All too often debates on best scientific practices descend into a chaotic mire of accusations, hurt feelings, and offended egos. As I mentioned in my previous post, I therefore decided to write a list of guidelines that I believe could help improve scientific discourse. It applies as much to replication attempts as to other scientific disagreements, say, when reanalysing someone else’s data or spotting a mistake they made.
Note that these are general points and should not be interpreted as relating to any particular case. Furthermore I know I am no angel. I have broken many of these rules before and fallible as I am I may end up doing so again. I hope that –I- learn from them but I hope they will also be useful for others. If you can think of additional rules please leave a comment!
1. Talk to the original authors
Don’t just send them a brusque email requesting data or with some basic questions about their paradigm (if you want to replicate their research). I mean actually talk and discuss with them, ideally in person at a conference or during a visit perhaps. Obviously this won’t always be possible. Either way, be open and honest about what you’re doing, why you want the data, why you want to replicate and how. Don’t be afraid to say that you find the results implausible, especially if you can name objective reasons for it.
One of my best experiences at a conference was when a man (whose name I unfortunately can’t remember) waited for me at my poster as I arrived at the beginning of my session. He said “I’m very skeptical of your results”. We had a very productive, friendly discussion and I believe it greatly improved my follow-up research.
2. Involve the original authors in your efforts
Suggest to the original authors to start a collaboration. It doesn’t need to be “adversarial” in the formal sense although it could be if you clearly disagree. But either way everyone will be better off if you work together instead of against each other. Publications are a currency in our field and I don’t see that changing anytime soon. I think you may be surprised how much more amenable many researchers will be to your replication/reanalysis effort if you both get a publication out of it.
3. Always try to be nice
If someone makes an error, point it out in an objective but friendly manner. Don’t let that manuscript you submitted/published to a journal in which you ridicule their life’s work be the first time they hear about it. Avoid emotional language or snarky comments.
I know I have a sarcastic streak so I have been no saint when it comes to that. I may have learned from a true master…
4. Don’t accuse people without hard evidence
Give people the benefit of the doubt. Don’t just blankly insinuate the original authors used questionable research practices no matter how wide-spread they apparently are. In the end you don’t know they engaged in bad practices unless you saw it yourself or some trustworthy whistle-blower told you. Statistics may indicate it but they don’t prove it.
5. Apologise even if (you think) you did no wrong
You might know this one if you’re married… We all make mistakes and slip up sometimes. We say things that come across as more offensive than intended. Sometimes we can find it very hard to understand what made the other person angry. Usually if you try you can empathise. It also doesn’t matter if you’re right. You should still say sorry because that is the right thing to do.
I am very sorry if I offended Eric-Jan Wagenmakers or any of his co-authors with my last post. Perhaps I spoke too harshly. I have the utmost respect for EJ and his colleagues and I do appreciate that they initiated the discussion we are having!
6. Admit that you could be wrong
We are all wrong, frequently. There are few things in life that I am very confident about. I believe scientists should be skeptical, including of their own beliefs. I remain somewhat surprised just with how much fervent conviction many scientists argue. I’d expect this from religious icons or political leaders. To me the best thing about being a scientist is the knowledge that we just don’t really know all that much.
I find it very hard to fathom that people can foretell the future or that their voting behaviour changes months later just because they saw a tiny flag in the corner of the screen. I just don’t think that’s plausible. But I don’t know for sure. It is possible that I’m wrong about this. It has happened before.
7. Don’t hound individuals
Replicating findings in the general field is fair enough. It is even fair enough if your replication is motivated by “I just cannot believe this!” even though this somewhat biases your expectations, which I think is problematic. But if you replicate or reanalyse some findings try not to do it only to the same person all the time. This looks petty and like a vendetta. And take a look around you. Even if you haven’t tried to replicate any of Research X’s findings, there is a chance a lot of other people already have. Don’t pester that one person and force them into a multi-front war they can’t possibly win with their physical and mental health intact.
This is one of the reasons I removed my reanalysis of Bem 2011’s precognition data from my bootstrapping manuscript.
8. Think of the children!
In the world we currently live in, researcher’s livelihoods depend on their reputation, their publication record and citations, their grant income etc. Yes, I would love for grant and hiring committees to only value trust-seekers who do creative and rigorous research. But in many cases it’s not a reality (yet?) and so it shouldn’t be surprising when some people react with panic and anger when they are criticised. It’s an instinct. Try to understand that. Saying “everyone makes mistakes” or “replication is necessary” isn’t really enough. Giving them a way to keep their job and their honour might (see rule 2).
