Repeated-Measures Designs: Univariate or Multivariate Analysis of Variance?

1997 ◽  
Vol 85 (1) ◽  
pp. 193-194
Author(s):  
Peter Hassmén
Keyword(s):  
Multivariate Analysis ◽  
Analysis Of Variance ◽  
Repeated Measures ◽  
Type I Error ◽  
Univariate Analysis ◽  
Type I ◽  
Multivariate Analysis Of Variance ◽  
Repeated Measures Analysis ◽  
Alpha Level ◽  
Repeated Measures Designs

Violation of the sphericity assumption in repeated-measures analysis of variance can lead to positively biased tests, i.e., the likelihood of a Type I error exceeds the alpha level set by the user. Two widely applicable solutions exist, the use of an epsilon-corrected univariate analysis of variance or the use of a multivariate analysis of variance. It is argued that the latter method offers advantages over the former.

scholarly journals Repeated measures in randomized block and split-plot experiments

1993 ◽  
Vol 23 (4) ◽  
pp. 625-639 ◽  
Author(s):  
M.L. Gumpertz ◽  
C. Brownie
Keyword(s):  
Multivariate Analysis ◽  
Analysis Of Variance ◽  
Loblolly Pine ◽  
Repeated Measures ◽  
Univariate Analysis ◽  
Complete Analysis ◽  
Phosphorus Fertilization ◽  
Multivariate Analysis Of Variance ◽  
Repeated Measures Data ◽  
Split Plot

Randomized block and split-plot designs are among the most commonly used experimental designs in forest research. Measurements for plots in a block (or subplots in a whole plot) are correlated with each other, and these correlations must be taken into account when analyzing repeated-measures data from blocked designs. The analysis is similar to repeated-measures analysis for a completely randomized design, but test statistics must allow for random block × time effects, and standard errors for treatment means must also incorporate block to block variation and variation among plots within a block. Two types of statistical analysis are often recommended for repeated-measures data: analysis of contrasts of the repeated factor and multivariate analysis of variance. A complete analysis of repeated measures should usually contain both of these components, just as in univariate analysis of variance it is often necessary to decompose the main effects into single degree of freedom contrasts to answer the research objectives. We demonstrate the multivariate analysis of variance and the analysis of contrasts in detail for two experiments. In addition, estimation of coefficients assuming a polynomial growth curve is discussed in detail for one of these experiments. The first experiment, a randomized complete block design, is a forest nutrition study of the long-term effects of midrotation nitrogen and phosphorus fertilization on loblolly pine (Pinustaeda L.); the second experiment, a split-plot design, is an air-pollution study of the effects of ozone and acid precipitation on loblolly pine growth.

Freudian Symbols on Sexual and Creative Aspects of Stories

1998 ◽  
Vol 82 (3) ◽  
pp. 1059-1072
Author(s):  
Constance J. Larson
Keyword(s):  
College Students ◽  
Multivariate Analysis ◽  
Analysis Of Variance ◽  
Repeated Measures ◽  
Univariate Analysis ◽  
Visual Presentation ◽  
Pairwise Comparisons ◽  
Sexual Content ◽  
Multivariate Analysis Of Variance

Sexual content and creativity of stories and story titles was investigated. 96 college students responded to visual presentation of instances of theoretical Freudian symbols. Analyses subjected responses to a 2 (sex) × 2 (symbol) × 2 (mode) × 6 (subscales) analysis of variance with repeated measures on subscales and to multivariate analysis of variance procedures with four dependent measures. These showed men wrote masculine stories and women wrote feminine stories. Certain subscales were more sensitive to sexual content than others. Pairwise comparisons between the subscales among instances of symbols emerged as significant. In addition, subjects exposed to Male symbols wrote stories containing greater latent sexual content than subjects exposed to Female symbols. Creativity of story tides was evident only on a univariate analysis of variance.

scholarly journals Comparison of Some Robust Wilks’ Statistics for the One-Way Multivariate Analysis of Variance (MANOVA )

2019 ◽  
Vol 11 (2) ◽  
pp. 42-58
Author(s):  
Abdullah A. Ameen ◽  
Osama H. Abbas
Keyword(s):  
Multivariate Analysis ◽  
Analysis Of Variance ◽  
Type I Error ◽  
Error Rates ◽  
Type I ◽  
Test Statistics ◽  
Multivariate Analysis Of Variance ◽  
Power Of The Test ◽  
Monte Carlo Studies ◽  
The One

The classicalWilks' statistic is mostly used to test hypothesesin the one-way multivariate analysis of variance (MANOVA), which is highly sensitive to the effects of outliers. The non-robustness of the test statistics based on normal theory has led many authors to examine various options.In this paper, we presented a robust version of the Wilks' statistic and constructed its approximate distribution.A comparison was made between the proposed statistics and some Wilks' statistics. The Monte Carlo studies are used to obtain performance assessment of test statistics in different data sets.Moreover, the results of the type I error rate and the power of test were considered as statistical tools to compare test statistics.The study reveals that, under normally distributed, the type I error rates for the classical and the proposedWilks' statistics are close to the true significance levels, and the power of the test statistics are so close. In addition, in the case of contaminated distribution, the proposed statistic is the best.  

