Together with my co-host Smriti Mehta we’ve started a new podcast: Nullius in Verba. It’s a podcast about science – what it is, and what it could be. The introduction episode is up now, and new episodes will be released every other week starting this friday!

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We will release episodes on friday every other week (starting this friday). Topics in the first episodes are inspired by aphorisms in Francis Bacon’s ‘Novum Organum’ (the galleon in our logo comes from the title page of his 1620 book, where it is passing between the mythical Pillars of Hercules that stand either side of the Strait of Gibraltar, which have been smashed through by Iberian sailors, opening a new world for exploration and marking the exit from the well-charted waters of the Mediterranean into the Atlantic Ocean. Bacon hoped that empirical investigation will similarly smash the old scientific ideas and lead to greater understanding of nature and the world.

As we explain in the introduction, the title of the podcast comes from the motto of the Royal Society. 

Our logo is set in typeface Kepler by Robert Slimbach. Our theme song is Newton’s Cradle by Grandbrothers. You see we are going all in on subtle science references.

We hope you’ll enjoy listening along as we discuss themes like confirmation bias, skepticism, eminence, the ‘itch to publish’ and in the first episode, the motivations to do science.

This blog post is based on the chapter “Critical Levels, Statistical Language, and Scientific Inference” by Irwin D. J. Bross (1971) in the proceedings of the symposium on the foundations of statistical inference held in 1970. Because the conference proceedings might be difficult to access, I am citing extensively from the original source. Irwin D. J. Bross [1921-2004] was a biostatistician at Roswell Park Cancer Institute in Buffalo up to 1983.

Irwin D. J. Bross

Criticizing the use of thresholds such as an alpha level of 0.05 to make dichotomous inferences is of all times. Bross writes in 1981: “Of late the attacks on critical levels (and the statistical methods based on these levels) have become more frequent and more vehement.” I feel the same way, but it seems unlikely the vehemence of criticisms has been increasing for half a century. A more likely explanation is perhaps that some people, like Bross and myself, become increasingly annoyed by such criticisms.

Bross reflects on how very few justifications of the use of alpha levels exists in the literature, because “Elementary statistics texts are not equipped to go into the matter; advanced texts are too preoccupied with the latest and fanciest statistical techniques to have space for anything so elementary. Thus the justifications for critical levels that are commonly offered are flimsy, superficial, and badly outdated.” He notes how the use of critical values emerged in a time where statisticians had more practical experience, but that “Unfortunately, many of the theorists nowadays have lost touch with statistical practice and as a consequence, their work is mathematically sophisticated but scientifically very naive.”

Bross sets out to consider which justification can be given for the use of critical alpha levels. He would like such a justification to convince those who use statistical methods in their research, and statisticians who are familiar with statistical practice. He argues that the purpose of a medical researcher “is to reach scientific conclusions concerning the relative efficacy (or safety) of the drugs under test. From the investigator’s standpoint, he would like to make statements which are reliable and informative. From a somewhat broader standpoint, we can consider the larger communication network that exists in a given research area – the network which would connect a clinical pharmacologist with his colleagues and with the practicing physicians who might make use of his findings. Any realistic picture of scientific inference must take some account of the communication networks that exist in the sciences.”

It is rare to see biostatisticians explicitly embrace the pragmatic and social aspect of scientific inference. He highlights three main points about communication networks. “First, messages generate messages.” Colleagues might replicate a study, or build on it, or apply the knowledge. “A second key point is: discordant messages produce noise in the network”. “A third key point is: statistical methods are useful in controlling the noise in the network”. The critical level set by researchers controls the noise in the network. Too much noise in a network impedes scientific progress, because communication breaks down. He writes “Thus the specification of the critical levels […] has proved in practice to be an effective method for controlling the noise in communication networks.” Bross also notes that the critical alpha level in itself is not enough to reduce noise – it is just one component of a well-designed experiment that reduces noise in the network. Setting a sufficiently low alpha level is therefore one aspect that contributes to a system where people in the network can place some reliance on claims that are made because noise levels are not too high.

“This simple example serves to bring out several features of the usual critical level techniques which are often overlooked although they are important in practice. Clearly, if each investigator holds the proportion of false positive reports in his studies at under 5%, then the proportion of false positive reports from all of the studies carried out by the participating members of the network will be held at less than 5%. This property does not sound very impressive – it sounds like the sort of property one would expect any sensible statistical method to have. But it might be noted that most of the methods advocated by the theoreticians who object to critical levels lack this and other important properties which facilitate control of the noise level in the network.”

This point, common among all error statisticians, has repeatedly raised its head in response to suggestions to abandon statistical significance, or to stop interpreting p-values dichotomously. Of course, one can choose not to care about the rate at which researchers make erroneous claims, but it is important to realize the consequences of not caring about error rates. Of course, one can work towards a science where scientists no longer make claims, but generate knowledge through some other mechanism. But recent proposals to treat p-values as continuous measures of evidence (Muff et al., 2021; but see Lakens, 2022a) or to use estimation instead of hypothesis tests (Elkins et al., 2021; but see Lakens, 2022b) do not outline what such an alternative mode of knowledge generation would look like, or how researchers will be prevented from making claims about the presence or absence of effects.

Bross proposes an intriguing view on statistical inference where “statistics is used as a means of communication between the members of the network.” He views statistics not as a way to learn whether idealized probability distributions accurately reflect the empirical reality in infinitely repeated samples, but as a way to communicate assertions that are limited by the facts. He argues that specific ways of communicating only become widely used if they are effective. Here, I believe he fails to acknowledge that ineffective communication systems can also evolve, and it is possible that scientists en masse use techniques, not because they are efficient ways of communicating facts, but because they will lead to scientific publications. The idea that statistical inferences are a ‘mindless ritual’ has been proposed (Gigerenzer, 2018), and there is no doubt that many scientists simply imitate the practices they see. Furthermore, the replication crisis has shown that huge error rates in subfields of the scientific literature can exists for decades. The problems associated with these large error rates (e.g., failures to replicate findings, inaccurate effect size estimate) can sometimes only very slowly lead to a change in practice. So, arguing a practice survives because it works is risky. Whether current research practices are effective – or whether other practices would be more effective – requires empirical evidence. Randomized controlled trials seem a bridge to far to compare statistical approaches, but natural experiments by journals that abandon p-values support Bross’s argument to some extent. When the journal of Basic and Applied Psychology abandoned p-values, the consequence was that researchers claimed effects were present at a higher error rate than if claims had been limited by typical alpha level thresholds (Fricker et al., 2019).

