Rank test statistics for unbalanced nested designs

Journal of Educational and Behavioral Statistics, 1980

Extensions of the Kruskal-Wallis procedure for a factorial design are reviewed and researched under various degrees and kinds of nonnullity. It was found that the distributions of these test statistics are a Function of effects other than those being tested except under the completely null situation and their use is discouraged.

Journal of Mathematics and Statistics, 2012

Problem statement: In this study, we give a simple analytically tractable procedure for solving three-way unbalanced nested Analysis of Variance (ANOVA). In many realistic situations, unbalanced design was unavoidable due to natural constraints and missing data. Approach: Here, we present a comprehensive approach for addressing solutions of problems arising from unbalanced nested ANOVA. We consider the F-statistics under the different models. Results: Special attention was given to the construction of approximate F-test where exact F-test does not exist. Pseudo-degrees of freedoms were derived using the Satterthwaite's type approximation. Conclusion: In all derivations, we assume that the effects act independently and that the mean squares are independent. A numerical example is given to illustrate the solution procedure.

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.

1997

: In Balanced Incomplete Block Designs the presence of outliers in the data not only indicate non-normality, so that classical methods of analysis on the data are inappropriate, but also diminish the power of classical methods of analysis that assume normality of the data. One alternative is to use Durbin's nonparametric test. This research examined a rank transformation approach where all the data are ranked from smallest to largest, over all treatments and blocks. Then the usual F-test is computed on the ranks. This rank transformation approach is asymptotically distribution-free, and is very powerful in cases where outliers are present as compared with both the parametric F-test and Durbin's nonparametric test. In the case of normality of the data it has only a slight loss of power. Thus it is a good alternative procedure to consider when analyzing data from a Balanced Incomplete Block Design.

2020

The Mack-Wolfe and Kim-Kim statistics are two of the most commonly used non-parametric tests for the umbrella alternative problem when the underlying designs follow a CRD or an RCBD, respectively. In this paper, modifications of the Mack-Wolfe and Kim-Kim test are proposed to developtest statistics for the umbrella alternative with known peak when the data are mixture of a randomized complete block and a completely randomized design. The two proposed test statistics are compared to each other and some other existing tests. Results are given.

2007

Field experiments that involve nested structures may assign treatment conditions either to entire groups (such as classrooms or schools), or individuals within groups (such as students). Even though typically the interest in field experiments is in determining the significance of the overall treatment effect, it is equally important to examine the inconsistency of the treatment effect in different contexts, and understand how they vary. This study provides methods for computing power of tests for the variability of treatment effects in different clusters in three-level designs, where for example, students are nested within classrooms and classrooms are nested within schools. The power computations take into account clustering effects at the classroom and at the school level, and sample size effects (e.g., number of students, classrooms). The methods can also be applied to quasi-experimental studies that examine the significance of the variation of group differences in an outcome, or...

Psychophysiology, 2003

Standard least squares analysis of variance methods suffer from poor power under arbitrarily small departures from normality and fail to control the probability of a Type I error when standard assumptions are violated. These problems are vastly reduced when using a robust measure of location; incorporating bootstrap methods can result in additional benefits. This paper illustrates the use of trimmed means with an approximate degrees of freedom heteroscedastic statistic for independent and correlated groups designs in order to achieve robustness to the biasing effects of nonnormality and variance heterogeneity. As well, we indicate when a boostrap methodology can be effectively employed to provide improved Type I error control. We also illustrate, with examples from the psychophysiological literature, the use of a new computer program to obtain numerical results for these solutions.

Journal of Modern Applied Statistical Methods, 2013

A more powerful test is proposed for the treatment effect in two-level block randomized designs where random assignment takes place at the first level. When clustering at the second level is assumed to be known, the proposed test produces higher estimates of power than the typical test.

Journal of Statistical Computation and Simulation, 2004

Computational Statistics, 2021

In this thesis we propose permutation tests of previously developed statistics for the case of mixed paired and two-sample data. We also explore the different weighting schemes of previous tests to understand the strengths and weaknesses of each test. We compare the power and Type I error of our new tests and those previously developed through a simulation. Rank based statistics generally performed as well as if not better than parametric statistics for all distributions.