scholarly journals On a new approach to the analysis of variance for experiments with orthogonal block structure.

2018 ◽  
Vol 55 (2) ◽  
pp. 147-178
Author(s):  
Tadeusz Caliński ◽  
Idzi Siatkowski
Keyword(s):  
Experimental Data ◽  
Hypothesis Testing ◽  
Analysis Of Variance ◽  
Analytical Methods ◽  
Block Structure ◽  
Block Designs ◽  
New Approach ◽  
Testing Procedures

SummaryThe main estimation and hypothesis testing procedures are presented for experiments conducted in nested block designs of a certain type. It is shown that, under appropriate randomization, these experiments have the convenient orthogonal block structure. Due to this property, the analysis of experimental data can be performed in a comparatively simple way. Certain simplifying procedures are indicated. The main advantage of the presented methodology concerns the analysis of variance and related hypothesis testing procedures. Under the adopted approach one can perform these analytical methods directly, not by combining the results from analyses based on stratum submodels. The application of the presented theory is illustrated by three examples of real experiments in relevant nested block designs. The present paper is the second in the planned series concerning the analysis of experiments with orthogonal block structure.

scholarly journals On a New Approach to the Analysis of Variance for Experiments with Orthogonal Block Structure.

2017 ◽  
Vol 54 (2) ◽  
pp. 91-122
Author(s):  
Tadeusz Calinski ◽  
Idzi Siatkowski
Keyword(s):  
Experimental Data ◽  
Hypothesis Testing ◽  
Analysis Of Variance ◽  
Block Structure ◽  
Block Designs ◽  
New Approach ◽  
Testing Procedures

Abstract Summary The main estimation and hypothesis testing results are presented for experiments conducted in proper block designs. It is shown that, under appropriate randomization, these experiments have the convenient orthogonal block structure. Because of this, the analysis of experimental data can be performed in a comparatively simple way. Certain simplifying procedures are introduced. The main advantage of the presented methodology concerns the analysis of variance and related hypothesis testing procedures. Under the adopted approach one can perform them directly, not by combining results from intra-block and inter-block analyses. Application of the theory is illustrated by three examples of real experiments in proper block designs. This is the first of a projected series of papers concerning the analysis of experiments with orthogonal block structure.

scholarly journals On a new approach to the analysis of variance for experiments with orthogonal block structure. III. Experiments in row-column designs

2019 ◽  
Vol 56 (2) ◽  
pp. 183-213
Author(s):  
Tadeusz Caliński ◽  
Agnieszka Łacka ◽  
Idzi Siatkowski
Keyword(s):  
Experimental Data ◽  
Hypothesis Testing ◽  
Analysis Of Variance ◽  
Analytical Methods ◽  
Block Structure ◽  
Practical Application ◽  
New Approach ◽  
Testing Procedures ◽  
The Third

SummaryThe main estimation and hypothesis testing procedures are presented for experiments conducted in row-column designs of a certain desirable type. It is shown that, under appropriate randomization, these experiments have the convenient orthogonal block structure. Due to this property, the analysis of experimental data can be performed in a comparatively simple way. Relevant simplifying procedures are indicated. The main advantage of the presented methodology concerns the analysis of variance and related hypothesis testing procedures. Under the adopted approach one can perform these analytical methods directly, not by combining results from analyses based on some stratum submodels. Practical application of the presented theory is illustrated by four examples of real experiments in the relevant row-column designs. The present paper is the third in the projected series of publications concerning the analysis of experiments with orthogonal block structure.

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

2020 ◽  
Vol 57 (2) ◽  
pp. 151-175
Author(s):  
Tadeusz Caliński ◽  
Agnieszka Łacka ◽  
Idzi Siatkowski
Keyword(s):  
Experimental Data ◽  
Hypothesis Testing ◽  
Analysis Of Variance ◽  
Block Structure ◽  
Practical Application ◽  
Simple Manner ◽  
New Approach ◽  
Testing Procedures ◽  
Split Plot

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.

scholarly journals Specific residue: application of orthogonal contrasts when heteroscedasticity is present

2010 ◽  
Vol 67 (1) ◽  
pp. 117-125
Author(s):  
Maria Cristina Stolf Nogueira
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Analysis Of Variance ◽  
Residue Analysis ◽  
Sum Of Squares ◽  
Block Designs ◽  
Mean Square ◽  
Orthogonal Contrasts ◽  
Variance Homogeneity ◽  
Analyze Data

When experimental data are submitted to analysis of variance, the assumption of data homoscedasticity (variance homogeneity among treatments), associated to the adopted mathematical model must be satisfied. This verification is necessary to ensure the correct test for the analysis. In some cases, when data homoscedascity is not observed, errors may invalidate the analysis. An alternative to overcome this difficulty is the application of the specific residue analysis, which consists of the decomposition of the residual sum of squares in its components, in order to adequately test the correspondent orthogonal contrasts of interest between treatment means. Although the decomposition of the residual sum of squares is a seldom used procedure, it is useful for a better understanding of the residual mean square nature and to validate the tests to be applied. The objective of this review is to illustrate the specific residue application as a valid and adequate alternative to analyze data from experiments following completely randomized and randomized complete block designs in the presence of heteroscedasticity.

