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 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.

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 Making inference from wildlife collision data: inferring predator absence from prey strikes

PeerJ ◽  
2017 ◽  
Vol 5 ◽  
pp. e3014 ◽  
Author(s):  
Peter Caley ◽  
Geoffrey R. Hosack ◽  
Simon C. Barry
Keyword(s):  
Prey Species ◽  
Red Fox ◽  
Prey Availability ◽  
Numerical Response ◽  
Practical Application ◽  
Ecological Inference ◽  
Predator Species ◽  
New Approach ◽  
Predictive Probability ◽  
Irreducible Uncertainty

Wildlife collision data are ubiquitous, though challenging for making ecological inference due to typically irreducible uncertainty relating to the sampling process. We illustrate a new approach that is useful for generating inference from predator data arising from wildlife collisions. By simply conditioning on a second prey species sampled via the same collision process, and by using a biologically realistic numerical response functions, we can produce a coherent numerical response relationship between predator and prey. This relationship can then be used to make inference on the population size of the predator species, including the probability of extinction. The statistical conditioning enables us to account for unmeasured variation in factors influencing the runway strike incidence for individual airports and to enable valid comparisons. A practical application of the approach for testing hypotheses about the distribution and abundance of a predator species is illustrated using the hypothesized red fox incursion into Tasmania, Australia. We estimate that conditional on the numerical response between fox and lagomorph runway strikes on mainland Australia, the predictive probability of observing no runway strikes of foxes in Tasmania after observing 15 lagomorph strikes is 0.001. We conclude there is enough evidence to safely reject the null hypothesis that there is a widespread red fox population in Tasmania at a population density consistent with prey availability. The method is novel and has potential wider application.

scholarly journals Phenomenological nuclear density distributions

2020 ◽  
Vol 4 ◽  
pp. 85
Author(s):  
G. A. Lalazissis ◽  
C. P. Panos
Keyword(s):  
Experimental Data ◽  
Density Distribution ◽  
Electron Scattering ◽  
Nuclear Density ◽  
Practical Application ◽  
Density Distributions ◽  
Pionic Atoms

A recently proposed semiphenomenological density distribution for neutrons and protons in nuclei is discussed. This density was derived using the separation energies of the last neutron or proton. A com­parison is made with the symmetrised Fermi density distribution with parameters determined by fitting electron scattering experimental data and with a Fermi density with parameters coming from a recent anal­ysis of pionic atoms. Theoretical expressions for rms radii for neutron, proton and matter distributions are proposed, which give the average trend of the variation of these quantities as functions of Ν, Ζ and A respectively. To facilitate the use of the new density all the parameters needed in a practical application are tabulated for a series of nuclei. Some applications of the new density are also discussed.

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.

Split-Plot Analysis of Variance

2014 ◽  
pp. 71-75
Author(s):  
Richard A. Armstrong ◽  
Anthony C. Hilton
Keyword(s):  
Analysis Of Variance ◽  
Plot Analysis ◽  
Split Plot
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