A Comparison of Two Rank Tests for Repeated Measures Designs (original) (raw)
A Heteroscedastic, Rank-Based Approach for Analyzing 2 x 2 Independent Groups Designs
Journal of Modern Applied Statistical Methods, 2009
The ANOVA F is a widely used statistic in psychological research despite its shortcomings when the assumptions of normality and variance heterogeneity are violated. A Monte Carlo investigation compared Type I error and power rates of the ANOVA F, Alexander-Govern with trimmed means and Johnson transformation, Welch-James with trimmed means and Johnson Transformation, Welch with trimmed means, and Welch on ranked data using Johansen's interaction procedure. Results suggest that the ANOVA F is not appropriate when assumptions of normality and variance homogeneity are violated, and that the Welch/Johansen on ranks offers the best balance of empirical Type I error control and statistical power under these conditions.
The analysis of repeated measures designs: A review
British Journal of Mathematical and Statistical Psychology, 2001
Repeated measures ANOVA can refer to many different types of analysis. Speci®cally, this vague term can refer to conventiona l tests of signi®cance, one of three univariate solutions with adjusted degrees of freedom, two different types of multivariate statistic, or approache s that combine univariate and multivariate tests. Accordingly, it is argued that, by only reporting probability values and referring to statistical analyses as repeated measures ANOVA, authors convey neither the type of analysis that was used nor the validity of the reported probability value, since each of these approache s has its own strengths and weaknesses. The various approache s are presented with a discussion of their strengths and weaknesses, and recommendations are made regarding the`best' choice of analysis. Additional topics discussed include analyses for missing data and tests of linear contrasts.
gazi university journal of science, 2019
Nonparametric tests are useful when underlying distribution of a population is unknown or sample size is quiet small to satisfy assumptions of a traditional F test. Nonparametric tests have a good usage in a sample which consists of observations from various populations, as well. Randomized block designs are purposive when experimental subjects vary in natural heterogeneity. Nonparametric tests which are suitable for two-way ANOVA designs where the blocks containing observations which follow an increasing or a decreasing trend are main focus of this study. A recently proposed nonparametric test which was developed as an alternative to Jonckheere test is modified for ordered alternative hypotheses in randomized complete block designs. This modification test and several nonparametric tests for detecting ordered alternative hypotheses in randomized complete block designs are compared empirically in a broad set of Monte Carlo simulations under different conditions. A numerical example is provided to illustrate test procedures. The modified test provides better performance than Jonckheere test in terms of type I error and power values whereas Hollander test provides slightly better power values among the other test statistics. In terms of type I error values, it can be stated that the most conservative test is Jonckheere test whereas, estimated type 1 error values of the other test statistics are usually closer to nominal level of alpha.
Rank-Score Tests in Factorial Designs with Repeated Measures
Journal of Multivariate Analysis, 1999
Nonparametric factorial designs for multivariate observations are considered under the framework of general rank-score statistics. Unlike most of the literature, we do not assume the continuity of the underlying distribution functions. The models studied include general repeated measures designs, compound symmetry designs, and designs for longitudinal data. In particular, designs for ordered categorical data are included. The vectors of the multivariate observations may have different lengths. Moreover, our general framework includes missing values and singular covariance matrices which occur quite frequently in practical data analysis problems. The asymptotic properties of the proposed statistics are studied under general nonparametric hypotheses as well as under a sequence of nonparametric contiguous alternatives. L 2-consistent estimators for the unknown covariance matrices are given and two types of quadratic forms are considered for testing the nonparametric hypotheses. The results are applied to a two-way mixed model assuming compound symmetry and to a factorial design for longitudinal data. The main idea of the proofs is based on some moment inequalities for empirical distribution functions in mixed models. The details are provided in the Appendix.
Analyzing Repeated Measures Designs Using Univariate and Multivariate Methods: A Primer
Similarities and differences in the univariate and multivariate analysis of repeated measures designs are discussed, using a hypothetical data set studying the effects of practice on the algebra performance of four students to illustrate both methods. When data are analyzed through the univariate approach and the homogeneity assumption is violated, three correcting factors are presented. When data are analyzed using the multivariate approach, the homogeneity assumption is not necessary. The paper also presents the effects on Type I and Type II error rates of violating or not violating the assumption of homogeneity of variance. Each approach has its own assumptions to meet, but the sphericity assumption of the univariate approach is almost always violated. Even when the normality assumption of the multivariate approach is violated, such violations are generally regarded as less serious than violations of the sphericity assumption. When the researcher's concern is committing a Type I or Type II error, and several assumptions hold, the multivariate approach is suggested. (Contains 11 tables, 2 figures, and 11 references.) (SLD)
Comparative Robustness of Recent Methods for Analyzing Multivariate Repeated Measures Designs
Educational and Psychological Measurement, 2007
This study evaluated the robustness of two recent methods for analyzing multivariate repeated measures when the assumptions of covariance homogeneity and multivariate normality are violated. Specifically, the authors' work compares the performance of the modified Brown—Forsythe (MBF) procedure and the mixed-model procedure adjusted by the Kenward—Roger solution available in SAS PROC MIXED. The authors found that, overall, the MBF procedure appeared to be the least sensitive to the factors examined in the present study; however, this is not necessarily the case for all data sets. As the results show, for tests of the between-subjects main effect, the MBF approach outperformed the mixed-model method when fitting either a patterned or nonpatterned covariance structure. But for tests of within-subjects effects, its Type I error control advantages decrease.
Computational Statistics & Data Analysis, 2003
Parametric methods are commonly used despite evidence that model assumptions are often violated. Various statistical procedures have been suggested for analyzing data from multiple-group repeated measures (i.e., split-plot) designs when parametric model assumptions are violated (e.g., Akritas and Arnold (J. Amer. Statist. Assoc. 89 (1994) 336); Brunner and Langer (Biometrical J. 42 (2000) 663)), including the use of Friedman ranks. The e ects of Friedman ranking on data and the resultant test statistics for single sample repeated measures designs have been examined (e.g., Harwell and Serlin (Comput. Statist. Data Anal. 17 (1994) 35; Comm. Statist. Simulation Comput. 26 (1997) 605); Zimmerman and Zumbo (J. Experiment. Educ. 62 (1993) 75)). However, there have been fewer investigations concerning Friedman ranks applied to multiple groups of repeated measures data (e.g., Beasley (J. Educ. Behav. Statist. 25 (2000) 20); Rasmussen (British J. Math. Statist. Psych. 42 (1989) 91)). We investigate the use of Friedman ranks for testing the interaction in a split-plot design as a robust alternative to parametric procedures. We demonstrated that the presence of a repeated measures main e ect may reduce the power of interaction tests performed on Friedman ranks. Aligning the data before applying Friedman ranks was shown to produce more statistical power than simply analyzing Friedman ranks. Results from a simulation study showed that aligning the data (i.e., removing main e ects) before applying Friedman ranks and then performing either a univariate or multivariate test can provide more statistical power than parametric tests if the error distributions are skewed.