Robustness of randomisation tests as alternative analysis methods for repeated measures design

Q4 Mathematics

Statistics in Transition Pub Date : 2022-12-01 DOI:10.2478/stattrans-2022-0043

A. Oladugba, Ajali John Obasi, O. C. Asogwa

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Abstract

Abstract Randomisation tests (R-tests) are regularly proposed as an alternative method of hypothesis testing when assumptions of classical statistical methods are violated in data analysis. In this paper, the robustness in terms of the type-I-error and the power of the R-test were evaluated and compared with that of the F-test in the analysis of a single factor repeated measures design. The study took into account normal and non-normal data (skewed: exponential, lognormal, Chi-squared, and Weibull distributions), the presence and lack of outliers, and a situation in which the sphericity assumption was met or not under varied sample sizes and number of treatments. The Monte Carlo approach was used in the simulation study. The results showed that when the data were normal, the R-test was approximately as sensitive and robust as the F-test, while being more sensitive than the F-test when data had skewed distributions. The R-test was more sensitive and robust than the F-test in the presence of an outlier. When the sphericity assumption was met, both the R-test and the F-test were approximately equally sensitive, whereas the R-test was more sensitive and robust than the F-test when the sphericity assumption was not met.

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随机试验作为重复测量设计的替代分析方法的稳健性

摘要当数据分析中违反经典统计方法的假设时，随机检验（R检验）经常被提出作为假设检验的替代方法。在单因素重复测量设计的分析中，评估了R检验在I型误差和功率方面的稳健性，并将其与F检验的稳健性进行了比较。该研究考虑了正态和非正态数据（偏斜：指数分布、对数正态分布、卡方分布和威布尔分布）、异常值的存在和缺乏，以及在不同样本量和处理次数下是否满足球形假设的情况。模拟研究采用蒙特卡罗方法。结果表明，当数据正常时，R检验与F检验一样灵敏和稳健，而当数据具有偏斜分布时，R测试比F检验更灵敏。在存在异常值的情况下，R检验比F检验更灵敏、更稳健。当满足球形度假设时，R检验和F检验的灵敏度大致相等，而当不满足球形度假定时，R试验比F检验更灵敏和稳健。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics in Transition Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

9 weeks

期刊介绍： Statistics in Transition (SiT) is an international journal published jointly by the Polish Statistical Association (PTS) and the Central Statistical Office of Poland (CSO/GUS), which sponsors this publication. Launched in 1993, it was issued twice a year until 2006; since then it appears - under a slightly changed title, Statistics in Transition new series - three times a year; and after 2013 as a regular quarterly journal." The journal provides a forum for exchange of ideas and experience amongst members of international community of statisticians, data producers and users, including researchers, teachers, policy makers and the general public. Its initially dominating focus on statistical issues pertinent to transition from centrally planned to a market-oriented economy has gradually been extended to embracing statistical problems related to development and modernization of the system of public (official) statistics, in general.