A letter to the co-author Blakeley McShane

Dear professor,

    我今天一整天都在阅读您的文章《废止统计显著性》。由于语言背景问题，对于我来说有点难以理解您的完整思想，所以不得不借助古狗翻译。
    I have been reading your another paper “Abandon Statistical Significance” all day today. It is a little bit hard to me to understand your whole ideas due to the linguistic background. I have to borrow 个google-translate. 
    我原本以为在统计学自身的逻辑系统中，统计显著性应该不会成为一个问题。现在的它之所以成了一个问题应该是由于某种误解。
    I thought the statistical significance should not be a problem in the logical system of statistics itself. The problem might be caused by sort of misunderstandings. 
    让我们以t检验为例。假设我们有了两个样本均数x_bar1和x_bar2，并且可以很容易得到它们之间的差值：x_bar1减去x_bar2。这个差值在经典的数学看来是一个绝对真，也就是它们之间确实存在差异，只要其结果不等于0。但是，以统计学的观点看，这个差值由两个部分构成，或者说，它有两个来源，一是系统误差，另一个是随机误差。t检验法构造了一个t统计量来以概率测量这个随机误差在总差值中的大小。因此，我们不得不使用两分法来对上述两个样本均数之间的差异作出某种判断。我想这就是用t检验能够发现的所谓的“显著性”。
    Let’s take the t-test as an example. We have two sample means x_bar1 and x_bar2, and easily to find the difference between them, x_bar1 minus x_bar2. This difference is absolutely true in a classical mathematical point of view . But in the statistical point of view, this difference is composed of two parts, or it has two different sources, one is systematic error, and the other is random error. The t-test constructed the t statistic to measure a probabilistic magnitude of the random error in the total difference. Therefore, we have to take dichotomization to make a judgement. I think this is the so-called significance that we can find with the t-test. 
    所以，如果总差异中随机误差发生的可能性小于某个临界值，例如目前使用的0.05(也就是说，在t统计量的算法下随机误差占总差异不到5%)，我们就可以说两样本均数之间的差异是显著的；反之就不显著。
    So, we can say the difference is significant if the probability of random error is happening less than 0.05 threshold; otherwise it is not significant. 
    当然，这个0.05的临界值是主观确定的，但看起来我们也没有其它办法能确定一个“客观的”临界值。
    Of course, the threshold 0.05 is arbitrarily made. But it looks like that we could have no other ways to do so. 
    然而，总差值中的系统误差或随机误差的真实大小是未知的，我们也没有办法知道它们。上述的t统计量仅仅只是提供了一个统计的途径在概率尺度上估计它们。事实上，t统计量本身也是一个测量尺度。一旦把它概率化，我们就有了一个关于t分布的概率尺度。这就是为何我们能用一个t值得到一个概率值，即p值。
    However, the true magnitude of either systematic error or random error in the total difference is unknown. We have no way to know them. The t statistic just provides a statistical way to estimate them in a probability scale. Actually the t statistic itself is also a measurement scale. Once it 
is probabilized, we have the probability scale. That is why we can obtain a p-value through a t-value. 
    因此，我的观点是，不是我们要如何痴迷两分法。我们不得不采用两分法是因为我们试图检验的总差异只有两个来源。反之，如果我们不采用两分法，我们将落入某种蒙昧的境地。
    So, in my opinion, it is not that we are “dichotomania”. We have to take the dichotomy because the difference that we try to test has only two sources. In contrary, if we don’t take the dichotomy, we will fall into a situation with some ignorance.
    在您的文章中，我看到您在多处说到“针对零效应或零系统误差的无效假设”。我想说的是，“零系统误差”应该被“总差异中的随机误差足够大（即大到不可忽视）”所取代。对于统计的显著性检验来说，这样的陈述应该会更好，从而可以合理地解释结果，并消除某些误解。
    I can see in your paper, you often say the null hypothesis for zero effect or zero systematic error. I would like to say that the “zero systematic error” should be replaced by “random error is large enough in the total difference”. This might be better for doing significance test and consequently to explain the results and eliminate some sorts of misunderstanding.

Best regards!
Yours sincerely,
Ligong Chen, MD/MPH