多變量群組標準化效用估計

Abstract

大多數的實驗設計中，研究者所關心的是在虛無假設下，多組平均數是否具有顯著差異；然而相於顯著水準，「效用值」在實務上較少人使用，但其為客觀評估差異的大小或是關聯強度的一項衡量方法，並且在學術期刊中，使人更加容易理解研究發現的重要性。然而，效用值的計算會隨著各研究實驗設計、統計方法使用的差異而不同，本文針對多變量變異數分析中的標準化期望值之變異數進行估計，採隨機模擬的方式，藉由多變量近似的抽樣分配，找出最佳的效用值估計方法以及針對估計量實際上非負數特性進行校正，並且比較在多變量以及單變量模型中，各估計量表現的異同。

What concerns most of the researchers is whether there is significant difference between groups under null hypothesis. Comparing with significant value, “effect sizes” are not used frequently in practice. They are objective measures of the size of difference or the strength of the association. With effect size, the important of findings can be fully understood. However, they can be measured differently depending on experimental designs and statistical methods. The aim of this article is to give a proper estimation of f-squared in multivariate analysis of variance and the adjustments according to nonnegative property are included. In addition, the comparison of univariate and multivariate effect-size measures is concerned since the approximate distribution in multivariate analysis leads to the bias in estimation. Properties of these estimators are studied using Monte Carlo simulation methods.