Whether efficient or not, statistical language surrounding critical thresholds is in widespread use. Bross discusses how an alpha level of 5% or 1% is a convention. Like many linguistic conventions, the threshold of 5% is somewhat arbitrary, and reflects the influence of statisticians like Karl Pearson and Ronald Fisher. However, the threshold is not completely arbitrary. Bross asks us to imagine what would have happened had the alpha level of 0.001 been proposed, or an alpha level of 0.20. In both cases, he believes the convention would not have spread – in the first case because in many fields there are not sufficient resources to make claims at such a low error rate, and in the second case because few researchers would have found that alpha level a satisfactory quantification of ‘rare’ events. He, I think correctly, observes this means that the alpha level of 0.05 is not completely arbitrary, but that it reflects a quantification of ‘rare’ that researchers believe has sufficient practical value to be used in communication. Bross argues that the convention of a 5% alpha level spread because it sufficiently matched with what most scientists considered as an appropriate probability level to define ‘rare’ events, for example as when Fisher (1956) writes “Either an exceptionally rare chance has occurred, or the theory of random distribution is not true.”

Of course, one might follow Bross and ask “But is there any reason to single out one particular value, 5%, instead of some other value such as 3.98% or 7.13%?”. He writes: “Again, inconformity with the linguistic patterns in setting conventions it is natural to use a round number like 5%. Such round numbers serve to avoid any suggestion that the critical value has been gerrymandered or otherwise picked to prove a point in a particular study.From an abstract standpoint, it might seem more logical to allow a range of critical values rather than to choose one number but to do so would be to go contrary to the linguistic habits of fact-limited languages. Such languages tend to minimize the freedom of choice of the speaker in order to insure that a statement results from factual evidence and not from a little language-game played by the speaker.”

In a recent paper we made a similar point (Uygun Tunç et al., 2021): “The conventional use of an alpha level of 0.05 can also be explained by the requirement in methodological falsificationism that statistical decision procedures are specified before the data is analyzed (see Popper, 2002, sections 19-20; Lakatos, 1978, p. 23-28). If researchers are allowed to set the alpha level after looking at the data there is a possibility that confirmation bias (or more intentional falsification-deflecting strategies) influences the choice of an alpha level. An additional reason for a conventional alpha level of 0.05 is that before the rise of the internet it was difficult to transparently communicate the pre-specified alpha level for any individual test to peers. The use of a default alpha level therefore effectively functioned as a pre-specification. For a convention to work as a universal pre-specification, it must be accepted by nearly everyone, and be extremely resistant to change. If more than a single conventional alpha level exists, this introduces the risk that confirmation bias influences the choice of an alpha level.” Our thoughts seem to be very much aligned with those of Bross.

Bross continues and writes “Anyone familiar with certain areas of the scientific literature will be well aware of the need for curtailing language-games. Thus if there were no 5% level firmly established, then some persons would stretch the level to 6% or 7% to prove their point. Soon others would be stretching to 10% and 15% and the jargon would become meaningless. Whereas nowadays a phrase such as statistically significant difference provides some assurance that the results are not merely a manifestation of sampling variation, the phrase would mean very little if everyone played language-games. To be sure, there are always a few folks who fiddle with significance levels-who will switch from two-tailed to one-tailed tests or from one significance test to another in an effort to get positive results. However such gamesmanship is severely frowned upon and is rarely practiced by persons who are native speakers of fact-limited scientific languages– it is the mark of an amateur.”

We struggled with the idea that changing the alpha level (and especially increasing the alpha level) might confuse readers when ‘statistically significant’ no longer means ‘rejected with a 5% alpha level) in our recent paper on justifying alpha levels (Maier & Lakens, 2022). We wrote “Finally, the use of a high alpha level might be missed if readers skim an article. We believe this can be avoided by having each scientific claim accompanied by the alpha level under which it was made. Scientists should be required to report their alpha levels prominently, usually in the abstract of an article alongside a summary of the main claim.” It might in general be an improvement if people write ‘we reject an effect size of X at an alpha level of 5%’, but this is especially true of researchers choose to deviate from the conventional 5% alpha level.

I like how Bross has an extremely pragmatic but still principled view on statistical inferences. He writes: “This means that we have to abandon the traditional prescriptive attitude and adopt the descriptiveapproach which is characteristic of the empirical sciences. If we do so, then we get a very different picture of what statistical and scientific inference is all about. It is very difficult, I believe, to get such a picture unless you have had some first hand experience as an independent investigator in a scientific study. You then learn that drawing conclusions from statistical data can be a traumatic experience. A statistical consultant who takes a detached view of things just does not feel this pain.” This point is made by other applied statisticians, and it is a really important one. There are consequences of statistical inferences that you only experience when you spend several years trying to answer a substantive research question. Without that experience, it is difficult to give practical recommendations about what researchers should want when using statistics.

He continues “What you want – and want desperately – is all the protection you can get against the “slings and arrows of outrageous fortune”. You want to say something informative and useful about the origins and nature of a disease or healthhazard. But you do not want your statement to come back and haunt you for the rest of your life.” Of course, Bross should have said ‘One thing you might want’ (because now his statement is just another example of The Statistician’s Fallacy (Lakens, 2021)). But with this small amendment, I think there are quite some scientists who want this from their statistical inferences. He writes “When you announce a new finding, you put your scientific reputation on the line. You colleagues probably cannot remember all your achievements, but they will never forget any of your mistakes! Second thoughts like these produce an acute sense of insecurity.” Not all scientists might feel like this, I hope we are willing to forget some mistakes people make, and I fear the consequences of making too many incorrect claims on the reputation of a researcher is not as severe as Bross suggests[i]. But I think many fellow researchers will experience some fear their findings do not hold up (at least until they have been replicated several times), and that hearing researchers failed to replicate a finding yields some negative affect.

I think Bross hits the nail on the head when it comes to thinking about justifications of the use of alpha levels as thresholds to make claims. The justification for this practice is social and pragmatic in nature, not statistical (cf. Uygun Tunç et al., 2021). If we want to evaluate if current practices are useful or not, we have to abandon a prescriptive approach, and rely on a descriptive approach (Bross, p. 511). Anyone proposing an alternative to the use of alpha levels should not make prescriptive arguments, but provide descriptive data (or at least predictions) that highlight how their preferred approach to statistical inferences will improve communication between scientists.

References

Bross, I. D. (1971). Critical levels, statistical language and scientific inference. In Foundations of statistical inference (pp. 500–513). Holt, Rinehart and Winston.

Elkins, M. R., Pinto, R. Z., Verhagen, A., Grygorowicz, M., Söderlund, A., Guemann, M., Gómez-Conesa, A., Blanton, S., Brismée, J.-M., Ardern, C., Agarwal, S., Jette, A., Karstens, S., Harms, M., Verheyden, G., & Sheikh, U. (2021). Statistical inference through estimation: Recommendations from the International Society of Physiotherapy Journal Editors. Journal of Physiotherapy. https://doi.org/10.1016/j.jphys.2021.12.001

Fisher, R. A. (1956). Statistical methods and scientific inference (Vol. viii). Hafner Publishing Co.

