標準化線性組合之信賴區間研究

Abstract

效果量(Effect size)，透過標準化的方式，讓我們可以比較不同量度變數之間差異的統計方法。近年來許多的頂尖期刊也紛紛要求學者在研究中除了提出p-value來做決策判斷時，也應附效果量來作為衡量影響效果的依據。本研究針對Douglas G. Bonett(2008)所提出的兩個標準化平均數線性組合(Standardized Linear Contrasts of Means)模型進行探討，分別為平均變異數模型及單組標準差模型。Bonett在文章中所發表的模擬數據，其準確度令人驚艷。但是其發表的模擬數據過於保守，所計算出來的信賴區間分佈也並未分析，不免讓人懷疑是否有偏差。本研究擴大其模擬數據的多樣性以及複雜性，整理各種模擬情境下的數據表現，分析公式可能在何種情境下發生偏誤及原因，希望能作為之後研究者在使用上的一個參考，也為本研究主要貢獻。

Effect size is a simple statistic method that help researcher to compare data with different calibration. This article focuses on confidence intervals for Standardized Linear Contrasts of Means which proposing by Douglas G. Bonett (2008). These methods are easy to compute, do not require equal population variance, and perform better than the currently available methods. It’s a fantasy find about this research areas. However, Bonett just reported some conservative data about confidence intervals. He also did not discuss the shape of confidence intervals. To confirm the formula correctness, I test these equations rigorously and analysis the data. If any researchers want to use these equations to compute confidence intervals, I hope this article will be a reference.