Pairwise Multiple Comparisons in Repeated Measures Designs

1980 ◽  
Vol 5 (3) ◽  
pp. 269-287 ◽  
Author(s):  
Scott E. Maxwell
Keyword(s):  
Repeated Measures ◽  
Mixed Model ◽  
Multiple Comparisons ◽  
Error Rates ◽  
Type I ◽  
Omnibus Test ◽  
Mixed Model Approach ◽  
Significant Difference ◽  
Repeated Measures Designs ◽  
Necessary And Sufficient

Five methods of performing pairwise multiple comparisons in repeated measures designs were investigated. Tukey's Wholly Significant Difference (WSD) test, recommended by most experimental design texts, requires that all differences between pairs of means have a common variance. However, this assumption is equivalent to the sphericity condition that is necessary and sufficient for the validity of the mixed-model approach to the omnibus test. Monte Carlo methods revealed that Tukey's WSD leads to an inflated alpha level when the sphericity assumption is not met. Consideration of both Type I and Type II error rates found in the simulated conditions for the five procedures suggests that a Bonferroni method utilizing a separate error term for each comparison should be employed.

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.

A Monte Carlo Comparison of Seven ε-Adjustment Procedures in Repeated Measures Designs With Small Sample Sizes

1994 ◽  
Vol 19 (1) ◽  
pp. 57-71 ◽  
Author(s):  
Stephen M. Quintana ◽  
Scott E. Maxwell
Keyword(s):  
Repeated Measures ◽  
Type I Error ◽  
Error Rates ◽  
Small Sample ◽  
Small Samples ◽  
Type I ◽  
Sample Sizes ◽  
Type I Error Rates ◽  
Repeated Measures Designs ◽  
Small Sample Sizes

The purpose of this study was to evaluate seven univariate procedures for testing omnibus null hypotheses for data gathered from repeated measures designs. Five alternate approaches are compared to the two more traditional adjustment procedures (Geisser and Greenhouse’s ε̂ and Huynh and Feldt’s ε̃), neither of which may be entirely adequate when sample sizes are small and the number of levels of the repeated factors is large. Empirical Type I error rates and power levels were obtained by simulation for conditions where small samples occur in combination with many levels of the repeated factor. Results suggested that alternate univariate approaches were improvements to the traditional approaches. One alternate approach in particular was found to be most effective in controlling Type I error rates without unduly sacrificing power.

scholarly journals Sisvar: a Guide for its Bootstrap procedures in multiple comparisons

2014 ◽  
Vol 38 (2) ◽  
pp. 109-112 ◽  
Author(s):  
Daniel Furtado Ferreira
Keyword(s):  
Scientific Community ◽  
Type I Error ◽  
Multiple Comparisons ◽  
Error Rates ◽  
Type I ◽  
Type I Error Rates ◽  
Statistical Analysis System ◽  
Scientific Results ◽  
Analysis System ◽  
Multiple Comparison Procedures

Sisvar is a statistical analysis system with a large usage by the scientific community to produce statistical analyses and to produce scientific results and conclusions. The large use of the statistical procedures of Sisvar by the scientific community is due to it being accurate, precise, simple and robust. With many options of analysis, Sisvar has a not so largely used analysis that is the multiple comparison procedures using bootstrap approaches. This paper aims to review this subject and to show some advantages of using Sisvar to perform such analysis to compare treatments means. Tests like Dunnett, Tukey, Student-Newman-Keuls and Scott-Knott are performed alternatively by bootstrap methods and show greater power and better controls of experimentwise type I error rates under non-normal, asymmetric, platykurtic or leptokurtic distributions.

scholarly journals Improved Small Sample Inference Methods for a Mixed-Effects Model for Repeated Measures Approach in Incomplete Longitudinal Data Analysis

Stats ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 174-188
Author(s):  
Yoshifumi Ukyo ◽  
Hisashi Noma ◽  
Kazushi Maruo ◽  
Masahiko Gosho
Keyword(s):  
Clinical Trial ◽  
Repeated Measures ◽  
Type I Error ◽  
Mixed Effects ◽  
Error Rates ◽  
Small Sample ◽  
Mixed Effects Model ◽  
Model Complexity ◽  
Type I ◽  
Inference Methods