Fricker, R. D., Burke, K., Han, X., & Woodall, W. H. (2019). Assessing the Statistical Analyses Used in Basic and Applied Social Psychology After Their p-Value Ban. The American Statistician, 73(sup1), 374–384. https://doi.org/10.1080/00031305.2018.1537892

Gigerenzer, G. (2018). Statistical Rituals: The Replication Delusion and How We Got There. Advances in Methods and Practices in Psychological Science, 1(2), 198–218. https://doi.org/10.1177/2515245918771329

Lakens, D. (2021). The practical alternative to the p value is the correctly used p value. Perspectives on Psychological Science, 16(3), 639–648. https://doi.org/10.1177/1745691620958012

Lakens, D. (2022a). Why P values are not measures of evidence. Trends in Ecology & Evolution. https://doi.org/10.1016/j.tree.2021.12.006

Lakens, D. (2022b). Correspondence: Reward, but do not yet require, interval hypothesis tests. Journal of Physiotherapy, 68(3), 213–214. https://doi.org/10.1016/j.jphys.2022.06.004

Maier, M., & Lakens, D. (2022). Justify Your Alpha: A Primer on Two Practical Approaches. Advances in Methods and Practices in Psychological Science, 5(2), 25152459221080396. https://doi.org/10.1177/25152459221080396

Muff, S., Nilsen, E. B., O’Hara, R. B., & Nater, C. R. (2021). Rewriting results sections in the language of evidence. Trends in Ecology & Evolution. https://doi.org/10.1016/j.tree.2021.10.009

Uygun Tunç, D., Tunç, M. N., & Lakens, D. (2021). The Epistemic and Pragmatic Function of Dichotomous Claims Based on Statistical Hypothesis Tests. PsyArXiv. https://doi.org/10.31234/osf.io/af9by

Recently a new category of studies have started to appear in the psychological literature that provide the strongest support to date for a replication crisis in psychology: Large scale collaborative replication studies where the authors of the original study are directly involved in the study. These replication studies have often provided conclusive demonstrations of the absence of any effect large enough to matter. Despite considerable attention for these extremely interesting projects, I don’t think the scientific community has fully appreciated what we have learned from these studies.

Three examples of Collaborative Author Involved Replication Studies

Vohs and colleagues (2021) performed a multi-lab replication study of the ego-depletion effect, which (deservedly) has become a poster child of non-replicable effects in psychology. The teams used different combinations of protocols, allowing an unsuccessful prediction to generalize across minor variations in how the experiment was operationalized. Across these conditions, a non-significant effect was observed of d = 0.06, 95%CI[-0.02;0.14]. Although the authors regrettably did not specify a smallest effect size of interest in their frequentist analyses, they mention “we pitted a point-null hypothesis, which states that the effect is absent, against an informed one-sided alternative hypothesis centered on a depletion effect (?) of 0.30 with a standard deviation of 0.15” in their Bayesian analyses. Based on the confidence interval, we can reject effects of d = 0.3, and even d = 0.2, suggesting that we have extremely informative data concerning the absence of an effect most ego-depletion researchers would consider is large enough to matter.

Morey et al (2021) performed a multi-lab replication study of the Action-Sentence Compatibility effect (Glenberg & Kaschak, 2002). I cited the original paper in my PhD thesis, and it was an important finding that I built on, so I was happy to join this project. As written in the replication study, the original team, together with the original authors, “established and pre-registered ranges of effects on RT that we would deem (a) uninteresting and inconsistent with the ACE theory: less than 50 ms.” An effect between 50 ms and 100 ms was seen as inconsistent with the previous literature, but in line with predictions of the ACE effect. The replication study consisted (after exclusions) of 903 native English speakers, and 375 non-native English speakers. The original study had used 44, 70, and 72 participants across 3 studies. The conclusion in the replication study was that  the median ACE interactions were close to 0 and all within the range that we pre-specified as negligible and inconsistent with the existing ACE literature. There was little heterogeneity.

Last week, Many Labs 4 was published (Klein et al., 2022). This study was designed to examine the mortality salience effect (which I think deserve the same poster child status of a non-replicable effect in psychology, but which seems to have gotten less attention so far). Data from 1550 participants was collected across 17 labs, some which performed the study with involvement of the original author, and some which did not. Several variations of the analyses were preregistered, but none revealed the predicted effect, Hedges’ g = 0.07, 95% CI = [-0.03, 0.17] (for exclusion set 1). The authors did not provide a formal sample size justification based on a smallest effect size of interest, but in a sensitivity power analysis indicate they had 95% power for effect sizes of d = 0.18 to d = 0.21. If we assume all authors found effect sizes around d = 0.2 small enough to no longer support their predictions, we can see based on the confidence intervals that we can indeed exclude effect sizes large enough to matter. The mortality salience effect, even with involvement of the original authors, seems to be too small to matter. There was little heterogeneity in effect sizes (in part because the absence of an effect).

These are just three examples (there are more, of which the multi-lab test of the facial feedback hypothesis by Coles et al., 2022, is worth highlighting), but they highlight some interesting properties of collaborative author involved replication studies. I will highlight four strengths of these studies.

Four strengths of Collaborative Author Involved Replication Studies

1) The original authors are extensively involved in the design of the study. They sign off on the final design, and agree that the study is, with the knowledge they currently have, the best test of their prediction. This means the studies tell us something about the predictive validity of state of the art knowledge in a specific field. If the predictions these researchers make are not corroborated, the knowledge we have accumulated in these research areas are is not reliable enough to make successful predictions.

2) The studies are not always direct replications, but the best possible test of the hypothesis, in the eyes of the researchers involved. Criticism on past replication studies has been that directly replicating a study performed many years ago is not always insightful, as the context has changed (even though Many Labs 5 found no support for this criticism). In this new category of collaborative author involved replication studies, the original authors are free to design the best possible test of their prediction. If these tests fail, we can not attribute the failure to replicate to the ‘protective belt’ of auxiliary hypotheses that no longer hold. Of course, it is possible that the theory can be adjusted in a constructive manner after this unsuccessful prediction. But at this moment, these original authors do not have a solid understanding of their research topic to be able to predict if an effect will be observed.

3) The other researchers involved in these projects often have extensive expertise in the content area. They are not just researchers interested in mechanistically performing a replication study on a topic they have little expertise with. Instead, many of the researchers consists of peers who have worked in a specific research area, published on the topic of the replication study, but have collectively developed some doubts about the reliability of past claims, and have decided to spend some of their time replicating a previous finding.

4) The statistical analyses in these studies yield informative conclusions. The studies typically do not conclude the prediction was unsuccessful based on p> 0.05 in a small sample. In the most informative studies, original authors have explicitly specified a smallest effect size of interest, which makes it possible to perform an equivalence test, and statistically reject the presence of any effect deemed large enough to matter. In other cases, Bayesian hypothesis tests are performed which provide support for the null, compared to the alternative, model. This makes these replications studies severe tests of the predicted effect. In cases where original authors did not specify a smallest effect size of interest, the very large sample sizes allow readers to examine effects that can be rejected based on the observed confidence interval, and in all the studies discussed here, we can reject the presence of effects large enough to be considered meaningful. There is most likely not a PhD student in the world who would be willing to examine these effects, given the size that remains possible after these collaborative author involved replication studies. We can never conclude an effect is exactly zero, but that hardly matters – the effects are clearly too small to study.

