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題名：教學實驗中的考驗力分析
作者：張漢宜
作者(外文)：Chang, Han-I
校院名稱：國立高雄師範大學
系所名稱：教育學系
指導教授：謝季宏
學位類別：博士
出版日期：2003
主題關鍵詞：統計考驗力；樣本大小；效果值；statistical power；sample size；effect size
原始連結：連回原系統網址new window
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本研究旨在分析教學實驗中的統計考驗力並且探討統計考驗力與信度的關係。根據這個主旨，本研究的目的陳述如下：一、分析教學實驗的統計考驗力，並利用現有的電腦軟體，設計一個分析多變項統計考驗力的簡易程序。二、比較教學實驗與非實驗教育研究的統計考驗力。三、比較本研究的結果與國外的研究結果是否有差異。四、探討增加信度是否能提高統計考驗力。五、根據研究結果對教學實驗的研究提出建議。
本研究所分析的教學實驗有53篇，共1427項統計考驗；非實驗教育研究有53篇，共4330項統計考驗；整體教育研究有106篇，總共5757項統計考驗。將樣本大小、顯著水準與效果值輸入統計考驗力軟體即可計算出統計考驗力。樣本大小的訊息是根據每一項考驗所實際使用的人數而來的；顯著水準訂定為.05，所有的考驗都以無向考驗的方式來處理；效果值則是使用Cohen(1988)所定義的小、中與大三種效果值。本研究也利用現有的統計考驗力軟體設計一個計算多變項統計考驗力的計算程序。
研究結果發現教學實驗偵測小、中與大效果的統計考驗力分別是.20, .65, 與.87。非實驗教育研究偵測小、中與大效果的統計考驗力分別是.62, .97, 與.99。整體教育研究偵測小、中與大效果的統計考驗力分別是.41, .81, 與.93。非實驗教育研究偵測小、中與大效果的統計考驗力都顯著高於教學實驗的統計考驗力。整體教育研究偵測小、中與大效果的統計考驗力都顯著高於國外研究的統計考驗力。統計考驗力與信度之間並無直接關係。但是，如果測量誤差變異數保持不變，提高信度會降低統計考驗力；如果真分數變異數保持不變，增加信度會提高統計考驗力。
根據以上的結果，本研究的結論可以條列如下：
一、教學實驗的統計考驗力略顯不足；統計結論效度似乎偏低。
(一)偵測小效果的統計考驗力略為低落；
(二)偵測中效果的統計考驗力呈現臨界現象；
(三)偵測大效果的統計考驗力尚稱充足。
二、非實驗教育研究偵測小、中與大效果的統計考驗力都高於教學實驗的統計考驗力。
三、整體教育研究偵測小、中與大效果的統計考驗力都高於國外研究的統計考驗力。
四、多變項考驗力的電腦計算程序能快速而正確地協助研究人員進行計算。
五、增加測驗的信度不必然提高統計考驗力。
(一)統計考驗力與信度之間並無直接的或函數關係；
(二)高信度不必然提高統計考驗力；
(三)低信度有可能導致高統計考驗力。
依據這些結論，本研究針對如何設計具有高統計考驗力的教學實驗、如何使用考驗力分析來決定樣本大小、如何使用統計考驗力的概念協助分析資料、如何降低測量誤差以提高統計考驗力、留意另類資料分析方法的潛力以及未來可能的研究方向等項目分別提出建議。
The purpose of this study is to analyze statistical power in instructional experiment research and explore the relation between statistical power and reliability of measurement. First of all, statistical power in instructional experiment research would be assessed and a procedure for calculating multivariate statistical power was constructed using a power software. Second, statistical power in instructional experiment research was compared to that of non-experimental educational research. Third, statistical power in instructional experiment researches combined with non-experimental educational researches were compared to that of foreign power studies. Fourth, this study would explore if power can increase as reliability of measurement increases. Finally, suggestions for future research were recommended.
A total of 106 theses and dissertations were examined. Of the total, 53 were instructional experiment research investigations, and 53 were non-experimental educational research investigations. The total number of tests for which power was calculated was5757: 1427 in instructional experiment research and 4330 in non-experimental educational research. Power is a function of sample size, significance level, and effect size, and could be calculated by power software. In order to maintain consistency between this and other reported statistical power surveys, a number of conditions were standardized (1)α was held at a uniform value of .05; (2)all statistical tests utilized were assumed to be nondirectional in nature; (3)Cohen’s(1988)definitions of small, medium, and large effect sizes were adopted. A procedure for calculating multivariate statistical power was constructed using a power software.
Power of instructional experiment research to detect small, medium, and large effects was .20, .65, .and 87, respectively. Power of non-experimental educational research to detect small, medium, and large effects was .62, .97, .and .99, respectively. Power of instructional experiment research combined with non-experimental educational research to detect small, medium, and large effects was .62, .97, .and .99, respectively. For all levels of effect size, the difference between power of non-experimental educational research and power of instructional experiment research. was statistically significant. For all levels of effect size, the difference between power of instructional experiment research combined with non-experimental educational research and power of foreign power studies was statistically significant .There is a relation between statistical power and reliability of measurement. However, it is not a functional relation unless one other variable — either true variance or error variance — has a definite value. Specifically, if the measurement-theoretic true variance is assumed to be constant, then power is a monotonic increasing function of the reliability coefficient. In addition, if the error variance is assumed to be constant, then power is a monotonic decreasing function of the reliability coefficient.
The conclusions of this research were as following:
1. The statistical power of instructional experiment research was low.
(1)Power to detect small effects was poor.
(2)Power to detect medium effects was marginal.
(3)Power to detect large effects was adequate.
2. For all levels of effect size, power of non-experimental educational research was higher than that of instructional experiment research.
3. For all levels of effect size, power of instructional experiment research combined with non-experimental educational research was higher than that of foreign power studies. .
4. The procedure for calculating multivariate statistical power can assist researchers in computing correct power quickly.
5.Statistial power does not always increase as reliability increases.
(1)There is not a functional relation between statistical power and reliability of measurement.
(2)Increasing reliability does not necessarily increase statistical power.
(3)It is possible that statistical power increases as reliability decreases.
Recommendations for designing instructional experiment research with high power, for the procedure of determining sample size, for analyzing data using power analysis, and for reducing measurement error, and suggestions for future research are discussed.
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