Imagine you are a radio astronomer and you suddenly stumble across a signal from outer space that appears to be evidence of an extra-terrestrial intelligence. Let’s also assume you already confidently ruled out any trivial artifactual explanation to do with naturally occurring phenomena or defective measurements. How could you confirm that this signal isn’t simply a random fluke?
This is actually the premise of the novel Contact by Carl Sagan, which happens to be one of my favorite books (I never watched the movie but only caught the end which is nothing like the book so I wouldn’t recommend it…). The solution to this problem proposed in the book is that one should quantify how likely the observed putative extraterrestrial signal would be under the assumption that it is the product of random background radiation.
This is basically what a p-value in frequentist null hypothesis significance testing represents. Using frequentist inference requires that you have a pre-specified hypothesis and a pre-specified design. You should have an effect size in mind, determine how many measurements you need to achieve a particular statistical power, and then you must carry out this experiment precisely as planned. This is rarely how real science works and it is often put forth as one of the main arguments why we should preregister our experimental designs. Any analysis that wasn’t planned a priori is by definition exploratory. The most extreme form of this argument posits that any experiment that hasn’t been preregistered is exploratory. While I still find it hard to agree with this extremist position, it is certainly true that analytical flexibility distorts the inferences we can make about an observation.
This proposed frequentist solution is therefore inappropriate for confirming our extraterrestrial signal. Because the researcher stumbled across the signal, the analysis is by definition exploratory. Moreover, you must also beware of the base-rate fallacy: even an event extremely unlikely under the null hypothesis is not necessarily evidence against the null hypothesis. Even if p=0.00001, a true extraterrestrial signal may be even less likely, say, p=10-100. Even if extra-terrestrial signals are quite common, given the small amount of space, time, and EM bands we have studied thus far, how probable is it we would just stumble across a meaningful signal?
None of that means that exploratory results aren’t important. I think you’d agree that finding credible evidence of an extra-terrestrial intelligence capable of sending radio transmissions would be a major discovery. The other day I met up with Rob McIntosh, one of the editors for Registered Reports at Cortex, to discuss the distinction between exploratory and confirmatory research. A lot of the criticism of preregistration focuses on whether it puts too much emphasis on hypothesis-driven research and whether it in turn devalues or marginalizes exploratory studies. I have spent a lot of time thinking about this issue and (encouraged by discussions with many proponents of preregistration) I have come to the conclusion that the opposite is true: by emphasizing which parts of your research are confirmatory I believe exploration is actually valued more. The way scientific publishing works conventionally many studies are written up in a way that pretends to be hypothesis-driven when in truth they weren’t. Probably for a lot of published research the truth lies somewhere in the middle.
So preregistration just keeps you honest with yourself and if anything it allows you to be more honest about how you explored the data. Nobody is saying that you can’t explore, and in fact I would argue you should always include some exploration. Whether it is an initial exploratory experiment that you did that you then replicate or test further in a registered experiment, or whether it is a posthoc robustness test you do to ensure that your registered result isn’t just an unforeseen artifact, some exploration is almost always necessary. “If we knew what we were doing, it would not be called research, would it?” (a quote by Albert Einstein, apparently).
One idea I discussed with Rob is whether there should be a publication format that specifically caters to exploration (Chris Chambers has also mentioned this idea previously). Such Exploratory Reports would allow researchers to publish interesting and surprising findings without first registering a hypothesis. You may think this sounds a lot like what a lot of present day high impact papers are like already. The key difference is that these Exploratory Reports would contain no inferential statistics and critically they are explicit about the fact that the research is exploratory – something that is rarely the case in conventional studies. However, this idea poses a critical challenge: on the one hand you want to ensure that the results presented in such a format are trustworthy. But how do you ensure this without inferential statistics?
Proponents of the New Statistics (which aren’t actually “new” and it is also questionable whether you should call them “statistics”) will tell you that you could just report the means/medians and confidence intervals, or perhaps the whole distributions of data. But that isn’t really helping. Inspecting confidence intervals and how far they are from zero (or another value of no interest) is effectively the same thing as a significance test. Even merely showing the distribution of observations isn’t really helping. If a result is so blatantly obvious that it convinces you by visual inspection (the “inter-ocular trauma test”), then formal statistical testing would be unnecessary anyway. If the results are even just a little subtler, it can be very difficult to decide whether the finding is interesting. So the way I see it, we either need a way to estimate statistical evidence, or you need to follow up the finding with a registered, confirmatory experiment that specifically seeks to replicate and/or further test the original exploratory finding.
