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.

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. 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 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 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.

A New Modeling Approach to Reacting Dispersed Flow in Smelting Cyclones

2000 ◽  
Author(s):  
M. Modigell ◽  
M. Weng
Keyword(s):  
Experimental Data ◽  
Flow Field ◽  
Gas Flow ◽  
Equilibrium Calculation ◽  
New Approach ◽  
Reaction Progress ◽  
Numeric Simulation ◽  
Thermodynamic Equilibrium Calculation ◽  
Simulation Results ◽  
Comparison With Experimental Data

Abstract The present paper proposes a new approach to analyse the conversion of complexly composed particles that are dispersed in a cyclone gas flow at high temperatures. The numeric simulation of flow field and particle trajectories is coupled with a thermodynamic equilibrium calculation which describes the particle reaction progress. First simulation results and the comparison with experimental data are shown in this paper.

scholarly journals Key factors in psychotherapy training: an analysis of trainers’, trainees’ and psychotherapists’ points of view

2019 ◽  
Vol 22 (3) ◽  
Author(s):  
Diego Rocco ◽  
Alessandro Gennaro ◽  
Lorena Filugelli ◽  
Patrizia Squarcina ◽  
Elena Antonelli
Keyword(s):  
Analysis Of Variance ◽  
Clinical Training ◽  
Ad Hoc ◽  
Training Programs ◽  
Psychotherapy Training ◽  
Theoretical Background ◽  
Key Factors ◽  
New Approach ◽  
Research Gap ◽  
Points Of View

The literature on clinical training lacks identifications of the factors that are most relevant in training programs; accordingly, the main aim of this work is to fill this research gap by assessing which factors that trainers, trainees and psychotherapists consider most relevant in psychotherapy training programs. A secondary aim is to identify whether these factors differ among trainers, trainees and psychotherapists. An ad hoc questionnaire was created and administered at 24 psychotherapy schools from 14 institutions; the sample included 641 trainees, 172 trainers and 218 psychotherapists of various theoretical orientations. The questionnaire included 63 items and used a 5-point Likert scale. An exploratory factor analysis was completed to identify the latent structure. The reliability of the dimensions was then checked. Finally, an analysis of variance and a multivariate analysis of variance were completed to achieve the study’s aims. Four factors emerged from the study’s results: trainers’ relational characteristics, supervision, transmission of clinical know-how, and theoretical background and technical support. All these factors displayed acceptable reliability and internal consistency. Moreover, their relative rankings varied based on the participants’ roles and theoretical backgrounds. This study’s results indicate that the new instrument’s psychometric qualities are acceptable. It thus could be used to develop a new approach to psychotherapy training, as this study’s results regarding trainees’ needs underline the differences between trainees’ perceptions of those needs, as compared to trainers’ and psychotherapists’ perceptions.

New approach to obtain high resolution using conventional block designs in PET

2006 ◽  
Vol 53 (1) ◽  
pp. 18-24 ◽  
Author(s):  
M. Aykac ◽  
R. Grazioso ◽  
K. Bean ◽  
M. Schmand
Keyword(s):  
High Resolution ◽  
Block Designs ◽  
New Approach
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