The Steel Man for Replication Crisis Deniers

Given the reward structures in science, it is extremely rewarding for individual researchers to speak out against the status quo. Currently, the status quo is that the scientific community has accepted there is a replication crisis. Some people attempt to criticize this belief. This is important. All established beliefs in science should be open to criticism.

Most papers that aim to challenge the fact that many scientific domains have a surprising difficulty successfully replicating findings once believed reliable focus on the 100 studies in the Replicability Project: Psychology that was started a decade ago, and published in 2015. This project was incredibly successful in creating awareness of concerns around replicability, but it was not incredibly informative about how big the problem was.

In the conclusion of the RP:P, the authors wrote: “After this intensive effort to reproduce a sample of published psychological findings, how many of the effects have we established are true? Zero. And how many of the effects have we established are false? Zero. Is this a limitation of the project design? No. It is the reality of doing science, even if it is not appreciated in daily practice. Humans desire certainty, and science infrequently provides it. As much as we might wish it to be otherwise, a single study almost never provides definitive resolution for or against an effect and its explanation.” The RP:P was an important project, but it is no longer the project to criticize if you want to provide evidence against the presence of a replication crisis.

Since the start of the RP:P, other projects have aimed to complement our insights about replicability. Registered Replication Reports focused on single studies, replicated in much larger sample sizes, to reduce the probability of a Type 2 error. These studies often quite conclusively showed original studies did not replicate, and a surprisingly large number yielded findings not statistically different from 0, despite sample sizes much larger than psychologists would be able to collect in normal research lines. Many Labs studies focused on a smaller set of studies, replicated many times, sometimes with minor variations to examine the role of possible moderators proposed to explain failures to replicate, which were typically absent.

The collaborative author involved replications are the latest addition to this expanding literature that consistently shows great difficulties in replicating findings. I believe they currently make up the steel man for researchers motivated to cast doubt on the presence of a replication crisis. I believe the fact that these large projects with direct involvement of the original authors can not find support for predicted effects are the strongest evidence too date that we have a problem replicating findings. Of course, these studies are complemented by Registered Replication Reports and Many Labs studies, and together they make up the Steel Man to argue against if you are a Replication Crisis Denier.

References

Coles, N. A., March, D. S., Marmolejo-Ramos, F., Larsen, J., Arinze, N. C., Ndukaihe, I., Willis, M., Francesco, F., Reggev, N., Mokady, A., Forscher, P. S., Hunter, J., Gwenaël, K., Yuvruk, E., Kapucu, A., Nagy, T., Hajdu, N., Tejada, J., Freitag, R., … Marozzi, M. (2022). A Multi-Lab Test of the Facial Feedback Hypothesis by The Many Smiles Collaboration. PsyArXiv. https://doi.org/10.31234/osf.io/cvpuw

Klein, R. A., Cook, C. L., Ebersole, C. R., Vitiello, C., Nosek, B. A., Hilgard, J., Ahn, P. H., Brady, A. J., Chartier, C. R., Christopherson, C. D., Clay, S., Collisson, B., Crawford, J. T., Cromar, R., Gardiner, G., Gosnell, C. L., Grahe, J., Hall, C., Howard, I., … Ratliff, K. A. (2022). Many Labs 4: Failure to Replicate Mortality Salience Effect With and Without Original Author Involvement. Collabra: Psychology, 8(1), 35271. https://doi.org/10.1525/collabra.35271

Morey, R. D., Kaschak, M. P., Díez-Álamo, A. M., Glenberg, A. M., Zwaan, R. A., Lakens, D., Ibáñez, A., García, A., Gianelli, C., Jones, J. L., Madden, J., Alifano, F., Bergen, B., Bloxsom, N. G., Bub, D. N., Cai, Z. G., Chartier, C. R., Chatterjee, A., Conwell, E., … Ziv-Crispel, N. (2021). A pre-registered, multi-lab non-replication of the action-sentence compatibility effect (ACE). Psychonomic Bulletin & Review. https://doi.org/10.3758/s13423-021-01927-8

Vohs, K. D., Schmeichel, B. J., Lohmann, S., Gronau, Q. F., Finley, A. J., Ainsworth, S. E., Alquist, J. L., Baker, M. D., Brizi, A., Bunyi, A., Butschek, G. J., Campbell, C., Capaldi, J., Cau, C., Chambers, H., Chatzisarantis, N. L. D., Christensen, W. J., Clay, S. L., Curtis, J., … Albarracín, D. (2021). A Multisite Preregistered Paradigmatic Test of the Ego-Depletion Effect. Psychological Science, 32(10), 1566–1581. https://doi.org/10.1177/0956797621989733

In a recent paper Muff, Nilsen, O’Hara, and Nater (2021) propose to implement the recommendation “to regard P-values as what they are, namely, continuous measures of statistical evidence“. This is a surprising recommendation, given that p-values are not valid measures of evidence (Royall, 1997). The authors follow Bland (2015) who suggests that “Itis preferable to think of the significance test probability as an index of the strength of evidence against the null hypothesis” and proposed verbal labels for p-values in specific ranges (i.e., p-values above 0.1 are ‘little to no evidence’, p-values between 0.1 and 0.05 are ‘weak evidence’, etc.). P-values are continuous, but the idea that they are continuous measures of ‘evidence’ has been criticized (e.g., Goodman & Royall, 1988). If the null-hypothesis is true, p-values are uniformly distributed. This means it is just as likely to observe a p-value of 0.001 as it is to observe a p-value of 0.999. This indicates that the interpretation of p = 0.001 as ‘strong evidence’ cannot be defended just because the probability to observe this p-value is very small. After all, if the null hypothesis is true, the probability of observing p = 0.999 is exactly as small.

The reason that small p-values can be used to guide us in the direction of true effects is not because they are rarely observed when the null-hypothesis is true, but because they are relatively less likely to be observed when the null hypothesis is true, than when the alternative hypothesis is true. For this reason, statisticians have argued that the concept of evidence is necessarily ‘relative’. We can quantify evidence in favor of one hypothesis over another hypothesis, based on the likelihood of observing data when the null hypothesis is true, compared to this probability when an alternative hypothesis is true. As Royall (1997, p. 8) explains: “The law of likelihood applies to pairs of hypotheses, telling when a given set of observations is evidence for one versus the other: hypothesis A is better supported than B if A implies a greater probability for the observations than B does. This law represents a concept of evidence that is essentially relative, one that does not apply to a single hypothesis, taken alone.” As Goodman and Royall (1988, p. 1569) write, “The p-value is not adequate for inference because the measurement of evidence requires at least three components: the observations, and two competing explanations for how they were produced.”

