Random effects one-way analysis of variance.

2017 ◽  
pp. 288-304
Author(s):  
M. Kaps ◽  
W. R. Lamberson
Keyword(s):  
Random Effects ◽  
Analysis Of Variance

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.

Some Remarks on the Expected Mean Squares in Analysis of Variance in the Assessment of Individual Differences in Learning

1978 ◽  
Vol 47 (3_suppl) ◽  
pp. 1289-1290
Author(s):  
Gary C. Ramseyer ◽  
Kenneth L. Leicht
Keyword(s):  
Individual Differences ◽  
Random Effects ◽  
Analysis Of Variance ◽  
Fixed Effects ◽  
Tests Of Significance ◽  
Learner Interactions ◽  
Illustrative Application

Leicht, et al. (1978) proposed that learning units, e.g., lists, passages, be randomization units, rather than learners (subjects) as is typical, so that the significance of trial-learner interactions can be tested with analysis of variance. In an illustrative application of the suggested rearrangement, learners were arbitrarily selected (fixed-effects factor). If the investigator wishes greater generalizability of individual differences in learning, learners must be randomly selected from a specified population (random-effects factor). The appropriate expected mean squares and tests of significance are presented for both models and subsequent comments are made.

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