9. Science should seek to explain
In my opinion the purpose of scientific research is to explain how the universe works (or even just that tiny part of the universe between your ears). This is what should motivate all our research, including the research that scrutinises and/or corrects previous claims. That’s why I am so skeptical of Many Labs and most direct replication projects in general. They do not explain anything. They are designed to prove the null hypothesis, which is conceptually impossible. It is fine to disbelieve big claims, in fact that’s what scientists should do. But if you don’t believe some finding, think about why you don’t believe it and then seek to disprove it by showing how simpler explanations could have produced the same finding. Showing that you, following the same recipe as the original authors, failed to reproduce the same result is pretty weak evidence – it could just mean that you are a bad cook. In general, sometimes we can’t trust our own motivations. If you really disbelieve some finding, try to think what kind of evidence could possibly convince you that it is true. Then, go and test it.
A few months ago a study from EJ Wagenmakers’ lab (Boekel et al. in Cortex) failed to replicate 17 structural brain-behaviour correlations reported in the published literature. The study was preregistered by uploading the study protocol to a blog and so was what Wagenmakers generally refers to as “purely confirmatory“. As Wagenmakers is also a vocal proponent of Bayesian inferential methods, they used a one-tailed Bayesian hypothesis tests to ask whether their replication evidence supported the original findings. A lot has already been written about the Boekel study and I was previously engaged in a discussion on it. Therefore, in the interest of brevity (and thus the time Alexander Etz’s needs to spend on reading it :P) I will not cover all the details again but cut right to the case (It is pretty long anyway despite by earlier promises…)
Ryota Kanai, author of several of the results Boekel et al. failed to replicate, has now published a response in which he reanalyses their replication data. He shows that at least one finding (a correlation between grey matter volume in the left SPL and a measure of distractibility as quantified by a questionnaire) replicates successfully if the same methods as his original study are used. In fact, while Kanai does not report these statistics, using the same Bayesian replication test for which Boekel reported “anecdotal” evidence* for the null hypothesis (r=0.22, BF10=0.8), Kanai’s reanalysis reveals “strong” evidence for the alternative hypothesis (r=0.48, BF10=28.1). This successful replication is further supported by a third study that replicated this finding in an independent sample (albeit with some of the same authors as the original study). Taken together this suggests that at least for this finding, the failure to replicate may be due to methodological differences rather than that the original result was spurious.
Now, disagreements between scientists are common and essential to scientific progress. Replication is essential for healthy science. However, I feel that these days, as a field, psychology and neuroscience researchers are going about it in the wrong way. To me this case is a perfect illustration of these problems. In my next post I will summarise this one in a positive light by presenting ten simple rules for a good replication effort (and – hand on my heart – that one will be short!)
1. No such thing as “direct replication”
Recent years have seen the rise of numerous replication attempts with a particular emphasis on “direct” replications, that is, the attempt to exactly reproduce the experimental conditions that generated the original results. This is in contrast to “conceptual” replications in which a new experiment follows the spirit of a previous one but the actual parameters may be very different. So for instance a finding that exposing people to a tiny picture of the US flag influences their voting behaviour months in the future could be interpreted as conceptually replicating the result that people walk more slowly when they were primed with words describing the elderly.
However, I believe this dichotomy is false. The “directness” of a replication attempt is not categorical but exists on a gradual spectrum. Sure, the examples of conceptual replications from the social priming literature are quite distinct from Boekel’s attempt to replicate the brain-behaviour correlations or all the other Many Labs projects currently being undertaken with the aim to test (or disprove?) the validity of social psychology research.
However, there is no such thing as a perfectly direct replication. The most direct replication would be an exact carbon copy of the original, with the same participants, tested at the same time in the same place under the exact same conditions. This is impossible and nobody actually wants that because it would be completely meaningless other than testing just how deterministic our universe really is. What people mean when they talk about direct replications is that they match the experimental conditions reasonably well but use an independent sample of participants and (ideally) independent experimenters. Just how “direct” the replication is depends on how closely matched the experimental parameters are. By that logic, I would call the replication attempt of Boekel et al. less direct than say Wagenmakers et al’s replication of Bem’s precognition experiments. Boekel’s experiments were not matched at least with those by Kanai on a number of methodological points. However, even for the precognition replication Bem challenged Wakenmakers** on the directness of their methods because his replication attempt did not use the same software and stimuli as the original experiment.