In practice, the problem of interpreting p-values as evidence in absence of a clearly defined alternative hypothesis is that they at best serve as proxies for evidence, but not as a useful measure where a specific p-value can be related to a specific strength of evidence. In some situations, such as when the null hypothesis is true, p-values are unrelated to evidence. In practice, when researchers examine a mix of hypotheses where the alternative hypothesis is sometimes true, p-values will be correlated with measures of evidence. However, this correlation can be quite weak (Krueger, 2001), and in general this correlation is too weak for p-values to function as a valid measure of evidence, where p-values in a specific range can directly be associated with ‘strong’ or ‘weak’ evidence.

Why single p-values cannot be interpreted as the strength of evidence

The evidential value of a single p-value depends on the statistical power of the test (i.e., on the sample size in combination with the effect size of the alternative hypothesis). The statistical power expresses the probability of observing a p-value smaller than the alpha level if the alternative hypothesis is true. When the null hypothesis is true, statistical power is formally undefined, but in practice in a two-sided test ?% of the observed p-values will fall below the alpha level, as p-values are uniformly distributed under the null-hypothesis. The horizontal grey line in Figure 1 illustrates the expected p-value distribution for a two-sided independent t-test if the null-hypothesis is true (or when the observed effect size Cohen’s d is 0). As every p-value is equally likely, they can not quantify the strength of evidence against the null hypothesis.

Figure 1: P-value distributions for a statistical power of 0% (grey line), 50% (black curve) and 99% (dotted black curve). 

If the alternative hypothesis is true the strength of evidence that corresponds to a p-value depends on the statistical power of the test. If power is 50%, we should expect that 50% of the observed p-values fall below the alpha level. The remaining p-values fall above the alpha level. The black curve in Figure 1 illustrates the p-value distribution for a test with a statistical power of 50% for an alpha level of 5%. A p-value of 0.168 is more likely when there is a true effect that is examined in a statistical test with 50% power than when the null hypothesis is true (as illustrated by the black curve being above the grey line at p = 0.168). In other words, a p-value of 0.168 is evidence foran alternative hypothesis examined with 50% power, compared to the null hypothesis.

If an effect is examined in a test with 99% power (the dotted line in Figure 1) we would draw a different conclusion. With such high power p-values larger than the alpha level of 5% are rare (they occur only 1% of the time) and a p-value of 0.168 is much more likely to be observed when the null-hypothesis is true than when a hypothesis is examined with 99% power. Thus, a p-value of 0.168 is evidence against an alternative hypothesis examined with 99% power, compared to the null hypothesis.

Figure 1 illustrates that with 99% power even a ‘statistically significant’ p-value of 0.04 is evidence for of the null-hypothesis. The reason for this is that the probability of observing a p-value of 0.04 is more likely when the null hypothesis is true than when a hypothesis is tested with 99% power (i.e., the grey horizontal line at p = 0.04 is above the dotted black curve). This fact, which is often counterintuitive when first encountered, is known as the Lindley paradox, or the Jeffreys-Lindley paradox (for a discussion, see Spanos, 2013).

Figure 1 illustrates that different p-values can correspond to the same relative evidence in favor of a specific alternative hypothesis, and that the same p-value can correspond to different levels of relative evidence. This is obviously undesirable if we want to use p-values as a measure of the strength of evidence. Therefore, it is incorrect to verbally label any p-value as providing ‘weak’, ‘moderate’, or ‘strong’ evidence against the null hypothesis, as depending on the alternative hypothesis a researcher is interested in, the level of evidence will differ (and the p-value could even correspond to evidence in favor of the null hypothesis).

All p-values smaller than 1 correspond to evidence for some non-zero effect

If the alternative hypothesis is not specified, any p-value smaller than 1 should be treated as at least some evidence (however small) for somealternative hypotheses. It is therefore not correct to follow the recommendations of the authors in their Table 2 to interpret p-values above 0.1 (e.g., a p-value of 0.168) as “no evidence” for a relationship. This also goes against the arguments by Muff and colleagues that ‘the notion of (accumulated) evidence is the main concept behind meta-analyses”. Combining three studies with a p-value of 0.168 in a meta-analysis is enough to reject the null hypothesis based on p < 0.05 (see the forest plot in Figure 2). It thus seems ill-advised to follow their recommendation to describe a single study with p = 0.168 as ‘no evidence’ for a relationship.

Figure 2: Forest plot for a meta-analysis of three identical studies yielding p = 0.168.

However, replacing the label of ‘no evidence’ with the label ‘at least some evidence for some hypotheses’ leads to practical problems when communicating the results of statistical tests. It seems generally undesirable to allow researchers to interpret any p-value smaller than 1 as ‘at least some evidence’ against the null hypothesis. This is the price one pays for not specifying an alternative hypothesis, and try to interpret p-values from a null hypothesis significance test in an evidential manner. If we do not specify the alternative hypothesis, it becomes impossible to conclude there is evidence for the null hypothesis, and we cannot statistically falsify any hypothesis (Lakens, Scheel, et al., 2018). Some would argue that if you can not falsify hypotheses, you have a bit of a problem (Popper, 1959).

Interpreting p-values as p-values

Instead of interpreting p-values as measures of the strength of evidence, we could consider a radical alternative: interpret p-values as p-values. This would, perhaps surprisingly, solve the main problems that Muff and colleagues aim to address, namely ‘black-or-white null-hypothesis significance testing with an arbitrary P-value cutoff’. The idea to interpret p-values as measures of evidence is most strongly tried to a Fisherian interpretation of p-values. An alternative statistical frequentist philosophy was developed by Neyman and Pearson (1933a) who propose to use p-values to guide decisions about the null and alternative hypothesis by, in the long run, controlling the Type I and Type II error rate. Researchers specify an alpha level and design a study with a sufficiently high statistical power, and reject (or fail to reject) the null hypothesis.

Neyman and Pearson never proposed to use hypothesis tests as binary yes/no test outcomes. First, Neyman and Pearson (1933b) leave open whether the states of the world are divided in two (‘accept’ and ‘reject’) or three regions, and write that a “region of doubt may be obtained by a further subdivision of the region of acceptance”. A useful way to move beyond a yes/no dichotomy in frequentist statistics is to test range predictions instead of limiting oneself to a null hypothesis significance test (Lakens, 2021). This implements the idea of Neyman and Pearson to introduce a region of doubt, and distinguishes inconclusive results (where neither the null hypothesis nor the alternative hypothesis can be rejected, and more data needs to be collected to draw a conclusion) from conclusive results (where either the null hypothesis or the alternative hypothesis can be rejected.

In a Neyman-Pearson approach to hypothesis testing the act of rejecting a hypothesis comes with a maximum long run probability of doing so in error. As Hacking (1965) writes: “Rejection is not refutation. Plenty of rejections must be only tentative.” So when we reject the null model, we do so tentatively, aware of the fact we might have done so in error, and without necessarily believing the null model is false. For Neyman (1957, p. 13) inferential behavior is an: “act of will to behave in the future (perhaps until new experiments are performed) in a particular manner, conforming with the outcome of the experiment”. All knowledge in science is provisional.

