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研究设计中统计功效的重要性
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我的稿件因研究“功效不足”而被退回。这是什么意思？我已经采用了最佳的研究方法。
在统计学里，“功效”指的是您的研究是否能鉴定具有重要权益的效应。基本上，进行研究设计时，必须考虑到以下四个必要的因素：
1. 样本数：单位（例如，病人）的数目，通常以“N”做代表。
2. 研究效应的大小：一般而言，若想达到的效应越大，所需的样本量相对较小。
3. α水平：统计意义的阈值（可定为.001、.05或.1）。当数据的p值等于或超越此临界值时，代表您的研究成果不具任何统计意义。
4. 功效：这是个数值，代表您能得到某个效应的可能性。
该怎么确定你研究的功效？以上列出的四个因素是相互关联的，若你有其中三个因素的数值，就能计算出第四个因素的数值。通常α水平是固定的（你得在.001、.05或.1之间选其一），在查阅相关文献后，你对研究效应的大小会有个概念。若想让研究取得有力的功效，就得关注样本数的多寡。
多数权威期刊如《自然》（Nature）都会要求对研究制定的样本量做出解释，以证明成果带有足够的功效。《自然》也提供了具体的指导方针，建议在研究的样本量小的情况下应该进行那些测试。其他期刊如《英国外科学杂志》（British Journal of Surgery）指定稿件必需包含明确的功效计算法。有些期刊如《分子遗传学和新陈代谢杂志》（Molecular Genetics and Metabolism）更直接的表明：“递交的稿件若没有附加功效的计算，将一概被拒绝，并在未经审核的情况下退还给作者。”除了跟医学和生命科学有关的期刊外，其他类型的期刊也同样对统计功效有着同样严格的要求。比如，美国心理学会发表的《心理学研究报告准则》（Reporting Standards for Research in Psychology）就强力的推荐作者于稿件内的研究方法部分阐明对功效的分析。
在申请研究基金时，若能把功效的计算包括在申请书里，能帮助评审评估研究的可行性。
相信你已经注意到以上的说明并没不包括研究所采用的方法。这是因为功效与研究方法两者间并无相互关系。即使研究的功效很低（例如样本量太小，不能适当检测出所研究的效应），仍然能进行严格的测试，如进行临床试验时采用随机化分组。其实，期刊评审指的是你研究的功效并不足以把研究时所观察到的效应当成是可靠和可复制的。
不幸的是，当研究完成后，功效就很难再修改。因此，在开始收集数据前，请先向统计学家进行谘询，确定研究的设计是否有足够的功效。现在这个阶段，你的选项包括把稿件投给一份对功效要求较不严格的期刊，或者进行更深一层的实验以克服此限制。
祝你好运！
﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎﹎
英文原文
My paper was rejected because my study was “underpowered”? What does this mean? I was careful about using the best methodology.
In statistics, “power” refers to the ability of your study to identify effects of substantial interest. Basically, at the time of designing your study, you need to consider four essential factors:
1. Sample size, i.e., the number of units (e.g., patients), usually represented as “N.”
2. Size of the effect that you are interested in (usually, if you are looking for a large effect, you don’t need as big a sample as you would if you were looking for a small effect)
3. Alpha level: This is your significance threshold (it can be .001, .05, or .1). If your p values are at or above this level, you say that your result is not statistically significant.
4. Power: This is a value representing the likelihood of you finding an effect.
How do you determine the power of your study? The above four parameters are interrelated, so if you have the values for three of them, you can calculate the value of the fourth. But usually, the alpha level is fixed (you generally have to choose between .001, .05, and .1) and by reviewing the literature, you will know roughly how large or small your effect can possibly be (effect size). So if you want your study to have good power, you will need to focus on sample size.
Many prestigious journals like Nature require you to justify your sample size, so as to show that you have enough power. Nature also offers specific guidelines about what kind of tests you should conduct when your sample size is small. Others, like the British Journal of Surgery, want power calculations to be clearly stated in the manuscript. Still others, like Molecular Genetics and Metabolism, clearly state that “[s] ubmitted manuscripts without a power calculation will be rejected and returned to authors without review.” And it’s not just medical and life science journals that are strict about statistical power—the American Psychological Association also strongly recommends reporting a power analysis in the methods section of psychology papers, in its Reporting Standards for Research in Psychology.
It also helps to show your power calculations when applying for a grant, so that reviewers can gauge the robustness of your study.
You’ll notice that your methodology has not been mentioned in my explanation. This is because your power is independent of your methodology. You can conduct the most rigorous tests, such as randomized clinical trials, even if your study has low statistical power (e.g., your sample size is too small for you to appropriately detect the effects you have chosen to study). What the journal reviewer means is that your study does not have sufficient power for the observed effects to be considered reliable and reproducible.
Unfortunately, it’s very difficult to fix power after you have conducted your research. It’s therefore important to consult a statistician before you start data collection, to check whether your study design has enough power. Some of the options you have available at this stage are to choose a journal that is not very strict about power or perhaps to conduct further experiments to overcome this limitation.
I wish you much luck.
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