Controversies like this reveal several issues. While you can strive to match the conditions of an original experiment as closely as possible, there will always be discrepancies. Ideally the original authors and the “replicators”*** can reach a consensus as to whether or not the discrepancies should matter. However, even if they do, this does not mean that they are unimportant. Saying that “original authors agreed to the protocol” means that a priori they made the assumption that methodological differences are insignificant. This does not mean that this assumption is correct. In the end this is an empirical question.
Discussions about failed replications are often contaminated with talk about “hidden moderators”, that is, unknown factors and discrepancies between the original experiment and the replication effort. As I pointed out under the guise of my alter ego****, I have little patience for this argument. It is counter-productive because there are always unknown factors. Saying that unknown factors can explain failures to replicate is an unfalsifiable hypothesis and a truism. The only thing that should matter in this situation is empirical evidence for additional factors. If you cannot demonstrate that your result hinges on a particular factor, this argument is completely meaningless. In the case of Bem’s precognition experiments, this could have been done by conducting an explicit experiment that compares the use of his materials with those used by Wagenmakers, ideally in the same group of participants. However, in the case of these brain-behaviour correlations this is precisely what Kanai did in his reply: he reanalysed Boekel’s data using the methods he had used originally and he found a different result. Importantly, this does not necessarily prove that Kanai’s theory about these results is correct. However, it clearly demonstrates that the failure to replicate was due to another factor that Boekel et al. did not take into account.
2. Misleading dichotomy
I also think the dichotomy between direct and conceptual replication is misleading. When people conduct “conceptual” replications the aim is different but equally important: direct replications (in so far that they exist) can test whether specific effects are reproducible. Conceptual replications are designed to test theories. Taking again the elderly-walking-speed and voting-behaviour priming examples from above, whether or not you believe that such experiments constitute compelling evidence for this idea, they are both experiments aiming to test the idea that subtle (subconscious?) information can influence people’s behaviour.
There is also a gradual spectrum for conceptual replication but here it depends on how general the overarching theory is that the replication seeks to test. These social priming examples clearly test a pretty diffuse theory of subconscious processing. By the same logic one could say that all of the 17 results scrutinised by Boekel test the theory that brain structure shares some common variance with behaviour. This theory is not only vague but so generic that it is almost meaningless. If you honestly doubt that there are any structural links between brain and behaviour, may I recommend checking some textbooks on brain lesions or neurodegenerative illness in your local library?
A more meaningful conceptual replication would be to show that the same grey matter volume in the SPL not only correlates with a cognitive failure questionnaire but with other, independent measures of distractibility. You could even go a step further and show that this brain area is somehow causally related to distraction. In fact, this is precisely what Kanai’s original study did.
I agree that replicating actual effects (i.e. what is called “direct” replication) is important because it can validate the existence of previous findings and – as I described earlier – help us identify the factors that modulate it. You may however also consider ways to improve your methodology. A single replication with a demonstrably better method (say, better model fits, higher signal-to-noise ratios, or more precise parameter estimates) is worth a 100 direct replications from a Many Labs project. In any of these cases, the directness of your replication will vary.
In the long run, however, conceptual replication that tests a larger overarching theory is more important than showing that a specific effect exists. The distinction between these two is very blurred though. It is important to know what factors modulate specific findings to derive a meaningful theory. Still, if we focus too much on Many Labs direct replication efforts, science will slow down to a snail’s pace and waste an enormous amount of resources (and taxpayer money). I feel that these experiments are largely designed to deconstruct the social priming theory in general. And sure, if the majority of these findings fail to replicate in repeated independent attempts, perhaps we can draw the conclusion that current theory is simply wrong. This happens a lot in science – just look at the history of phrenology or plate tectonics or our model of the solar system.
However, wouldn’t it be better to replace subconscious processing theory with a better model that actually describes what is really going on than to invest years of research funds and effort to prove the null hypothesis? As far as I can tell, the current working theory about social priming by most replicators is that social priming is all about questionable research practices, p-hacking, and publication bias. I know King Ioannidis and his army of Spartans show that the situation is dire***** – but I am not sure it is realistically that dire.