scholarly journals Repeated Measures Analyses for Tree Fruit Experiments

HortScience ◽  
1995 ◽  
Vol 30 (4) ◽  
pp. 845C-845
Author(s):  
Richard P. Marini
Keyword(s):  
Repeated Measures ◽  
Type I Error ◽  
Univariate Analysis ◽  
Type I ◽  
Cross Sectional ◽  
Data Set ◽  
Repeated Measures Analysis ◽  
Tree Fruit ◽  
Split Plot ◽  
Main Effects

Experiments with perennial crops often span several years, and a response variable may be measured on the same plant at several points in time. Such data are often analyzed as a split-plot design, taking time as the split-plot factor. In other cases, separate analyses are performed for each time. The mathematical conditions required for validity of these types of analyses might not hold because measurements repeated on the same plant are not independent. Annual trunk cross-sectional-area (TCSA) measurements from a peach tree training experiment will be used to compare two methods of analyses. The 6-year experiment was a factorial of two heading heights at planting (low vs. high) and two tree forms (central leader vs. open vase). Univariate analysis of variance (ANOVA) and a multivariate repeated measures analysis (MANOVA) was performed. Main effects and interactions were more often significant with ANOVA than with MANOVA. ANOVA performed each year inflated the probability of falsely rejecting a true null hypothesis (Type I error), and was not appropriate for this data set.

scholarly journals Cognitive flexibility of smokers in the context of social anxiety

2020 ◽  
pp. 93-99
Keyword(s):  
Multivariate Analysis ◽  
Social Anxiety ◽  
Analysis Of Variance ◽  
Cognitive Flexibility ◽  
Univariate Analysis ◽  
Multivariate Analysis Of Variance ◽  
Nicotine Abuse ◽  
Significant Difference ◽  
Wilks Lambda ◽  
Study Population

Background: The cognitiveCognitive dysfunction may be an important factor in smoking and nicotine abuse. However, there are very few studies that have examined the effects of psychiatric conditions on the cognitive flexibility of smokers. Objectives: This research was conducted with the aim of examination theto examine cognitive flexibility (perceive theperceived controllability and cognitive alternatives) ofamong smokers in the context of with social anxiety. MaterialMaterials and methods: The research was a study withpresent causal-comparative design. The populationstudy was allconducted on 60 smoker students ofstudying at Arak University, Arak, Iran, in 2018-2019 years. For selecting the research sample the. The study population was selected using the purposive sampling was usedtechnique. At first, the participants completed the Social Phobia Inventory (SPIN) and Cognitive Flexibility Inventory (CFI).. Then, based on the cutoff point scores of SPIN (19 to above),≤), the participants were divided into two smoker groups (n=30 in each group) were selected: smoker groupsof smokers with and without social anxiety. (n=30 in each group). Finally, these groups were compared in perceive the terms of perceived controllability and cognitive alternatives by Multivariate Analysis of Variance (MANOVA).using the multivariate analysis of variance. Results: The results indicated a significant difference in the linerlinear composition of the dependent variables ofin the two groups (wilks,Wilks’ lambda= 0/.799, F50,2= 6/.726, p= P=0/.004). UnivariateThe results of the univariate analysis of variance indicated that the smoker group with social anxiety had lower perceive theperceived controllability and cognitive alternatives, compared to the smoker group without social anxiety. Conclusion: In generalAs the findings indicated, the level of cognitive flexibility in the smokers with and without social anxiety iswas different. Therefore, it is necessary to consideringconsider the evaluation and treatment of cognitive deficits in smokers based on their level of social anxiety.

A Monte Carlo Study on the Performance of a Corrected Formula for ɛ̃ Suggested by Lecoutre

1994 ◽  
Vol 19 (2) ◽  
pp. 119-126 ◽  
Author(s):  
Ru San Chen ◽  
William P. Dunlap
Keyword(s):  
Group Treatment ◽  
Repeated Measures ◽  
Type I Error ◽  
Monte Carlo Study ◽  
Error Rates ◽  
Type I ◽  
Type I Errors ◽  
Repeated Measures Designs ◽  
Number Of Treatment ◽  
Present Simulation

Lecoutre (1991) has pointed out an error in the Huynh and Feldt (1976) formula for ɛ̃ used to adjust the degree of freedom for an approximate test in repeated measures designs with two or more independent groups. The present simulation study confirms that Lecoutre’s corrected ɛ̃ yields less biased estimation of population ɛ and reduces Type I error rates when compared to Huynh and Feldt’s (1976) ɛ̃. The increased accuracy in Type I errors for group-treatment interactions may become substantial when sample sizes are close to the number of treatment levels.

Bayesian Full Rank MANOVA/MANCOVA: An Intermediate Exposition with Interactive Computer Examples

1979 ◽  
Vol 4 (4) ◽  
pp. 357-404 ◽  
Author(s):  
George G. Woodworth
Keyword(s):  
Multivariate Analysis ◽  
Multiple Regression ◽  
Analysis Of Variance ◽  
Univariate Analysis ◽  
Full Rank ◽  
Multivariate Analysis Of Variance

Computation and interpretation of Bayesian full-rank multivariate analysis of variance and covariance is described and illustrated in an exposition intended for readers familiar with univariate analysis of variance and multiple regression.

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