Correction: Computing the Analysis of Variance Table for Experiments Involving Qualitative Factors and Zero Amounts of Quantitative Factors

1974 ◽  
Vol 28 (3) ◽  
pp. 112 ◽  
Keyword(s):  
Analysis Of Variance ◽  
Variance Table ◽  
Qualitative Factors

scholarly journals Random effects models for complex designs

2020 ◽  
Vol 29 (12) ◽  
pp. 3695-3706
Author(s):  
RG Jarrett ◽  
VT Farewell ◽  
AM Herzberg
Keyword(s):  
Random Effects ◽  
Analysis Of Variance ◽  
Two Phase ◽  
Full Account ◽  
Medical Practitioners ◽  
Random Effects Models ◽  
Multiple Measurements ◽  
Variance Table ◽  
Error Terms ◽  
Phase Design

Plaid designs are characterised by having one set of treatments applied to rows and another set of treatments applied to columns. In a 2003 publication, Farewell and Herzberg presented an analysis of variance structure for such designs. They presented an example of a study in which medical practitioners, trained in different ways, evaluated a series of videos of patients obtained under a variety of conditions. However, their analysis did not take full account of all error terms. In this paper, a more comprehensive analysis of this study is presented, informed by the recognition that the study can also be regarded as a two-phase design. The development of random effects models is outlined and the potential importance of block-treatment interactions is highlighted. The use of a variety of techniques is shown to lead to a better understanding of the study. Examination of the variance components involved in the expected mean squares is demonstrated to have particular value in identifying appropriate error terms for F-tests derived from an analysis of variance table. A package such as ASReml can also be used provided an appropriate error structure is specified. The methods presented can be applied to the design and analysis of other complex studies in which participants supply multiple measurements under a variety of conditions.

scholarly journals Effect of Experimental Blocking on the Suppression of Spatial Dependence Potentially Attributable to Physicochemical Properties of Soils

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Aquiles E. Darghan ◽  
Giovanni Reyes ◽  
Carlos A. Rivera ◽  
Edwin F. Grisales
Keyword(s):  
Analysis Of Variance ◽  
Spatial Dependence ◽  
Linear Modeling ◽  
Basic Principles ◽  
Independence Assumption ◽  
Additional Advantage ◽  
Standard Linear ◽  
Variance Table ◽  
Edaphic Properties

One of the basic principles of experimental design is blocking, which is an important factor in the treatment of the systematic spatial variability that can be found in the edaphic properties where agricultural experiments are conducted. Blocking has a mitigating or suppressing effect on the spatial dependence in the residuals of a model, something desirable in standard linear modeling, specifically in design models. Some computer programs yield a p value associated with the blocking effect in the analysis of variance table that in many cases has been incorrectly used to discard it, and although it may improve some properties of the analysis, it may affect the independence assumption required in several models. Therefore, the present research recommends the use of the H statistic associated with the corrected blocking efficiency to show the role of blocking in modeling with the incorporation of an additional advantage rarely considered related to the suppression or mitigation of spatial dependence. With the use of the Moran index, the spatial dependence of the residuals was studied in a simple factorial design in a completely randomized and blocking field layout, which evidenced the advantages of blocking in the mitigation or suppression of the spatial dependence despite the apparently little or no importance it seems to show in the analysis of variance table.

Using the randomisation in specifying the ANOVA model and table for properly and improperly replicated grazing trials

1998 ◽  
Vol 38 (4) ◽  
pp. 325 ◽  
Author(s):  
C. J. Brien ◽  
C. G. B. Demétrio
Keyword(s):  
Analysis Of Variance ◽  
Experimental Unit ◽  
Anova Model ◽  
Variance Table ◽  
Error Terms

Summary. A method for deriving the analysis of variance for an experiment is presented and applied to grazing trials. A special feature of grazing trials, specifically utilised by our method, is that they involve at least 2 randomisations: treatments are randomised to field units (for example paddocks or plots), and field units are randomised to animals. Randomisation results in the confounding (‘mixing up’) of terms and our method includes separate terms in the analysis of variance table for confounded terms so that all sources of variability in the experiment have terms for them included in the table and the confounding between the sources of variability in the experiment is explicitly displayed in the table. This information is used in determining the valid error terms and we will present examples that show how to ascertain these for effects of interest and hence which effects can be tested. In this it fulfils the same role as the contentious process of identifying the experimental unit. It will be demonstrated that the inclusion of separate terms for confounded terms results in improper replication in grazing trials being automatically signalled, and makes its ramifications clear.