3. A fallacious power fallacy
Another issue with the Boekel replications, which is also discussed in Kanai’s response, is that the sample size they used was very small. For the finding that Kanai reanalysed the sample size was only 36. Across the 17 results they failed to replicate, their sample size ranged between 31-36. This is in stark contrast with the majority of the original studies many of which used samples well above 100. Only for one of the replications, which was of one of their own findings, Boekel et al. used a sample that was actually larger (n=31) than that in the original study (n=9). It seems generally accepted that larger samples are better, especially for replication attempts. A recent article recommended a sample size for replications two and a half times larger than the original. This may be a mathematical rule of thumb but it is hardly realistic, especially for neuroimaging experiments.
Thus I can understand why Boekel et al. couldn’t possibly have done their experiment on hundreds of participants. However, at the very least you should think that a direct replication effort should at least try to match the sample of the original study not one that is four times smaller. In our online discussions Wagenmakers explained the small sample by saying that they “simply lacked the financial resources” to collect more data. I do not think this is a very compelling argument. Using the same logic I could build a lego version of the Large Hadron Collider in my living room but fail to find the Higgs boson – only to then claim that my inadequate methodology was due to the lack of several billion dollars on my bank account******.
I must admit I sympathise a little with Wagenmakers here because it isn’t like I never had to collect more data for an experiment than I had planned (usually this sort of optional stopping happens at the behest of anonymous peer reviewers). But surely you can’t just set out to replicate somebody’s research, using a preregistered protocol no less, with a wholly inadequate sample size? As a matter of fact,their preregistered protocol states the structural data for this project (which is the expensive part) had already been collected previously and that the maximum sample of 36 was pre-planned. While they left “open the possibility of testing additional participants” they opted not to do so even though the evidence for half of the 17 findings remained inconclusively low (more on this below). Presumably this was as they say because they ran “out of time, money, or patience.”
In the online discussion Wagenmakers further states that power is a pre-experimental concept and refers to another publications by him and others in which they describe a “power fallacy.” I hope I am piecing together their argument accurately in my own head. Essentially statistical power tells you how probable it is that you can detect evidence for a given effect with your planned sample size. It thus quantifies the probabilities across all possible outcomes given these parameters. I ran a simulation to do this for the aforementioned correlation between left SPL grey matter and cognitive failure questionnaire scores. So I drew 10,000 samples of 36 participants each from a bivariate Gaussian distribution with a correlation of rho=0.38 (i.e. the observed correlation coefficient in Kanai’s study). I also repeated this for the null hypothesis so I drew similar samples from an uncorrelated Gaussian distribution. The histograms in the figure below show the distributions of the 10,000 Bayes factors calculated using the same replication test used by Boekel et al. for the alternative hypothesis in red and the null hypothesis in blue.
Out of those 10,000 simulations in the red curve only about 62% would pass the criterion for “anecdotal” evidence of BF10=3. Thus even if the effect size originally reported by Kanai’s study had been a perfect estimate of the true population effect (which is highly improbable) only in somewhat less than two thirds of replicate experiments should you expect conclusive evidence supporting the alternative hypothesis. The peak of the red distribution is in fact very close to the anecdotal criterion. With the exception of the study by Xu et al. (which I am in no position to discuss) this result was in fact one of the most highly powered experiments in Boekel’s study: as I showed in the online discussion the peaks of expected Bayes factors of the other correlations were all below the anecdotal criterion. To me this suggests that the pre-planned power of these replication experiments was wholly insufficient to give the replication a fighting chance.
Now, Wagenmakers’ reasoning of the “power fallacy” however is that after the experiment is completed power is a meaningless concept. It doesn’t matter what potential effect sizes (and thus Bayesian evidence) one could have gotten if one repeated the experiment infinitely. What matters is the results and evidence they did find. It is certainly true that a low-powered experiment can produce conclusive evidence in favour of a hypothesis – for example the proportion of simulations at the far right end of the red curve would very compellingly support H1 while those simulations forming the peak of the blue curve would afford reasonable confidence that the null hypothesis is true. Conversely, a high-powered experiment can still fail to provide conclusive evidence. This essentially seems to be Wagenmakers’ argument of the power fallacy: just because an experiment had low power doesn’t necessarily mean that its results are uninterpretable.