Furthermore, it is important to remember that hypothesis tests reject a statistical hypothesis, but not a theoretical hypothesis. As Neyman (1960, p. 290) writes: “the frequency of correct conclusions regarding the statistical hypothesis tested may be in perfect agreement with the predictions of the power function, but not the frequency of correct conclusions regarding the primary hypothesis”. In other words, whether or not we can reject a statistical hypothesis in a specific experiment does not necessarily inform us about the truth of the theory. Decisions about the truthfulness of a theory requires a careful evaluation of the auxiliary hypotheses upon which the experimental procedure is built (Uygun Tunç & Tunç, 2021).

Neyman (1976) provides some reporting examples that reflect his philosophy on statistical inferences: “after considering the probability of error (that is, after considering how frequently we would be in error if in conditions of our data we rejected the hypotheses tested), we decided to act on the assumption that “high” scores on “potential” and on “education” are indicative of better chances of success in the drive to home ownership”. An example of a shorter statement that Neyman provides reads: “As a result of the tests we applied, we decided to act on the assumption (or concluded) that the two groups are not random samples from the same population.”

A complete verbal description of the result of a Neyman-Pearson hypothesis test acknowledges two sources of uncertainty. First, the assumptions of the statistical test must be met (i.e., data is normally distributed), or any deviations should be small enough to not have any substantial effect on the frequentist error rates. Second, conclusions are made “Without hoping to know. whether each separate hypothesis is true or false” (Neyman & Pearson, 1933a). Any single conclusion can be wrong, and assuming the test assumption are met, we make claims under a known maximum error rate (which is never zero). Future replication studies are needed to provide further insights about whether the current conclusion was erroneous or not.

After observing a p-value smaller than the alpha level, one can therefore conclude: “Until new data emerges that proves us wrong, we decide to act as if there is an effect, while acknowledging that the methodological procedure we base this decision on has, a maximum error rate of alpha% (assuming the statistical assumptions are met), which we find acceptably low.” One can follow such a statement about the observed data with a theoretical inference, such as “assuming our auxiliary hypotheses hold, the result of this statistical test corroborates our theoretical hypothesis”. If a conclusive test result in an equivalence test is observed that allows a researcher to reject the presence of any effect large enough to be meaningful, the conclusion would be that the test result does not corroborate the theoretical hypothesis.

The problem that the common application of null hypothesis significance testing in science is based on an arbitrary threshold of 0.05 is true (Lakens, Adolfi, et al., 2018). There are surprisingly few attempts to provide researchers with practical approaches to determine an alpha level on more substantive grounds (but see Field et al., 2004; Kim & Choi, 2021; Maier & Lakens, 2021; Miller & Ulrich, 2019; Mudge et al., 2012). It seems difficult to resolve in practice, both because at least some scientist adopt a philosophy of science where the goal of hypothesis tests is to establish a corpus of scientific claims (Frick, 1996), and any continuous measure will be broken up in a threshold below which a researcher are not expected to make a claim about a finding (e.g., a BF < 3, see Kass & Raftery, 1995, or a likelihood ratio lower than k = 8, see Royall, 2000). Although it is true that an alpha level of 0.05 is arbitrary, there are some pragmatic arguments in its favor (e.g., it is established, and it might be low enough to yield claims that are taken seriously, but not high enough to prevent other researchers from attempting to refute the claim, see Uygun Tunç et al., 2021).

If there really no agreement on best practices in sight?

One major impetus for the flawed proposal to interpret p-values as evidence by Muff and colleagues is that “no agreement on a way forward is in sight”. The statement that there is little agreement among statisticians is an oversimplification. I will go out on a limb and state some things I assume most statisticians agree on. First, there are multiple statistical tools one can use, and each tool has their own strengths and weaknesses. Second, there are different statistical philosophies, each with their own coherent logic, and researchers are free to analyze data from the perspective of one or multiple of these philosophies. Third, one should not misuse statistical tools, or apply them to attempt to answer questions the tool was not designed to answer.

It is true that there is variation in the preferences individuals have about which statistical tools should be used, and the philosophies of statistical researchers should adopt. This should not be surprising. Individual researchers differ in which research questions they find interesting within a specific content domain, and similarly, they differ in which statistical questions they find interesting when analyzing data. Individual researchers differ in which approaches to science they adopt (e.g., a qualitative or a quantitative approach), and similarly, they differ in which approach to statistical inferences they adopt (e.g., a frequentist or Bayesian approach). Luckily, there is no reason to limit oneself to a single tool or philosophy, and if anything, the recommendation is to use multiple approaches to statistical inferences. It is not always interesting to ask what the p-value is when analyzing data, and it is often interesting to ask what the effect size is. Researchers can believe it is important for reliable knowledge generation to control error rates when making scientific claims, while at the same time believing that it is important to quantify relative evidence using likelihoods or Bayes factors (for example by presented a Bayes factor alongside every p-value for a statistical test, Lakens et al., 2020).

Whatever approach to statistical inferences researchers choose to use, the approach should answer a meaningful statistical question (Hand, 1994), the approach to statistical inferences should be logically coherent, and the approach should be applied correctly. Despite the common statement in the literature that p-values can be interpreted as measures of evidence, the criticism against the coherence of this approach should make us pause. Given that coherent alternatives exist, such as likelihoods (Royall, 1997) or Bayes factors (Kass & Raftery, 1995), researchers should not follow the recommendation by Muff and colleagues to report p = 0.08 as ‘weak evidence’, p = 0.03 as ‘moderate evidence’, and p = 0.168 as ‘no evidence’.

References

Bland, M. (2015). An introduction to medical statistics (Fourth edition). Oxford University Press.

Field, S. A., Tyre, A. J., Jonzén, N., Rhodes, J. R., & Possingham, H. P. (2004). Minimizing the cost of environmental management decisions by optimizing statistical thresholds. Ecology Letters, 7(8), 669–675. https://doi.org/10.1111/j.1461-0248.2004.00625.x

Frick, R. W. (1996). The appropriate use of null hypothesis testing. Psychological Methods, 1(4), 379–390. https://doi.org/10.1037/1082-989X.1.4.379

Goodman, S. N., & Royall, R. (1988). Evidence and scientific research. American Journal of Public Health, 78(12), 1568–1574.

