線性複迴歸所需樣本數目之討論

A Discussion of the Sample Size Required in Multiple Linear Regressions

盧成皆(Sing-Kai Lo)

《護理研究》 5卷4期 (1997/08) Pp. 377-383

摘要

線性複迴歸是護理研究中經常使用的分析方法之一，樣本數目的計算則幾乎是所有研究的重要課題。在使用線性複迴歸時所需的樣本數，部份研究者會有一種觀念：每一個自變項約需五名個案，本文即對此建議及相關問題深入探討。本研究利用統計軟體、並固定顯著水平爲5%，求出在不同的複相關係數(R^2)、不同的自變項數目、及不同檢力的情況下使用線性複迴歸需要多大的樣本。結果顯示，每一個自變項所需的樣本數目，會因R^2、自變項數目等的組合不一樣而有非常大的差異。以本研究所設定的值爲例，R^2的範圍爲0.1至0.9，並有2個至30個自變項，若要達到80%以上的統計檢力，則需6名至296名個案不等；以中位數計算的話，是「平均」每個自變項約需5名個案，磆其差異十分大，由2名到59名都有可能。除了樣本數目的計算之外，本文並對計算過程中所涉及的統計前題假設、及在應用時所需考慮的各種問題加以討論，提供護理研究人員參考。

關鍵字

線性複回歸 ； 樣本數目 ； 護理研究

並列摘要

Multiple linear regression (MLR) is one of the most commonly used analysitical techniques in nursing research. On the other hand, pre-study sample size calculation is important in almost all types of research. It has been suggested, as a rule of thumb, that when using MLR, 5 cases are needed for each independent variable. It was therefore the aim of this study to examine the validity of the suggested rule. A statistical software was used for the calculation of sample size. Parameters used as inputs to the sample size program included 5% alpha, a population R-squared of 0.1 to 0.9, and numbers of independent variables ranging from 2 to 30. It was found that to achieve a statistical power of at least 80%, 6 to 296 cases would be required for different combinations of parameters. If the median is used as the measure of central tendency, then “on average”, 5 cases will be needed for each independent variable. However, the variation was so large that the sample size required for each independent variable could be between 2 and 59; again, depending on the combination of parameters. Nevertheless, the number of additional cases required for each additional independent variable is usually below 5, suggesting that the rule of thumb mentioned above is conservative. In addition to sample size derivation, we also discuss the statistical assumptions involved in the computations, as well as some practical considerations for future reference.

並列關鍵字

multiple linear regression ； sample size ； nursing research