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怎么正确表现P值？
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[本文提供英文版于下方]
我一直都很小心处理论文里的P值，但最近同行评审员说我的“统计报告不完整”，要求我修改。究竟哪里出错了？
基本上来说，P值是只用来告诉读者2群体/关系间的差异是因为凑巧或是因为你在研究的变量。根据包含《自然》提供的信息的统计指南，任何的变化、差异或关系都该有称作“显著性”的P值，再来，显著性阈值（也就是你用来判断显著性的P值）可能是.05、.001或.01，建议在论文的方法章节说明你研究里使用的显著性阈值，简单用一句“The significance threshold was set at .05”即可。
然而，P值无法告诉读者一效果、变化、关系的强度或大小，所以，你不能只有P值，提供的检验统计量（t、F、U等）、相关分析或回归系数（Pearson’s r、Spearman’s rho等）、或效应值估量（eta-squared、partial-eta-squared、omega-squared等）。
我们拿以下句子为例：“We found a significant relationship between anxiety and job satisfaction (p < .05).”；这里，你想要说的是你发现足够的证据证明该关系不是凑巧发生，但读者不知道该关系是直接或反比（也就是说到底是焦虑程度越高工作满足感越高或焦虑程度越低工作满足感越高？），再来，该关系是强或弱？为了读者着想，你也应该提供P值的相关系数。如果在上面的句子结尾加上“r = -.78”，读者就可以知道这是强烈反比关系，也就对你的研究发现有更清楚的了解。
再举一例：“We found a significant difference between pretest and posttest scores.”。我建议要呈现：第一，检验统计量，如此读者知道你用何检验统计量检测差异；第二，效应值估量，如此读者可以知道差异有多大，即使只有前测和后测的平均分数也足够让读者了解你发现的效应值大小。
此外，最好提供真正的P值，这种做法能促进科学诚信。在上面的句子里，P值可能是“.048”，技术上看来低于“.05”，但由于非常接近，可能会被解读为P值是.51，那就不是统计相关了。如果P值是低于.001，通常会说“p < .001”，除此之外要提供精确的P值，尤其是针对主要成果。
接下来，我想分享一些我遇过有关P值的基本错误如下：
1. “p = .00”或“p < .00”
从技术上来说，P值不可等于0，有些统计分析软件会给你P值等于0的结果，但这很有可能是自动四舍五入或无条件舍去小数点后数值的结果。所以，试着用“p < .001”取代“p = .000”，该表达方式被广为接受且基本上不改变P值呈现的重要性。还有，P值永远都是介于0到1之间，且不可能为负。
2. “p < .03”
许多期刊都接受用表示关系的α值（统计显著性阈值）来表示P值，也就是p < .05、p < .01、p < .001，它也可以用绝对值表示，例如p = .03或p = .008。不过，如果数值不是α值，P值基本上不用大于（>）或小于（<）符号。
最后，一个小技巧：科学、技术和医学领域许多单位多建议不可能大于1的数值（意即有统计显著性的相关、比例和水平）前面不加0，也就是说“p < 0.05”应该要写成“p < .05”。
或许你可以看看结果章节里的P值呈现方式是否可以依照上面提及的几点改进。在《应用生理学杂志》编辑部可以找更多指南细节。祝你再投顺利！
如果你还有什么问题，欢迎随时留言。
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What is the correct way to report p values?
I have always been very careful to provide p values in my papers. But I recently was asked to revise a paper because the peer reviewer said that “statistical reporting is incomplete.” What was wrong?
In general, p values tell readers only whether any difference between groups, relationship, etc., is likely to be due to chance or to the variable(s) you are studying. According to most statistical guidelines, including those provided by Nature, you need to provide a p value for any change, difference, or relationship called “significant.” Further, because the significance threshold (i.e., the p value that you use as a cutoff for determining significance) can be .05, .001, or .01, it’s advisable to state the significance threshold used in your research in the Methods section of your paper. A sentence like “The significance threshold was set at .05” is all that is required.
However, a p value cannot tell readers the strength or size of an effect, change, or relationship. Therefore, you should avoid reporting nothing else but p values. It’s always a good idea to provide a test statistic (t, F, U, etc.), correlation or regression coefficient (Pearson’s r, Spearman’s rho, etc.), or measure of effect size (eta-squared, partial-eta-squared, omega-squared, etc.).
Let’s take the example of the sentence “We found a significant relationship between anxiety and job satisfaction (p < .05).” Here, all you are telling the readers is that you have enough evidence that this relationship is unlikely to be due to chance. Readers don’t know whether this relationship is direct or inverse (i.e., did participants with higher anxiety have higher job satisfaction or did participants with lower anxiety have higher job satisfaction?). Further, was this relationship strong or weak? For the benefit of the reader, you should also report a correlation coefficient along with the p value. If you add “r = -.78” in the parentheses at the end of the above sentence, your readers will understand that this is a strong inverse relationship. Thus, they get a better idea of your actual findings.
Here’s another example: “We found a significant difference between pretest and posttest scores.” I would recommend reporting (a) the test statistic so that the reader knows what statistical test you performed to examine this difference and (b) a measure of effect size so that the reader understands how large this difference is. Even the mean pretest and posttest scores could be sufficient for readers to understand the size of the effect you have found.
In addition, it’s a good idea to report exact p values, since this practice makes for greater scientific integrity. In the above sentence, the p value could be “.048”; this value is technically below “.05” but so close to .05 that it would probably need to be treated like a p value of .51, which is not statistically significant. Typically, if the exact p value is less than .001, you can merely state “p < .001.” Otherwise, report exact p values, especially for primary outcomes.
Furthermore, here are a couple of basic errors I’ve come across with regard to p values:
1. “p = .00” or “p < .00”
Technically, p values cannot equal 0. Some statistical programs do give you p values of .000 in their output, but this is likely due to automatic rounding off or truncation to a preset number of digits after the decimal point. So, consider replacing "p = .000" with "p < .001," since the latter is considered more acceptable and does not substantially alter the importance of the p value reported. And p always lies between 0 and 1; it can never be negative.
2. “p < .03”
Many journals accept p values that are expressed in relational terms with the alpha value (the statistical significance threshold), that is, “p < .05,” “p < .01,” or “p < .001.” They can also be expressed in absolute values, for example, “p = .03” or “p = .008.” However, p values are conventionally not used with the greater than (>) or less than (<) sign when what follows the sign is not the alpha value.
One last tip: Many authorities in scientific, technical, and medical fields recommend that a zero should not be inserted before a decimal fraction when the number cannot be greater than 1 (e.g., correlations, proportions, and levels of statistical significance); that is, “p < 0.05” should be written as “p < .05.”
Perhaps you should go over the Results section of your paper and check whether the reporting of p values can be improved on the basis of the above tips. More detailed guidelines are provided in this editorial in the Journal of Applied Physiology . Good luck with the resubmission!
Do write in a comment with any further questions you may have.
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