Friedman test is a nonparametric method that proposed for analyzing data from a randomized complete block design as a robust alternative to parametric method and widely applied in many fields such as agriculture, biology, business, education, and medicine. After the null hypothesis of no treatment effects is rejected, the post-hoc pairwise comparisons must be applied to identify where the differences occur. As the number of groups increases, the number of required comparisons becomes large and this may increase the type I error. The aim of this study is twofold. The main aim is to suggest expression that facilitates the plotting Friedman test by gathering the test and pairwise comparisons in one simple step. The second aim is to derive the sampling distribution of the suggested expression by utilizing method of moments that helps in obtaining the decision limit. An application and simulation study are carried out to show the advantage of the suggested method and to compute the empirical type I error. The results are of great value where the proposed method makes huge reduction in the number of required tests to show where the discrepancies occur, holds the type I error close to the nominal value and provides visual, deep insight and understanding where the treatment effects occur.
翻译:弗里德曼测试是一种非参数性方法,建议用来分析来自随机整块设计的数据,作为衡量方法的可靠替代方法,并广泛应用于农业、生物学、商业、教育和医学等许多领域。在否定不产生治疗效果的无效假设后,必须应用后对称比较来确定差异发生地点。随着组群数量的增加,所需比较的数量就会增加,这可能会增加I型错误。本研究的目的是双重的。主要目的是建议一种表达方式,通过收集测试和对称比较来便利绘制弗里德曼测试图案。第二个目的是利用有助于获得决定限制的瞬间方法,得出建议表达方式的抽样分布。进行了应用和模拟研究,以显示所建议的方法的优势,并计算经验型I错误。如果拟议方法大量减少所需测试以显示差异发生地点,结果就非常有价值,将I型错误与名义价值相近,并在治疗效果发生之处提供直观、深入的洞察和理解。