Wild bootstrapping rank-based procedures: Multiple testing in nonparametric factorial repeated measures designs

A novel longitudinal rank-sum test for multiple primary endpoints in clinical trials: Applications to neurodegenerative disorders

Neurodegenerative disorders such as Alzheimer's disease (AD) present a significant global health challenge, characterized by cognitive decline, functional impairment, and other debilitating effects. Current AD clinical trials often assess multiple longitudinal primary endpoints to comprehensively evaluate treatment efficacy. Traditional methods, however, may fail to capture global treatment effects, require larger sample sizes due to multiplicity adjustments, and may not fully exploit multivariate longitudinal data. To address these limitations, we introduce the Longitudinal Rank Sum Test (LRST), a novel nonparametric rank-based omnibus test statistic. The LRST enables a comprehensive assessment of treatment efficacy across multiple endpoints and time points without multiplicity adjustments, effectively controlling Type I error while enhancing statistical power. It offers flexibility against various data distributions encountered in AD research and maximizes the utilization of longitudinal data. Extensive simulations and real-data applications demonstrate the LRST's performance, underscoring its potential as a valuable tool in AD clinical trials. Nonparametrics, Global test, rank-sum-type test, U-Statistics.

Ranking procedures for repeated measures designs with missing data: Estimation, testing and asymptotic theory

We develop purely nonparametric methods for the analysis of repeated measures designs with missing values. Hypotheses are formulated in terms of purely nonparametric treatment effects. In particular, data can have different shapes even under the null hypothesis and therefore, a solution to the nonparametric Behrens-Fisher problem in repeated measures designs will be presented. Moreover, global testing and multiple contrast test procedures as well as simultaneous confidence intervals for the treatment effects of interest will be developed. All methods can be applied for the analysis of metric, discrete, ordinal, and even binary data in a unified way. Extensive simulation studies indicate a satisfactory control of the nominal type-I error rate, even for small sample sizes and a high amount of missing data (up to 30%). We apply the newly developed methodology to a real data set, demonstrating its application and interpretation.

Small sample sizes: A big data problem in high-dimensional data analysis

In many experiments and especially in translational and preclinical research, sample sizes are (very) small. In addition, data designs are often high dimensional, i.e. more dependent than independent replications of the trial are observed. The present paper discusses the applicability of max t-test-type statistics (multiple contrast tests) in high-dimensional designs (repeated measures or multivariate) with small sample sizes. A randomization-based approach is developed to approximate the distribution of the maximum statistic. Extensive simulation studies confirm that the new method is particularly suitable for analyzing data sets with small sample sizes. A real data set illustrates the application of the methods.

Peer Tutoring Effects on Students' Mathematics Anxiety: A Middle School Experience

In this research the effects of reciprocal peer tutoring on students' mathematics anxiety levels were examined. A pretest posttest with control group design was used at a public middle school in Spain. A total of 420 students in 7th, 8th, and 9th grades participated in the study, of which 215 were female and 205 were male. Students were randomly assigned and equally distributed by course grade (140 in each course grade) and experimental condition (210 in the experimental group and 210 in the control group). Quantitative data were gathered using the Mathematics Anxiety Scale developed by Chiu and Henry (1990). Qualitative information was gathered during eight focus group sessions that were held with students. Two main factors were analyzed using the quantitative and qualitative information: mathematics learning anxiety and mathematics evaluation anxiety. Results were analyzed by gender and course grade. Statistically significant improvements were reported for both male and female students in the experimental group and for each course grade for both factors. No statistically significant differences were reported for students in the control group in any case. A moderate effect size was reported for mathematics evaluation anxiety (Hedge's g = 0.42), and a large effect size was reported for mathematics learning anxiety (Hedge's g = 0.84). Information obtained from the focus groups was consistent with the reported quantitative results. The main conclusion is that peer tutoring may be very beneficial for reducing middle school students' mathematics anxiety, regardless of their gender or grade.