OPTIMAL TESTING IN A FIXED-EFFECTS FUNCTIONAL ANALYSIS OF VARIANCE MODEL

2004 ◽  
Vol 02 (04) ◽  
pp. 323-349 ◽  
Author(s):  
FELIX ABRAMOVICH ◽  
ANESTIS ANTONIADIS ◽  
THEOFANIS SAPATINAS ◽  
BRANI VIDAKOVIC
Keyword(s):  
Functional Analysis ◽  
Hypothesis Testing ◽  
Analysis Of Variance ◽  
Fixed Effects ◽  
Wavelet Coefficients ◽  
Variance Model ◽  
Testing Procedures ◽  
Functional Interactions ◽  
Wide Range ◽  
Main Effects

We consider the testing problem in a fixed-effects functional analysis of variance model. We test the null hypotheses that the functional main effects and the functional interactions are zeros against the composite nonparametric alternative hypotheses that they are separated away from zero in L2-norm and also possess some smoothness properties. We adapt the optimal (minimax) hypothesis testing procedures for testing a zero signal in a Gaussian "signal plus noise" model to derive optimal (minimax) non-adaptive and adaptive hypothesis testing procedures for the functional main effects and the functional interactions. The corresponding tests are based on the empirical wavelet coefficients of the data. Wavelet decompositions allow one to characterize different types of smoothness conditions assumed on the response function by means of its wavelet coefficients for a wide range of function classes. In order to shed some light on the theoretical results obtained, we carry out a simulation study to examine the finite sample performance of the proposed functional hypothesis testing procedures. As an illustration, we also apply these tests to a real-life data example arising from physiology. Concluding remarks and hints for possible extensions of the proposed methodology are also given.

Theoretical Interpretation of High-Performance Chromatographic Data for a Heterogeneous Series of Compounds

1992 ◽  
Vol 57 (1) ◽  
pp. 33-45
Author(s):  
Vladimír Jakuš
Keyword(s):  
Experimental Data ◽  
High Performance ◽  
Theoretical Interpretation ◽  
Retention Data ◽  
Theoretical Evaluation ◽  
New Approach ◽  
Free Energy Of Solvation ◽  
Rp Hplc ◽  
Mobile Phases ◽  
Reversed Phases

A new approach to theoretical evaluation of the Gibbs free energy of solvation was applied for estimation of retention data in high-performance liquid chromatography on reversed phases (RP-HPLC). Simple and improved models of stationary and mobile phases in RP-HPLC were employed. Statistically significant correlations between the calculated and experimental data were obtained for a heterogeneous series of twelve compounds.

scholarly journals Dimensioning a Call Center: Simulation or Queue Theory?

2009 ◽  
Vol 2 (2) ◽  
pp. 34 ◽  
Author(s):  
Marco Aurélio Carino Bouzada
Keyword(s):  
Analytical Method ◽  
Analytical Methods ◽  
Call Center ◽  
Experimental Approach ◽  
Call Centers ◽  
Experimental Methods ◽  
New Approach ◽  
Alternative Methodology ◽  
Queue Theory ◽  
Set Up

The objective of this paper is to establish a dichotomy - opposing analytical methods (such as Queue Theory) to experimental methods (such as Simulation) and discussing their adequateness to complex operations - set up in the matter of dimensioning the handling capacity of a large brazilian call centers company. The literature related to the application of such methods at call centers is reviewed, and the way the question is treated nowadays by the company is described. Then an experimental approach is suggested to be implemented as an alternative methodology to deal with the issue, instead of the analytical method in use. The results obtained are used to justify the adequacy of the experimental approach to the modern call centers operation, as long as it is possible to have the model closer to reality. The main implication points to a better understanding of the operation achieved with the new approach

scholarly journals Exact Solution for Viscoelastic Flow in Pipe and Experimental Validation

Polymers ◽  
2022 ◽  
Vol 14 (2) ◽  
pp. 334
Author(s):  
Ekaterina Vachagina ◽  
Nikolay Dushin ◽  
Elvira Kutuzova ◽  
Aidar Kadyirov
Keyword(s):  
Experimental Data ◽  
Exact Solution ◽  
Analytical Methods ◽  
Experimental Validation ◽  
Parametric Method ◽  
Fluid Flows ◽  
Parametric Representation ◽  
Viscoelastic Flow ◽  
Exponential Form ◽  
Image Velocimetry

The development of analytical methods for viscoelastic fluid flows is challenging. Currently, this problem has been solved for particular cases of multimode differential rheological equations of media state (Giesekus, the exponential form of Phan-Tien-Tanner, eXtended Pom-Pom). We propose a parametric method that yields solutions without additional assumptions. The method is based on the parametric representation of the unknown velocity functions and the stress tensor components as a function of coordinate. Experimental flow visualization based on the SIV (smoke image velocimetry) method was carried out to confirm the obtained results. Compared to the Giesekus model, the experimental data are best predicted by the eXtended Pom-Pom model.

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