However, in my opinion this argument serves to obfuscate the issue. I don’t believe that Wagenmakers is doing this on purpose but I think that he has himself fallen victim to a logical fallacy. It is a non-sequitur. While it is true that low-powered experiments can produce conclusive evidence, this does not make the evidence conclusive. In fact, it is the beauty of Bayesian inference that it allows quantification of the strength of evidence. The evidence Boekel et al. observed in was inconclusive (“anecdotal”) in 9 of the 17 replications. Only in 3 the evidence for the null hypothesis was anywhere close to “strong” (i.e. below 1/10 or very close to it).
Imagine you want to test if a coin is biased. You flip it once and it comes up heads. What can we conclude from this? Absolutely nothing. Even though the experiment has been completed it was obviously underpowered. The nice thing about Bayesian inference is that it reflects that fact.
4. Interpreting (replication) evidence
You can’t have it both ways. You either take Bayesian inference to the logical conclusion and interpret the evidence you get according to Bayesian theory or you shouldn’t use it. Bayes factor analysis has the potential to be a perfect tool for statistical inference. Had Boekel et al. observed a correlation coefficient near 0 in the replication of the distractibility correlation they would have been right to conclude (in the context of their test) that the evidence supports the null hypothesis with reasonable confidence.
Now a close reading of Boekel’s study shows that the authors were in fact very careful in how they worded the interpretation of their results. They say that they “were unable to successfully replicate any of these 17 correlations”. This is entirely correct in the context of their analysis. What they do not say, however, is that they were also unable to refute the previously reported effects even though this was the case for over half of their results.
Unfortunately, this sort of subtlety is entirely lost on most people. The reaction of many commenters on the aforementioned blog post, on social media, and in personal communications was to interpret this replication study as a demonstration that these structural brain-behaviour correlations have been conclusively disproved. This is in spite of the statement in the actual article that “a single replication cannot be conclusive in terms of confirmation or refutation of a finding.” On social media I heard people say that “this is precisely what we need more of.” And you can literally feel the unspoken, gleeful satisfaction of many commenters that yet more findings by some famous and successful researchers have been “debunked.”
Do we really need more low-powered replication attempts and more inconclusive evidence? As I described above, a solid replication attempt can actually inform us about the factors governing a particular effect, which in turn can help us formulate better theories. This is what we need more of. We need more studies that test assumptions but that also take all the available evidence into account. Many of these 17 brain-behaviour correlation results here originally came with internal replications in the original studies. As far as I can tell these were not incorporated in Boekel’s analysis (although they mentioned them). For some of the results independent replications – or at least related studies – had already been published and it seems odd that Boekel et al. didn’t discuss at least those that had already been published months earlier.
Also some results, like Kanai’s distractibility correlation, were accompanied in the original paper by additional tests of the causal link between the brain area and behaviour. In my mind, from a scientific perspective it is far more important to test those questions in detail rather than simply asking whether the original MRI results can be reproduced.
5. Communicating replication efforts
I think there is also a more general problem with how the results of replication efforts are communicated. Replication should be a natural component of scientific research. All too often failed replications result in mudslinging contests, heated debates, and sometimes in inappropriate comparisons of replication authors with video game characters. Some talk about how the reputation of the original authors is hurt by failed replication.
It shouldn’t have to be this way. Good scientists also produce non-replicable results and even geniuses can believe in erroneous theories. However, the way our publishing and funding system works as well as our general human emotions predispose us to having these unfortunate disagreements.
I don’t think you can solely place the blame for such arguments on the authors of the original studies. Because scientists are human beings the way you talk to them influences how they will respond. Personally I think that the reports of many high profile replication failures suffer from a lack of social awareness. In that sense the discussion surrounding the Boekel replications has actually been very amicable. There have been far worse cases where the whole research programs of some authors have been denigrated and ridiculed on social media, sometimes while the replication efforts were still on-going. I’m not going to delve into that. Perhaps one of the Neuroscience Devils wants to pick up that torch in the future.
However, even the Boekel study shows how this communication could have been done with more tact. The first sentences of the Boekel article read as follows:
“A recent ‘crisis of confidence’ has emerged in the empirical sciences. Several studies have suggested that questionable research practices (QRPs) such as optional stopping and selective publication may be relatively widespread. These QRPs can result in a high proportion of false-positive findings, decreasing the reliability and replicability of research output.”
