From another blog:
“…If there are 23 people in a room, the chance that two of them have the same birthday is 50 percent, while the chance that two of them were born on a particular day, say, January 1st, is quite low, a small fraction of a percent. The more you specify the coincidence, the rarer it is; the broader the range of coincidences at which you are ready to express surprise, the more likely it is that one will turn up.
Humans are notoriously incompetent at estimating these types of probabilities… which is why scientists (including particle physicists), when they see something unusual in their data, always try to quantify the probability that it is a statistical fluke — a pure chance event. You would not want to be wrong, and celebrate your future Nobel prize only to receive instead a booby prize. (And nature gives out lots and lots of booby prizes.) So scientists, grabbing their statistics textbooks and appealing to the latest advances in statistical techniques, compute these probabilities as best they can. Armed with these numbers, they then try to infer whether it is likely that they have actually discovered something new or not.
And on the whole, it doesn’t work. Unless the answer is so obvious that no statistical argument is needed, the numbers typically do not settle the question.
Despite this remark, you mustn’t think I am arguing against doing statistics. One has to do something better than guessing. But there is a reason for the old saw: “There are three types of falsehoods: lies, damned lies, and statistics.” It’s not that statistics themselves lie, but that to some extent, unless the case is virtually airtight, you can almost always choose to ask a question in such a way as to get any answer you want. … [For instance, in 1991 the volcano Pinatubo in the Philippines had its titanic eruption while a hurricane (or `typhoon’ as it is called in that region) happened to be underway. Oh, and the collapse of Lehman Brothers on Sept 15, 2008 was followed within three days by the breakdown of the Large Hadron Collider (LHC) during its first week of running… Coincidence? I-think-so.] One can draw completely different conclusions, both of them statistically sensible, by looking at the same data from two different points of view, and asking for the statistical answer to two different questions.
To a certain extent, this is just why Republicans and Democrats almost never agree, even if they are discussing the same basic data. The point of a spin-doctor is to figure out which question to ask in order to get the political answer that you wanted in advance. Obviously this kind of manipulation is unacceptable in science. Unfortunately it is also unavoidable.
Why? It isn’t just politics. One might expect problems in subjects with a direct political consequence, for example in demographic, medical or psychological studies. But even in these subjects, the problem isn’t merely political — it’s inherent in what is being studied, and how. …And the debate often boils down to this: is the question that you have asked in applying your statistical method the most even-handed, the most open-minded, the most unbiased question that you could possibly ask?
It’s not asking whether someone made a mathematical mistake. It is asking whether they cheated — whether they adjusted the rules unfairly — and biased the answer through the question they chose, in just the way that every Republican and Democratic pollster does.
Inevitably, the scientists proposing intelligent but different possible answers to this question end up not seeing eye-to-eye. They may continue to battle, even in public, because much is at stake. Biasing a scientific result is considered a terrible breach of scientific protocol, and it makes scientists very upset when they believe others are doing it. But it is best if the disputing parties come up with a convention that all subscribe to, even if they don’t like it. Because if each experimenter were to choose his or her own preferred statistical technique, in defiance of others’ views, then it would become virtually impossible to compare the results of two experiments, or combine them into a more powerful result.
Yes, the statistics experts at the two main LHC experiments, ATLAS and CMS, have been having such a debate, which has been quite public at times. Both sides are intelligent and make good points. There’s no right answer. Fortunately, they have reached a suitable truce, so in many cases the results from the two experiments can be compared.
But does the precise choice of question actually matter that much? I personally take the point of view that it really doesn’t. That’s because no one should take a hint of the presence (or absence) of a new phenomenon too seriously until it becomes so obvious that we can’t possibly argue about it anymore. If intelligent, sensible people can have a serious argument about whether a strange sequence of events could be a coincidence, then there’s no way to settle the argument except to learn more.
While my point of view is not shared explicitly by most of my colleagues, I would argue that this viewpoint is embedded in our culture. Particle physicists have agreed, by convention, not to view an observed phenomenon as a discovery until the probability that it be a statistical fluke be below 1 in a million, a requirement that seems insanely draconian at first glance. ….
Even when the probability of a particular statistical fluke, of a particular type, in a particular experiment seems to be very small indeed, we must remain cautious. There are hundreds of different types of experiments going on, collecting millions of data points and looking at the data in thousands of different ways. Is it really unlikely that someone, somewhere, will hit the jackpot, and see in their data an amazing statistical fluke that seems so impossible that it convincingly appears to be a new phenomenon? The probability of it happening depends on how many different experiments we include in calculating the probability, just as the probability of a 2011 New York hurriquake depends on whether we include other years, other cities, and other types of disasters.
This is sometimes called the “look-elsewhere effect”; how many other places did you look before you found something that seems exceptional? It explains how sometimes a seemingly “impossible” coincidence is, despite appearances, perfectly possible. And for the scientist whose earth-shattering “discovery” blows away in the statistical winds, it is the cause of a deeply personal form of natural disaster.”
Matt Strassler, “Nature is Full of Surprises”. My main rationale for posting this will be explained in [draft ii].
Very interesting post.
Surely what the physicists need to do is to distinguish between preliminary exploratory investigations and experiments that are designed to evaluate the questions that turn up as interesting in those explorations. The preliminary explorations will always be vulnerable to the ‘look elsewhere’ effect, but the designed experiments will not.
Frequentist methods will always be vulnerable to problematically high false positive error rates when large datasets are interrogated for information about lots of hypotheses. Presumably a Bayesian approach with a prior that takes the speculative nature of the exploration into account would be better.