The mixed-effects model for repeated measures (MMRM) approach has been widely applied for longitudinal clinical trials. Many of the standard inference methods of MMRM could possibly lead to the inflation of type I error rates for the tests of treatment effect, when the longitudinal dataset is small and involves missing measurements. We propose two improved inference methods for the MMRM analyses, (1) the Bartlett correction with the adjustment term approximated by bootstrap, and (2) the Monte Carlo test using an estimated null distribution by bootstrap. These methods can be implemented regardless of model complexity and missing patterns via a unified computational framework. Through simulation studies, the proposed methods maintain the type I error rate properly, even for small and incomplete longitudinal clinical trial settings. Applications to a postnatal depression clinical trial are also presented.

Music and mindfulness meditation: Comparing four music stimuli composed under similar principles

2020 ◽  
pp. 030573562096979
Author(s):  
Eugenia Hernandez-Ruiz ◽  
Abbey L Dvorak
Keyword(s):  
Repeated Measures ◽  
Mixed Model ◽  
Mindfulness Meditation ◽  
New Music ◽  
Original Music ◽  
Evidence Based ◽  
Supporting Evidence ◽  
Significant Preference ◽  
Repeated Measures Analysis ◽  
Significant Difference

Mindfulness meditation has frequently used sound and music as an important component. However, research on effective music stimuli is scarce. After a series of studies evaluating the most effective, useful, and preferred auditory stimuli, we were interested in exploring whether these effective musical features were transferred to new music. In this study, we evaluate our original music stimuli with three new stimuli composed under similar principles. Non-musician and musician participants ( N = 114) in a multisite study evaluated their mindfulness state after listening to four music stimuli, and rated their usefulness and preference. Results from a repeated-measures analysis of variance (ANOVA) at each site indicated no significant difference in mindfulness effectiveness. Friedman’s ANOVAs for the usefulness of the music stimuli showed similar non-significant results in both sites. A mixed model among sites did not show significant differences among groups. Preference rankings were not significantly different for non-musicians, but musicians did show a statistically significant preference of the Original stimuli over Stimulus 2, probably due to sound quality. These results indicate the feasibility of transferring previously researched and effective musical features to new stimuli. Identifying the effective “active ingredients” of music interventions may be one way of supporting evidence-based practice in music therapy.

Nonparametric Tests for Analyzing Interactions Among Intra-Block Ranks in Multiple Group Repeated Measures Designs

2000 ◽  
Vol 25 (1) ◽  
pp. 20-59 ◽  
Author(s):  
T. Mark Beasley
Keyword(s):  
Repeated Measures ◽  
Profile Analysis ◽  
Nonparametric Tests ◽  
Covariance Matrices ◽  
Statistical Properties ◽  
Multivariate Approach ◽  
Omnibus Test ◽  
Multiple Group ◽  
Multiple Groups ◽  
Repeated Measures Designs

This study developed an extension of the Hollander and Sethuraman (1978) statistic (B2 ) for testing discordance among intra-block rankings of K elements for multiple groups (J ≥ 2) of raters. B2 was demonstrated to be equivalent to the Pillai-Bartlett trace (V ) from a multivariate profile analysis performed on the ranks such that B2 = V (N - 1) Results confirmed the utility of B2 as an omnibus test of interaction (i.e., discordance) among intra-block ranks and demonstrated that it was more powerful than the multivariate approach to ranked data suggested by Serlin and Marascuilo (1983) . An extension of the Friedman (1937) two-way ANOVA for intra-block ranks was also developed. The adequacy of these procedures for testing interactions in multiple group repeated measures designs was investigated. The Friedman model demonstrated adequate statistical properties only when covariance matrices were spherical. Results also demonstrated that the Hollander-Sethuraman model was useful in testing interaction contrasts.

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.

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