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A note on the relations between two ternary balanced block designs and chemical balance weighing designs

Katarzyna Ambroży, Bronisław Ceranka (2001)

Discussiones Mathematicae Probability and Statistics

The paper studied the problem of estimating of the weights of p objects in n weighings using a chemical balance weighing design under the restriction on the number of objects which can be placed on the right and left pans, respectively. Conditions under which the estimated weights are uncorrelated are given. The incidence matrices of two ternary balanced block designs which are used to construct chemical balance weighing designs satisfying these conditions are considered.

A unified terminology in block designs

Tadeusz Caliński, Sanpei Kageyama (2004)

Discussiones Mathematicae Probability and Statistics

Partially efficiency balanced (PEB) designs with m efficiency classes have been defined by Puri and Nigam [15] as block designs which have simple analysis and, if properly used, allow the important contrasts to be estimated with desired efficiency. Such designs can be made available in varying replications and/or unequal block sizes. However, any block design is a PEB design with m efficiency classes for some m < v, where v is the number of treatments in the design. So the term "PEB" itself is...

Algebraic structureof step nesting designs

Célia Fernandes, Paulo Ramos, João Tiago Mexia (2010)

Discussiones Mathematicae Probability and Statistics

Step nesting designs may be very useful since they require fewer observations than the usual balanced nesting models. The number of treatments in balanced nesting design is the product of the number of levels in each factor. This number may be too large. As an alternative, in step nesting designs the number of treatments is the sum of the factor levels. Thus these models lead to a great economy and it is easy to carry out inference. To study the algebraic structure of step nesting designs we introduce...

Algunas soluciones aproximadas para diseños split-plot con matrices de covarianza arbitrarias.

Guillermo Vallejo Seco, José Ramón Escudero García (1998)


El presente trabajo revisa con cierto detalle diversos tipos de análisis para diseños split-plot que carecen del mismo número de unidades experimentales dentro de cada grupo y en los que se incumple el supuesto de esfericidad multimuestral. Específicamente, adoptando el enfoque multivariado de aproximar los grados de libertad desarrollado por Johansen (1980) y el procedimiento de aproximación general mejorada corregida basado en Huynh (1980) se muestra cómo obtener análisis robustos y poderosos...

A-optimal biased spring balance weighing design

Małgorzata Graczyk (2011)


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...

Certain new M-matrices and their properties with applications

Ratnakaram N. Mohan, Sanpei Kageyama, Moon H. Lee, G. Yang (2008)

Discussiones Mathematicae Probability and Statistics

The Mₙ-matrix was defined by Mohan [21] who has shown a method of constructing (1,-1)-matrices and studied some of their properties. The (1,-1)-matrices were constructed and studied by Cohn [6], Ehrlich [9], Ehrlich and Zeller [10], and Wang [34]. But in this paper, while giving some resemblances of this matrix with a Hadamard matrix, and by naming it as an M-matrix, we show how to construct partially balanced incomplete block designs and some regular graphs by it. Two types of these M-matrices...

Characterizing experimental designs by properties of the standard quadratic forms of observations

Czesław Stępniak (2007)

Applicationes Mathematicae

For any orthogonal multi-way classification, the sums of squares appearing in the analysis of variance may be expressed by the standard quadratic forms involving only squares of the marginal and total sums of observations. In this case the forms are independent and nonnegative definite. We characterize all two-way classifications preserving these properties for some and for all of the standard quadratic forms.

Contrastación de hipótesis en diseños multivariados split-plot con matrices de dispersión arbitrarias.

Guillermo Vallejo Seco, José Ramón Escudero García, Angel M. Fidalgo Aliste, M. Paula Fernández García (2000)


El presente trabajo examina diversos procedimientos para contrastar hipótesis nulas globales, correspondientes a datos obtenidos mediante diseños multivariados split-plot cuando se incumple el supuesto de homogeneidad de las matrices de dispersión. Un examen de estos procedimientos para un amplio número de variables confirma, por un lado, la robustez del procedimiento multivariado de Welch-James dado por Johansen (1980) para probar el efecto principal de los ensayos y, por otro, la robustez de la...

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