共變異數分析假設檢定之樣本數計算

Abstract

在社會科學研究中，當要研究某個議題時，因為條件是有限沒辦法對整體母體進行調查，只能透過抽取的樣本來推論母體的特徵，並根據收集得到的數據對研究對象做出預測或決策。因此，研究的成敗多數取決於樣本是否能解釋及代表母體，其中樣本數量會影響到估計能力。本研究探討共變異數分析透過假設檢定方法計算樣本數需求。模擬檢定標準化線性組合在設定各組平均效用、顯著水準、統計檢定力、隨機產生共變量組合之下，計算能夠滿足檢定力所需最小的樣本數要求。進一步調整相關參數讓拒絕寬度變動，進而分析拒絕寬度與樣本數之間的關係。

In social science, when doing research, because of the limitation of collecting overall data, we can only extract the features of population from characteristic of the sample, and based on the collected data we make a prediction or decision. Therefore, the success of the research depends on the amount of sample and whether they can stand for the rest of the population. The number of collected sample will affect to the correctness of the estimation. This thesis gives an Analysis of Covariance of the sample size that is required for hypothesis testing. We simulate hypothesis testing of standardized linear combination by setting conditions mean, significant level, power rate, random covariance, and calculating the minimum number of required sample. Then changing reject region by adjusting related parameters, and find out relationship between width of rejection and sample size.