of soil properties. Organic carbon, mineral nitrogen and sum of bases impact on the first functional principal component, whereas, magnesium, sum of bases and total nitrogen impact on the second functional principal component.
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