Equivalence of orthogonal and nonorthogonal analysis of variance.

Overall, John E.; Spiegel, Douglas K.; Cohen, Jacob

doi:10.1037/h0076381

Cited by 82 publications

(34 citation statements)

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“…As for reaction times, a two-way nonorthogonal ANOVA (Overall & Spiegel, 1969;Overall, Spiegel, & Cohen, 1975) indicated that the main effects of change amplitude, F(9, 558) ¼ 10.16, p , 0.01) and position, F(1, 558) ¼ 11.12, p , 0.01, are both significant, but interaction, F(9, 558) ¼ 0.83, ns, is not significant.…”

Section: Resultsmentioning

confidence: 88%

Temporal characteristics of depth perception from motion parallax

2013

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Temporal characteristics of depth perception from motion parallax were examined by modulating parallax intermittently while observers moved their head side to side. In Experiment 1, parallax of a fixed value was introduced only for the central 1/6 to 5/6 portion of each component head movement. It was found that the perceived depth was proportional to the temporal average of parallax-specified depth. In addition, observers did not notice any abrupt temporal change of depth. In Experiment 2, parallax was increased or decreased once per trial either at the center or the end of one of the component head movements, and observers judged the direction of depth change. Again, observers did not notice any abrupt change of depth. The percentage of correct responses was almost constant for large change amplitudes. Reaction times to the change were over 1 s even for the largest changes, and it increased for smaller change amplitudes. These results indicate that the mechanism for depth from parallax has a configuration similar to that proposed for structure from motion, and that it involves a temporal integration process with a relatively long time-constant.

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Section: Resultsmentioning

confidence: 88%

Temporal characteristics of depth perception from motion parallax

2013

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“…Those results indicate that the significant sex difference in alcohol behavior disappears when differences due to occupation are partialed out. The method of analysis and interpretation were same as discussed by Overall, Spiegel, and Cohen (1975). Because interest here is in illustrating the potential of general linear model analysis of categorical data, no further discussion of the results obtained from analysis of the 4-point alcohol behavior scale will be undertaken at this time.…”

Section: Recent Investigations Bymentioning

confidence: 99%

“…In a nonorthogonal design, the least squares regression method provides estimates of the same response probabilities that are estimated from the marginal response frequencies in a balanced design involving the same factors. This is an extension of the argument used by Overall, Spiegel, and Cohen (1975) in proposing a criterion for equivalence of orthogonal and nonorthogonal designs for ANOVA with quantitative dependent variables.…”

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confidence: 95%

“…For the simple examples of Table 1, equivalent estimates of the independent effects of Factors A and B could be obtained in other ways. The frequencies in each cell of the A x B design could be transformed to proportion of S and the esti- Table 1 Orthogonal and Nonorthogonal Designs with Equal Response Probabilities in Corresponding Cells It is important to emphasize that the recommended procedure for estimation of adjusted response probabilities in the analysis of categorical data involves &dquo;effects coding&dquo; of independent factors and Method 1 strategy, as described by Overall and Spiegel (1969) and Overall, Spiegel, and Cohen (1975). Several computer programs for nonorthogonal ANOVA or MANOVA include such analysis as an option.…”

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confidence: 99%

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Calculation of Adjusted Response Frequencies Using Least Squares Regression Methods

Overall

1980

Applied Psychological Measurement

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The use of general linear regression methods for the analysis of categorical data is recommended. The general linear model analysis of a 0,1 coded response variable produces estimates of the same response probabilities that might otherwise be estimated from frequencies in a multiway contingency table. When factors in the design are correlated, the regression analysis estimates the same response probabilities that would be estimated from the simple marginal frequencies in a balanced orthogonal design. The independent effects that are estimated by the regression analysis are the unweighted means of the response probabilities in various cells of a cross-classification design; however, it is not necessary that all cells in a complex design be filled in order for the estimates to have that interpretation. The advantages of the general linear model analysis include familiarity of most psychologists with the methods, availability of computer programs, and ease of application to problems that are too complex for development of complete multiway contingency tables.The estimation of response probabilities is one of the most important measurement problems in psychological research. The proportion of subjects producing a &dquo;positive&dquo; response in a given situation is the relative frequency estimate of response probability. In many situations, however, it is desirable to measure response probabilities APPLIED

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“…We use effects-coding of the factors in the matrices X and Z (Overall, Spiegel, and Cohen 1975). It is important to note that Equation 3 is the equation that is of key interest for inference.…”

Section: Banova Modelsmentioning

confidence: 99%

BANOVA: An R Package for Hierarchical Bayesian ANOVA

Chen¹,

Wedel²

2017

J. Stat. Soft.

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In this paper, we develop generalized hierarchical Bayesian ANOVA, to assist experimental researchers in the behavioral and social sciences in the analysis of experiments with within-and between-subjects factors. The method alleviates several limitations of classical ANOVA, still commonly employed in those fields of research. An accompanying R Package for BANOVA is developed. It offers statistical routines and several easy-to-use functions for estimation of hierarchical Bayesian ANOVA models that are tailored to the analysis of experimental research. MCMC simulation is used to simulate posterior samples of the parameters of each model specified by the user. The core program is written in R and JAGS. After preparing the data in the required format, users simply select an appropriate model, and can estimate it without any advanced coding being required. The main aim of the R package is to offer freely accessible resources for hierarchical Bayesian ANOVA analysis, which makes it easy to use for applied researchers.

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Equivalence of orthogonal and nonorthogonal analysis of variance.

Cited by 82 publications

References 16 publications

Temporal characteristics of depth perception from motion parallax

Temporal characteristics of depth perception from motion parallax

Calculation of Adjusted Response Frequencies Using Least Squares Regression Methods

BANOVA: An R Package for Hierarchical Bayesian ANOVA

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