群組標準化效用檢定之樣本數計算

Abstract

標準化效用，即效果量，為表示現象強度的定量測量，對於統計結果有實質性的解釋，因此在許多領域，報告中加註標準化效用被視為良好作法。若欲檢定樣本的實際標準化效用大小，經由假設檢定法，給定虛無假設之標準化效用值，探討在固定信心水準及檢定力下，對於實際標準化效用應該接受虛無假設，或因證據不足而拒絕虛無假設，檢視需要多少各群組內相同的最適樣本數和最適總樣本數。本研究討論柯恩f係數及均方根標準化效果，尋找此兩種效果量在各種條件組合下，各自的最適樣本數，以及比較此兩種效果在同條件組合下，最適樣本數之差異。

Standardized effect, known as effect size, is a quantitative measure of a phenomenon’s strength and a substantial explanation for statistical consequences. Hence, reporting effect sizes is considered good practice when presenting research findings in many fields. We want to examine the actual effect size of the sample. By hypothesis testing, we give effect size of the null hypothesis, confidence level, and power. We discuss how much the optimal equal sample size between groups and the optimal total sample size we need in order to decide accepting the null hypothesis of effect size or rejecting the null hypothesis with lack of evidence. In this study, we discuss Cohen’s f and root-mean-square standardized effect. Find each optimal sample sizes for these effect sizes under all possible combination of conditions and compare the difference of the optimal sample sizes under the same combination of conditions.