http://www.nature.com/news/
This article, once again attempt to justify accusations of doping on Ye with two rationals:
1) such a fast swim is an anomaly. 2) Drug test cannot rule out the possibility of doping.
These two might sound convincing and reasonable justifications, and let one to conclude that after all, all the accusations are not racism in nature, but based on hard scientific reasoning. Unfortunately, this is only wishful thinking, and the facade of scientific objectivity cannot withstand close scrutiny. To justify these accusations from these two observations, requires committing some serious fallacies in statistical reasoning.
First, there is a difference between how likely one is able to swim that fast without doping and how likely has she not been involved in doping given that she swam so fast. The low likelihood of the former does not necessarily imply the low likelihood of the latter. This is called Prosecutor's Fallacy. (See http://en.wikipedia.org/wiki/Prosecutor%27s_fallacy) According to Wikipedia (I know), "deliberate use of the prosecutor's fallacy is prosecutorial misconduct and can subject the prosecutor to official reprimand, disbarment or criminal punishment". Hence it is not some arcane fallacy I dig up to defend Ye. It is disappointing to witness that a magazine like Nature would allow such floppy reasoning. What is of concern, is conditional on such performance, how likely has Ye been involved in doping. The article, and the mass media, fails to give hard data to justify their accusation.
Second, on a related note, one friend on facebook pointed out: "What's interesting is that Katie Ledecky, a 15 year old, won the 800 free today. She shaved 21 second off her best time from last year. Ye Shiwen shaved 5 seconds off her best from last year (in a 400 meter race). So perhaps what Ye Shiwen did isn't that surprising." If Katie can improve 21 seconds without invoking any suspicion, it is very hard to justify accusations on Ye without resorting to racial factor (which could be justified, and will be the topic of my next blog). I am OK with taking racial factors into account, as long as 1) it is done properly (not leading to dogmatic prior) 2) it is openly acknowledged instead of denied.
Finally, the argument that test is not conclusive is red herring. The article seems to hint that now that the drug test does not rule out the possibility of Ye's doping, we should not drop our suspicion in response to the drug test result. However, every statistical test is not conclusive, and only suggestive. The key is that conditional on the result of the test, we do change our belief! At least, the likelihood of Ye doping is significantly reduced given the test result. The power of the test might not be high (which I think the article correctly point out), and we, as a result, will not as dramatically update our belief as what we would do if the power of the test is high, but to not to update our belief at all given the test result is to choose to deliberately ignore relevant evidence and information, not the trademark of a rational being. Consider this, SAT is a test for intelligence, though the power of the test is low, that is people might get higher score even if they are of mediocre intelligence. However, when you first encounter someone, who might look stupid, but you learnt that he got a really high score on SAT, you will need to update your belief about his intelligence if you are a rational being. Indeed, if you have little prior information about his intelligence (say the appearance is not a good indicator of intelligence), you will have to update your belief dramatically, despite the low power of SAT. This might sound paradoxical, but it reflects sound reasoning---in the absence of relevant information, a noisy signal, when compared to other information (that is null, and is of infinite noise), the relative noise ratio is zero! Unsurprisingly, you put all weights on this information (this is the idea behind Fisher Weighting). Hence, unless you have a pretty dogmatic prior concerning Ye, when the drug test is the only available relevant information, one would need to update his belief significantly, regardless the alleged power of the test.
These two logical flaws might be unnoticeable under first reading, but jumps out for any reader with a sense of basic (but correct) intuition about probability. It is a pity that Nature calls it fair-minded, but what is really annoying is the absence of sound logic under the pretense of sound logic.
