使用單組標準差之線性組合效用與樣本數計算

Abstract

效果量的概念在近期的心理學期刊逐漸受到重視，研究者除了說明假設檢定的結果是否顯著外，還必須說明其效果量的大小。其中最常使用計算效果量的方式，就是標準化後的兩母體平均數差異，若將兩平均數差異的概念延伸至多組，則稱之為標準化線性組合。Bonett是其中研究標準化線性組合的學者之一，他將此標準化線性組合定義為□，並提出了兩種不同標準化的方式，其中之一就是利用單組群體的標準差做為標準化。而在母體參數未知時，可利用樣本資料來估計效果量□，但只利用樣本來估計□會有抽樣誤差的存在，因此Bonett利用近似方法推導□的信賴區間，並利用信賴區間反推出樣本數的公式，如此一來，研究者可在欲達到的區間寬度或是效果量下，確定所需抽樣的樣本數為何。本次研究在計算各種參數組合下的樣本數，並計算期望寬度和容忍率來檢驗其樣本數公式是否能達到預期的效果。

Effect size has become an important concept in recent psychology journals, the research-ers have to report a sample value of effect size besides describe the hypothesis-testing results. One of the most uses in measures of effect size is a standardized difference between two means. If we extend the concept to groups, it called standardized linear contras of means. Bonett is one of the researcher that research standardized linear contrast of means, he defined the standardized linear contrast of means as delta, and proposing two different way to standardiz-er, one is use the single standard deviation. It exist sample error when only using the sample to estimate delta, therefore Bonnet use approximation method to derive the confidence interval of delta, and conduct the sample size formula by using the confidence interval, so researchers can determine the sample size under the desired width or effect size. In this study, all possible combination of parameters is to calculate the sample size, and also examine the sample size formula whether it can achieve the desired results by computing expected width and tolerance probability.