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.

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.

Personal Beliefs Scale Redux: A Model for Hypothesis Testing

1996 ◽  
Vol 78 (1) ◽  
pp. 195-203 ◽  
Author(s):  
Robert A. Embree
Keyword(s):  
Fuzzy Logic ◽  
Hypothesis Testing ◽  
Analysis Of Variance ◽  
Classical Logic ◽  
Second Order ◽  
Personal Beliefs ◽  
Important Distinction ◽  
Variance Model

Data obtained from the Personal Beliefs Scale of Embree and Embree were used to develop an analysis of variance model for mind-body belief which emphasized a distinction between “conventional” and “unconventional” mind-body beliefs. By means of this model a critically important distinction between high scoring second-order psychosomaticism subjects was achieved. It was proposed that subjects low in unconventional/high conventional tend to employ classical logic when rating mind-body belief items and that subjects high in unconventional/high conventional mind-body belief characteristically engage in fuzzy logic. Possible applications of the model in research were discussed.

Coherent Analysis-of-Variance Hypothesis-Testing Strategies: A General Model

1982 ◽  
Vol 7 (3) ◽  
pp. 193-206 ◽  
Author(s):  
M. Austin Betz ◽  
Joel R. Levin
Keyword(s):  
Hypothesis Testing ◽  
Analysis Of Variance ◽  
Hierarchical Model ◽  
The Other ◽  
Factorial Anova ◽  
Testing Strategies ◽  
Anova Model ◽  
Alternative Hypotheses ◽  
The One ◽  
Main Effects

Logically consistent (“coherent”) hypothesis-testing strategies for factorial analysis-of-variance (ANOVA) designs are proposed in the context of a hierarchical model. It is shown that all of the hypotheses associated with the “traditional” factorial ANOVA model (i.e., main effects and interactions) are conceptually independent and occupy the lowest levels of the hierarchy. A research example is presented to illustrate the kind of conclusions that legitimately follow from testing the traditional hypotheses on the one hand, versus a variety of alternative hypotheses on the other.

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. 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.

Selection of a Model for a Two-Factor Analysis of Variance

1966 ◽  
Vol 19 (3_suppl) ◽  
pp. 1319-1332 ◽  
Author(s):  
Leila S. Cain
Keyword(s):  
Factor Analysis ◽  
Empirical Evidence ◽  
Analysis Of Variance ◽  
Significant Interaction ◽  
Interaction Effects ◽  
Variance Model ◽  
Random Samples ◽  
Fixed Model ◽  
Main Effects ◽  
Selection Of

There are three models for a two-factor analysis of variance, Model I (effects fixed), Model II (effects random) and Model III (mixed). In Model I main effects and interaction effects may always be estimated, but the results of the analysis may not be generalized to any effects other than those represented in the study. If there is a significant interaction in Model II, neither main effects nor interaction effects may be meaningfully estimated, but the results of the analysis may be generalized to the populations of which the main effects are random samples. Empirical evidence suggests application of Model I procedures to Model II data can produce results comparable to those obtained by “proper” usage of Model I methods.

scholarly journals Bayesian modeling and significant features exploration in wavelet power spectra

2007 ◽  
Vol 14 (1) ◽  
pp. 79-88 ◽  
Author(s):  
D. V. Divine ◽  
F. Godtliebsen
Keyword(s):  
Data Analysis ◽  
Traditional Approach ◽  
Statistical Significance ◽  
Power Spectra ◽  
Simulated Data ◽  
Scale Space ◽  
Independent Random Variables ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Testing Procedures

Abstract. This study proposes and justifies a Bayesian approach to modeling wavelet coefficients and finding statistically significant features in wavelet power spectra. The approach utilizes ideas elaborated in scale-space smoothing methods and wavelet data analysis. We treat each scale of the discrete wavelet decomposition as a sequence of independent random variables and then apply Bayes' rule for constructing the posterior distribution of the smoothed wavelet coefficients. Samples drawn from the posterior are subsequently used for finding the estimate of the true wavelet spectrum at each scale. The method offers two different significance testing procedures for wavelet spectra. A traditional approach assesses the statistical significance against a red noise background. The second procedure tests for homoscedasticity of the wavelet power assessing whether the spectrum derivative significantly differs from zero at each particular point of the spectrum. Case studies with simulated data and climatic time-series prove the method to be a potentially useful tool in data analysis.

scholarly journals Pacing in Time-Limited Ultramarathons from 6 to 24 Hours—The Aspects of Age, Sex and Performance Level

2021 ◽  
Vol 13 (5) ◽  
pp. 2705
Author(s):  
Hagen Deusch ◽  
Pantelis T. Nikolaidis ◽  
José Ramón Alvero-Cruz ◽  
Thomas Rosemann ◽  
Beat Knechtle
Keyword(s):  
Analysis Of Variance ◽  
Coefficient Of Variation ◽  
Training Programs ◽  
Performance Level ◽  
Running Speed ◽  
And Performance ◽  
Main Effects ◽  
And Training ◽  
Age And Sex

(1) Background: Compared with marathon races, pacing in time-limited ultramarathons has only been poorly discussed in the literature. The aim of the present study was to analyze the interaction of performance level, age and sex with pacing during 6 h, 12 h or 24 h time-limited ultramarathons. (2) Methods: Participants (n = 937, age 48.62 ± 11.80 years) were the finishers in 6 h (n = 40, 17 women and 23 men), 12 h (n = 232, 77 women and 155 men) and 24 h (n = 665, 166 women and 409 men) ultramarathons. The coefficient of variation (CV), calculated as SD/mean, was used to described pacing. Low scores of CV denoted a more even pacing, and vice versa. A two-way analysis of variance examined the main effects and interactions of sex and race duration on age, race speed and pacing. (3) Results: More men participated in the longer race distances than in the shorter ones and men were older and faster than women. Comparing the 6 h, 12 h and 24 h races, the finishers in the 6 h were the fastest, the finishers in the 12 h were the oldest and the finishers in the 24 h showed the most variable pacing. Furthermore, the faster running speed in the 12 h (women, r = −0.64; men, r = −0.49, p < 0.001) and the 24 h (r = −0.47 in women and men, p < 0.001) was related to less variable pacing. (4) Conclusions: These data might help runners and coaches to choose the the proper duration of a race and training programs for their athletes.

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