Hand, D. J. (1994). Deconstructing Statistical Questions. Journal of the Royal Statistical Society. Series A (Statistics in Society), 157(3), 317–356. https://doi.org/10.2307/2983526

Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90(430), 773–795. https://doi.org/10.1080/01621459.1995.10476572

Kim, J. H., & Choi, I. (2021). Choosing the Level of Significance: A Decision-theoretic Approach. Abacus, 57(1), 27–71. https://doi.org/10.1111/abac.12172

Krueger, J. (2001). Null hypothesis significance testing: On the survival of a flawed method. American Psychologist, 56(1), 16–26. https://doi.org/10.1037//0003-066X.56.1.16

Lakens, D. (2021). The practical alternative to the p value is the correctly used p value. Perspectives on Psychological Science, 16(3), 639–648. https://doi.org/10.1177/1745691620958012

Lakens, D., Adolfi, F. G., Albers, C. J., Anvari, F., Apps, M. A. J., Argamon, S. E., Baguley, T., Becker, R. B., Benning, S. D., Bradford, D. E., Buchanan, E. M., Caldwell, A. R., Calster, B., Carlsson, R., Chen, S.-C., Chung, B., Colling, L. J., Collins, G. S., Crook, Z., … Zwaan, R. A. (2018). Justify your alpha. Nature Human Behaviour, 2, 168–171. https://doi.org/10.1038/s41562-018-0311-x

Lakens, D., McLatchie, N., Isager, P. M., Scheel, A. M., & Dienes, Z. (2020). Improving Inferences About Null Effects With Bayes Factors and Equivalence Tests. The Journals of Gerontology: Series B, 75(1), 45–57. https://doi.org/10.1093/geronb/gby065

Lakens, D., Scheel, A. M., & Isager, P. M. (2018). Equivalence testing for psychological research: A tutorial. Advances in Methods and Practices in Psychological Science, 1(2), 259–269. https://doi.org/10.1177/2515245918770963

Maier, M., & Lakens, D. (2021). Justify Your Alpha: A Primer on Two Practical Approaches. PsyArXiv. https://doi.org/10.31234/osf.io/ts4r6

Miller, J., & Ulrich, R. (2019). The quest for an optimal alpha. PLOS ONE, 14(1), e0208631. https://doi.org/10.1371/journal.pone.0208631

Mudge, J. F., Baker, L. F., Edge, C. B., & Houlahan, J. E. (2012). Setting an Optimal ? That Minimizes Errors in Null Hypothesis Significance Tests. PLOS ONE, 7(2), e32734. https://doi.org/10.1371/journal.pone.0032734

Neyman, J. (1957). “Inductive Behavior” as a Basic Concept of Philosophy of Science. Revue de l’Institut International de Statistique / Review of the International Statistical Institute, 25(1/3), 7–22. https://doi.org/10.2307/1401671

Neyman, J. (1960). First course in probability and statistics. Holt, Rinehart and Winston.

Neyman, J. (1976). Tests of statistical hypotheses and their use in studies of natural phenomena. Communications in Statistics – Theory and Methods, 5(8), 737–751. https://doi.org/10.1080/03610927608827392

Neyman, J., & Pearson, E. S. (1933a). On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 231(694–706), 289–337. https://doi.org/10.1098/rsta.1933.0009

Neyman, J., & Pearson, E. S. (1933b). The testing of statistical hypotheses in relation to probabilities a priori. Mathematical Proceedings of the Cambridge Philosophical Society, 29(04), 492–510. https://doi.org/10.1017/S030500410001152X

Royall, R. (1997). Statistical Evidence: A Likelihood Paradigm. Chapman and Hall/CRC.

Royall, R. (2000). On the probability of observing misleading statistical evidence. Journal of the American Statistical Association, 95(451), 760–768.

Spanos, A. (2013). Who should be afraid of the Jeffreys-Lindley paradox? Philosophy of Science, 80(1), 73–93.

Uygun Tunç, D., & Tunç, M. N. (2021). A Falsificationist Treatment of Auxiliary Hypotheses in Social and Behavioral Sciences: Systematic Replications Framework. In Meta-Psychology. https://doi.org/10.31234/osf.io/pdm7y

Uygun Tunç, D., Tunç, M. N., & Lakens, D. (2021). The Epistemic and Pragmatic Function of Dichotomous Claims Based on Statistical Hypothesis Tests. PsyArXiv. https://doi.org/10.31234/osf.io/af9by

If you have educational material that you think will do a better job at preventing p-value misconceptions than the material in my MOOC, join the p-value misconception eradication challenge by proposing an improvement to my current material in a new A/B test in my MOOC.

I launched a massive open online course “Improving your statistical inferences” in October 2016. So far around 47k students have enrolled, and the evaluations suggest it has been a useful resource for many researchers. The first week focusses on p-values, what they are, what they aren’t, and how to interpret them.

Arianne Herrera-Bennet was interested in whether an understanding of p-values was indeed “impervious to correction” as some statisticians believe (Haller & Krauss, 2002, p. 1) and collected data on accuracy rates on ‘pop quizzes’ between August 2017 and 2018 to examine if there was any improvement in p-value misconceptions that are commonly examined in the literature. The questions were asked at the beginning of the course, after relevant content was taught, and at the end of the course. As the figure below from the preprint shows, there was clear improvement, and accuracy rates were quite high for 5 items, and reasonable for 3 items.

We decided to perform a follow-up from September 2018 where we added an assignment to week one for half the students in an ongoing A/B test in the MOOC. In this new assignment, we didn’t just explain what p-values are (as in the first assignment in the module all students do) but we also tried to specifically explain common misconceptions, to explain what p-values are not. The manuscript is still in preparation, but there was additional improvement for at least some misconceptions. It seems we can develop educational material that prevents p-value misconceptions – but I am sure more can be done. 

In my paper to appear in Perspectives on Psychological Science on “The practical alternative to the p-value is the correctly used p-value” I write:

“Looking at the deluge of papers published in the last half century that point out how researchers have consistently misunderstood p-values, I am left to wonder: Where is the innovative coordinated effort to create world class educational materials that can freely be used in statistical training to prevent such misunderstandings? It is nowadays relatively straightforward to create online apps where people can simulate studies and see the behavior of p values across studies, which can easily be combined with exercises that fit the knowledge level of bachelor and master students. The second point I want to make in this article is that a dedicated attempt to develop evidence based educational material in a cross-disciplinary team of statisticians, educational scientists, cognitive psychologists, and designers seems worth the effort if we really believe young scholars should understand p values. I do not think that the effort statisticians have made to complain about p-values is matched with a similar effort to improve the way researchers use p values and hypothesis tests. We really have not tried hard enough.”

If we honestly feel that misconceptions of p-values are a problem, and there are early indications that good education material can help, let’s try to do all we can to eradicate p-value misconceptions from this world.

We have collected enough data in the current A/B test. I am convinced the experimental condition adds some value to people’s understanding of p-values, so I think it would be best educational practice to stop presenting students with the control condition.

However, I there might be educational material out there that does a much better job than the educational material I made, to train away misconceptions. So instead of giving all students my own new assignment, I want to give anyone who thinks they can do an even better job the opportunity to demonstrate this. If you have educational material that you think will work even better than my current material, I will create a new experimental condition that contains your teaching material. Over time, we can see which materials performs better, and work towards creating the best educational material to prevent misunderstandings of p-values we can.