In the case of our extra-terrestrial signal you may plan a new measurement. You know the location in the sky where the signal came from, so part of your preregistered methods is to point your radio telescope at the same point. You also have an idea of the signal strength, which allows you to determine the number of measurements needed to have adequate statistical power. Then you carry out this experiment, sticking meticulously to your planned recipe. Finally, you report your result and the associated p-value.
Sounds good in theory. In practice, however, this is not how science typically works. Maybe the signal isn’t continuous. There could be all sorts of reasons why the signal may only be intermittent, be it some interstellar dust clouds blocking the line of transmission, the transmitter pointing away from Earth due to the rotation of the aliens’ home planet, or even simply the fact that the aliens are operating their transmitter on a random schedule. We know nothing about what an alien species, let alone their civilization, may be like. Who is to say that they don’t just fall into random sleeping periods in irregular intervals?
So some exploratory, flexible analysis is almost always necessary. If you are too rigid in your approach, you are very likely to miss important discoveries. At the same time, you must be careful not to fool yourself. If we are really going down the route of Exploratory Reports without any statistical inference we need to come up with a good way to ensure that such exploratory findings aren’t mostly garbage. I think in the long run the only way to do so is to replicate and test results in confirmatory studies. But this could already be done as part of a Registered Report in which your design is preregistered. Experiment 1 would be exploratory without any statistical inference but simply reporting the basic pattern of results. Experiment 2 would then be preregistered and replicate or test the finding further.
However, Registered Reports can take a long time to publish. This may in fact be one of the weak points about this format that may stop the scientific community from becoming more enthusiastic about them. As long as there is no real incentive to doing slow science, the idea that you may take two or three years to publish one study is not going to appeal to many people. It will stop early career researchers from getting jobs and research funding. It also puts small labs in poorer universities at a considerable disadvantage compared to researchers with big grants, big data, and legions of research assistants.
The whole point of Exploratory Reports would be to quickly push out interesting observations. In some ways, this is then exactly what brief communications in high impact journals are currently for. I don’t think it will serve us well to replace the notion of snappy (and likely untrue) high impact findings with inappropriate statistical inferences with snappy (and likely untrue) exploratory findings without statistical inference. If the purpose of Exploratory Reports is solely to provide an outlet for quick publication of interesting results, we still have the same kind of skewed incentive structure as now. Also, while removing statistical inference from our exploratory findings may be better statistical practice I am not convinced that it is better scientific practice unless we have other ways of ensuring that these exploratory results are kosher.
The way I see it, the only way around this dilemma is to finally stop treating publications as individual units. Science is by nature a lengthy, incremental process. Yes, we need exciting discoveries to drive science forward. At the same time, replicability and robustness of our discoveries is critical. In order to combine these two needs I believe research findings should not be seen as separate morsels but as a web of interconnected results. A single Exploratory Report (or even a bunch of them) could serve as the starting point. But unless they are followed up by Registered Reports replicating or scrutinizing these findings further, they are not all that meaningful. Only once replications and follow up experiments have been performed the whole body of a finding takes shape. A search on PubMed or Google Scholar would not merely spit out the original paper but a whole tree of linked experiments.
The perceived impact and value of a finding thus would be related to how much of a interconnected body of evidence it has generated rather than whether it was published in Nature or Science. Critically, this would allow people to quickly publish their exciting finding and thus avoid being deadlocked by endless review processes and disadvantaged compared to other people who can afford to do more open science. At the same time, they would be incentivized to conduct followed up studies. Because a whole body of related literature is linked, it would however also be an incentive for others to conduct replications or follow up experiments on your exploratory finding.
There are obviously logistic and technical challenges with this idea. The current publication infrastructure still does not really allow for this to work. This is not a major problem however. It seems entirely feasible to implement such a system. The bigger challenge is how to convince the broader community and publishers and funders to take this on board.