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.
In this paper we study the problem of estimation of individual measurements of objects in a biased spring balance weighing design under assumption that the errors are uncorrelated and they have different variances. The lower bound for the variance of each of the estimated measurements for this design and the necessary and sufficient conditions for this lower bound to be attained are given. The incidence matrices of the balanced incomplete block designs are used for construction of the A-optimal...
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.
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.
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 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...
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...
The paper studies the estimation problem of individual weights of objects using a chemical balance weighing design under the restriction on the number times in which each object is weighed. Conditions under which the existence of an optimum chemical balance weighing design for objects implies the existence of an optimum chemical balance weighing design for objects are given. The existence of an optimum chemical balance weighing design for objects implies the existence of an optimum chemical...
In this paper we develop the theory of spring balance weighing designs with non-positive correlated errors for that the lower bound of the variance of estimated total weight is attained.
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...
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