If you are interested in working on improving p-value education material, take a look at the first assignment in the module that all students do, and look at the new second assignment I have created to train away misconception (and the answers). Then, create (or adapt) educational material such that the assignment is similar in length and content. The learning goal should be to train away common p-value misconceptions – you can focus on any and all you want. If there are multiple people who are interested, we collectively vote on which material we should test first (but people are free to combine their efforts, and work together on one assignment). What I can offer is getting your material in front of between 300 and 900 students who enroll each week. Not all of them will start, not all of them will do the assignments, but your material should reach at least several hundreds of learners a year, of which around 40% has a masters degree, and 20% has a PhD – so you will be teaching fellow scientists (and beyond) to improve how they work.  

I will incorporate this new assignment, and make it publicly available on my blog, as soon as it is done and decided on by all people who expressed interest in creating high quality teaching material. We can evaluate the performance by looking at the accuracy rates on test items. I look forward to seeing your material, and hope this can be a small step towards an increased effort in improving statistics education. We might have a long way to go to completely eradicate p-value misconceptions, but we can start.

On July 28, 2020, the first Dutch academic has been judged to have violated the code of conduct for research integrity for p-hacking and optional stopping with the aim of improving the chances of obtaining a statistically significant result. I think this is a noteworthy event that marks a turning point in the way the scientific research community interprets research practices that up to a decade ago were widely practiced. The researcher in question violated scientific integrity in several other important ways, including withdrawing blood without ethical consent, and writing grant proposals in which studies and data were presented that had not been performed and collected. But here, I want to focus on the judgment about p-hacking and optional stopping.

When I studied at Leiden University from 1998 to 2002 and commuted by train from my hometown of Rotterdam I would regularly smoke a cigar in the smoking compartment of the train during my commute. If I would enter a train today and light a cigar, the responses I would get from my fellow commuters would be markedly different than 20 years ago. They would probably display moral indignation or call the train conductor who would give me a fine. Times change.

When the reporton the fraud case of Diederik Stapel came out, the three committees were surprised by a research culture that accepted “sloppy science”. But it did not directly refer to these practices as violations of the code of conduct for research integrity. For example, on page 57 they wrote:

 “In the recommendations, the Committees not only wish to focus on preventing or reducing fraud, but also on improving the research culture. The European Code refers to ‘minor misdemeanours’: some data massage, the omission of some unwelcome observations, ‘favourable’ rounding off or summarizing, etc. This kind of misconduct is not categorized under the ‘big three’ (fabrication, falsification, plagiarism) but it is, in principle, equally unacceptable and may, if not identified or corrected, easily lead to more serious breaches of standards of integrity.”

Compare this to the reportby LOWI, the Dutch National Body for Scientific Integrity, for a researcher at Leiden University who was judged to violate the code of conduct for research integrity for p-hacking and optional stopping (note this is my translation from Dutch of the advice on page 17 point IV, and point V on page 4):

“The Board has rightly ruled that Petitioner has violated standards of academic integrity with regard to points 2 to 5 of the complaint.”

With this, LOWI has judged that the Scientific Integrity Committee of Leiden University (abbreviated as CWI in Dutch) ruled correctly with respect to the following:

“According to the CWI, the applicant also acted in violation of scientific integrity by incorrectly using statistical methods (p-hacking) by continuously conducting statistical tests during the course of an experiment and by supplementing the research population with the aim of improving the chances of obtaining a statistically significant result.”

As norms change, what we deemed a misdemeanor before, is now simply classified as a violation of academic integrity. I am sure this is very upsetting for this researcher. We’ve seen similar responses in the past years, where single individuals suffered more than average researcher for behaviors that many others performed as well. They might feel unfairly singled out. The only difference between this researcher at Leiden University, and several others who performed identical behaviors, was that someone in their environment took the 2018 Netherlands Code of Conduct for Research Integrity seriously when they read section 3.7, point 56:

Call attention to other researchers’ non-compliance with the standards as well as inadequate institutional responses to non-compliance, if there is sufficient reason for doing so.

When it comes to smoking, rules in The Netherlands are regulated through laws. You’d think this would mitigate confusion, insecurity, and negative emotions during a transition – but that would be wishful thinking. In The Netherlands the whole transition has been ongoing for close to two decades, from an initial law allowing a smoke-free working environment in 2004, to a completely smoke-free university campus in August 2020.

The code of conduct for research integrity is not governed by laws, and enforcement of the code of conduct for research integrity is typically not anyone’s full time job. We can therefore expect the change to be even more slow than the changes in what we feel is acceptable behavior when it comes to smoking. But there is notable change over time.

We see a shift from the “big three” types of misconduct (fabrication, falsification, plagiarism), and somewhat vague language of misdemeanors, that is “in principle” equally unacceptable, and might lead to more serious breaches of integrity, to a clear classification of p-hacking and optional stopping as violations of scientific integrity. Indeed, if you ask me, the ‘bigness’ of plagiarism pales compared to how publication bias and selective reporting distort scientific evidence.

Compare this to smoking laws in The Netherlands, where early on it was still allowed to create separate smoking rooms in buildings, while from August 2020 onwards all school and university terrain (i.e., the entire campus, inside and outside of the buildings) needs to be a smoke-free environment. Slowly but sure, what is seen as acceptable changes.

I do not consider myself to be an exceptionally big idiot – I would say I am pretty average on that dimension – but it did not occur to me how stupid it was to enter a smoke-filled train compartment and light up a cigar during my 30 minute commute around the year 2000. At home, I regularly smoked a pipe (a gift from my father). I still have it. Just looking at the tar stains now makes me doubt my own sanity.

This is despite that fact that the relation between smoking and cancer was pretty well established since the 1960’s. Similarly, when I did my PhD between 2005 and 2009 I was pretty oblivious to the error rate inflation due to optional stopping, despite that fact that one of the more important papers on this topic was published by Armitage, McPherson, and Rowe in 1969. I did realize that flexibility in analyzing data could not be good for the reliability of the findings we reported, but just like when I lit a cigar in the smoking compartment in the train, I failed to adequately understand how bad it was.

When smoking laws became stricter, there was a lot of discussion in society. One might even say there was a strong polarization, where on the one hand newspaper articles appeared that claimed how outlawing smoking in the train was ‘totalitarian’, while we also had family members who would no longer allow people to smoke inside their house, which led my parents (both smokers) to stop visiting these family members. Changing norms leads to conflict. People feel personally attacked, they become uncertain, and in the discussions that follow we will see all opinions ranging from how people should be free to do what they want, to how people who smoke should pay more for healthcare.

We’ve seen the same in scientific reform, although the discussion is more often along the lines of how smoking can’t be that bad if my 95 year old grandmother has been smoking a packet a day for 70 years and feels perfectly fine, to how alcohol use or lack of exercise are much bigger problems and why isn’t anyone talking about those.

But throughout all this discussion, norms just change. Even my parents stopped smoking inside their own home around a decade ago. The Dutch National Body for Scientific Integrity has classified p-hacking and optional stopping as violations of research integrity. Science is continuously improving, but change is slow. Someone once explained to me that correcting the course of science is like steering an oil tanker – any change in direction takes a while to be noticed. But when change happens, it’s worth standing still to reflect on it, and look at how far we’ve come.