论文标题
弗里德曼测试的图形方法:瞬间方法
A Graphical Approach for Friedman Test: Moments Approach
论文作者
论文摘要
Friedman测试是一种非参数方法,该方法提出了用于分析随机完整块设计的数据,作为参数方法的可靠替代品,并广泛应用于许多领域,例如农业,生物学,商业,教育和医学。在否定未治疗效果的零假设后,必须应用后成对的比较来确定差异的发生地点。随着组数量的增加,所需比较的数量变大,这可能会增加I型错误。这项研究的目的是双重的。主要目的是建议表达通过在一个简单的步骤中收集测试和成对比较来促进绘制弗里德曼测试。第二个目的是通过利用有助于获得决策限制的矩方法来得出建议表达的采样分布。进行了应用和仿真研究,以显示建议方法的优势并计算经验I型误差。结果具有很大的价值,即提出的方法大大减少了所需的测试数量以显示差异发生的位置,将I型误差保持在名义值附近,并提供视觉,深刻的见识,并了解治疗效果的发生位置。
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.