I know what Boekel et al. are trying to say here. EJ Wagenmakers has a declared agenda to promote “purely confirmatory” research in which experimental protocols are preregistered. There is nothing wrong with this per se. However, surely the choice of language here is odd? Preregistration is not the most relevant part about the Boekel study. It could have been done without it. It is fine to argue for why it is necessary in the article, but to actually start the article with a discussion of the replication crisis in the context of questionable research practices is very easy to be (mis?-)interpreted as an accusation. Whatever the intentions may have been, starting the article in this manner immediately places a spark of doubt in the reader’s mind and primes them to consider the original studies as being of a dubious nature. In fact, in the online debate Wagenmakers went a step further to suggest (perhaps somewhat tongue-in-cheek) that:
“For this particular line of research (brain-behavior correlations) I’d like to suggest an exploration-safeguard principle (ESP): after collecting the imaging data, researchers are free to analyze these data however they see fit. Data cleaning, outlier rejection, noise reduction: this is all perfectly legitimate and even desirable. Crucially, however, the behavioral measures are not available until after completion of the neuroimaging data analysis. This can be ensured by collecting the behavioral data in a later session, or by collaborating with a second party that holds the behavioral data in reserve until the imaging analysis is complete. This kind of ESP is something I can believe in.”
This certainly sounds somewhat accusatory to me. Quite frankly this is a bit offensive. I am all in favour of scientific skepticism but this is not the same as baseless suspicion. Having been on the receiving end of a particularly bad case of reviewer 2 once who made similar unsubstantiated accusations (and in fact ignored evidence to the contrary) I can relate to people who would be angered by that. For one thing such procedures are common in many labs conducting experiments like this. Having worked with Ryota Kanai in the past I have a fairly good idea of the meticulousness of his research. I also have great respect for EJ Wagenmakers and I don’t think he actually meant to offend anyone. Still, I think it could easily happen with statements like this and I think it speaks for Kanai’s character that he didn’t take offense here.
There is a better way. This recently published failure to replicate a link between visually induced gamma oscillation frequency and resting occipital GABA concentration is a perfect example of a well-written replication failure. There is no paranoid language about replication crises and p-hacking but a simple, factual account of the research question and the results. In my opinion this exposition certainly facilitated the rather calm reaction to this publication.
6. Don’t hide behind preregistration
Of course, the question about optional stopping and outcome-dependent analysis (I think that term was coined by Tal Yarkoni) could be avoided by preregistering the experimental protocols (in fact at least some of these original experiments were almost certainly preregistered in departmental project reviews). As opposed to what some may think, I am not opposed to preregistration as such. In fact, I fully intend to try it.
However, there is a big problem with this, which Kanai also discusses in his response. As a peer reviewer, he actually recommended Boekel et al. to use the same analysis pipeline he employed now to test for the effects. The reason Boekel et al. did not do this is that these methods were not part of the preregistered protocol. However, this did not stop them from employing other non-registered methods, which they report as exploratory analyses. In fact, we are frequently told that pre-registration does not preclude exploration. So why not here?
Moreover, preregistration is in the first instance designed to help authors control the flexibility of their experimental procedure. It should not be used as a justification to refuse performing essential analyses when reviewers ask for them. In this case, a cynic might say that Boekel et al. in fact did these analyses and chose not to report them because the results were inconsistent with the message they wanted to argue. Now I do not believe this to be the case but it’s an example of how unfounded accusations can go both ways in these discussions.
If this is how preregistration is handled in the future, we are in danger of slowing down scientific progress substantially. If Boekel et al. had performed these additional analyses (which should have been part of the originally preregistered protocol in the first place), this would have saved Kanai the time to do them himself. Both he and Boekel et al. could have done something more productive with their time (and so could I, for that matter :P).
It doesn’t have to go this way but we must be careful. If we allow this line of reasoning with preregistration, we may be able to stop the Texas sharpshooter from bragging but we will also break his rifle. It will then take much longer and more ammunition to finally hit the bulls-eye than is necessary.
*) I actually dislike categorical labels for Bayesian evidence. I don’t think we need them.
**) This is a pre-print manuscript. It keeps changing with on-going peer review so this statement may no longer be true when you read this.
***) Replicators is a very stupid word but I can’t think of a better, more concise one.
****) Actually this post was my big slip-up as Devil’s Neuroscientist. In that one a lot of Sam’s personality shown through, especially in the last paragraph.
*****) I should add that I am merely talking about the armies of people pointing out the proneness of false positives. I am not implying that all these researchers I linked to here agree with one another.
******) To be fair, I probably wouldn’t be able to find the Higgs boson even if I had the LHC.