One-Way between Subjects Design: Simulated Data and Analysis Using SAS

1994 ◽  
Vol 21 (1) ◽  
pp. 53-55 ◽  
Author(s):  
John F. Walsh
Keyword(s):  
Analysis Of Variance ◽  
Simulated Data ◽  
Data File ◽  
Individual Student ◽  
Data Sets ◽  
Statistical Software ◽  
Starting Values ◽  
Software Packages ◽  
Variance Table ◽  
The One

An SAS program enables instructors to provide individual students with simulated data for the one-way between subjects design. The instructor chooses the starting values: means, standard deviations, and number of subjects. For each student, the program produces an ASCII data file that can be analyzed by calculator or by many statistical software packages. For the instructor, the program produces a summary analysis of variance table for each analysis. Individual student names appear on the data sets and the summary file for the instructor.

scholarly journals Changes in Concentrations of Monovalent Basic Cations in the Water of the Čaradice Stream / Zmeny Koncentrácií Jednomocných Bázických Katiónov vo vode Vodného toku Čaradický Potok

2013 ◽  
Vol 16 (1) ◽  
pp. 4-9
Author(s):  
Jaroslav Noskovič ◽  
Eva Candráková ◽  
Mária Babošová ◽  
Jana Porhajašová
Keyword(s):  
Analysis Of Variance ◽  
Forest Ecosystem ◽  
Slovak Republic ◽  
Average Concentration ◽  
Reference Period ◽  
Spring Season ◽  
Qualitative Factors ◽  
The Government ◽  
The Village ◽  
Basic Cations

Abstract In the years 2005-2010, the changes in concentrations of monovalent basic cations in the Čaradice Stream were evaluated depending on the time and place of sampling in its longitudinal profile. Results show that the average concentration of Na+ in the whole period was 14.75 mg. dm-3. Its share in the total amount of monovalent basic cations of Na+ and K+ in the whole reference period was 76.32%. The mass ratio of Na+ : K+ in the whole period was 3.34 : 1. Depending on the time of sampling, the lowest average sodium concentrations of the whole period were recorded in the spring season with the minimum average in March. The highest average concentration of the whole reference period was recorded in September. Depending on the sampling site, the minimum average concentration was recorded in a forest ecosystem and an ecosystem of permanent grassland, and the maximum average concentration in the village Kozarovce. Using the analysis of variance, we detected a statistically significant effect of all three qualitative factors (year, month and place of sampling) on the change of concentration. According to the Regulation of the Government of the Slovak Republic No. 269/2010 Coll., the 90th percentile values of this indicator are lower than the recommended value. The average concentration of potassium in the whole reference period was 4.54 mg. dm-3. The share of K+ in the total amount of monovalent basic cations in the whole period reached 23.68%. The lowest average concentrations of the whole period were usually found in the spring season, with the minimum value in March. The maximum average concentration of the whole reference period was recorded in July. Similarly to Na+, the lowest average concentration of K+ was detected in a forest ecosystem and the highest one in the village Kozarovce. The effect of seasonality on the dynamics of Na+ and K+ concentrations during the period was not detected. Using the analysis of variance, we found a statistically significant effect of all three qualitative factors (year, month and place of sampling) on the change of concentration. In the Regulation of the Government of the Slovak Republic No. 269/2010 Coll., the recommended value for potassium is not specified. The discharge rate significantly affected the changes in concentrations of Na+ and K+ in the stream.

Expected mean squares.

2021 ◽  
pp. 244-251
Author(s):  
Edward F. Durner
Keyword(s):  
Statistical Theory ◽  
Analysis Of Variance ◽  
Anova Analysis ◽  
Theoretical Derivation ◽  
Snap Beans ◽  
Sources Of Variation ◽  
Variance Table

Abstract This chapter focuses on expected mean squares. Expected mean squares are formulas based on statistical theory identifying the components of variability in sources of variation of an ANOVA (analysis of variance) table. Their theoretical derivation is beyond the scope of this text, thus they are presented in a simpler way here, providing a method for deriving expected mean squares without a background in statistical theory. The productivity of 10 cultivars of snap beans was used as an example.

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