At least two key types of replication exist: direct and conceptual. Conceptual replication generally refers to cases where researchers ‘tweak’ the methods of previous studies [43] and when successful, may be informative with regard to the boundaries and possible moderators of an effect. When a conceptual replication fails, however, fewer clear implications exist for the original study because of likely differences in procedure or stimuli and so on. For this reason, we have seen an increased weight given to direct replications.

How often do direct and conceptual replications occur in psychology? Screening 100 of the most-cited psychology journals since 1900, Makel, Plucker & Hegarty [40] found that approximately 1.6 % of all psychology articles used the term replication in the text. A further more detailed analysis of 500 randomly selected articles revealed that only 68 % using the term replication were actual replications. They calculated an overall replication rate of 1.07 % and Makel et al. [40] found that only 18 % of those were direct rather than conceptual replications.

The lack of replication in psychology is systemic and widespread, and particularly the bias against publishing direct replications. In their survey of social science journal editors, Neuliep & Crandall [42] found almost three quarters preferred to publish novel findings rather than replications. In a parallel survey of reviewers for social science journals, Neuliep & Crandall [43] found over half (54 %) stated a preference for new findings over replications. Indeed, reviewers stated that replications were “Not newsworthy” or even a “Waste of space”. By contrast, comments from natural science journal editors present a more varied picture, with comments ranging from “Replication without some novelty is not accepted” to “Replication is rarely an issue for us…since we publish them.” [39].

Despite an enduring historical abandonment of replication, the tide appears to be turning. Makel et al. [40] found that the replication rate after the year 2000 was 1.84 times higher than for the period between 1950 and 1999. In a more recent evolution, several large-scale direct replication projects have emerged during the past 2 years including: the Many Labs project [33]; a set of preregistered replications published in a special issue of Social Psychology (Edited by [44]); the Reproducibility Project of the Open Science Collaboration [45]; and the Pipeline Project by Schweinsberg et al. [50]. In two of these projects (Many Labs by [33]; Pipeline Project by [50]), a group of researchers replicated samples of studies, with each group replicating all studies. In the two remaining projects, a number of research groups each replicated one study, selected from a sample of studies (Registered Reports by [44]; Open Science Collaboration, [45]). Each project ensured that replications were sufficiently powered (typically in excess of 90 % -thus offering a very good probability of detecting true effects) and where possible, used the original materials and stimuli as provided by the original authors. It is worth considering each in more detail.

Many Labs involved 36 research groups across 12 countries who replicated 13 psychological studies in over 6,000 participants. Studies of classic and newer effects were selected partly because they had simple designs that could be adapted for online administration. Reassuringly perhaps, 10 of the 13 effects replicated consistently across 36 different samples with, of course, some variability in the effect size reported compared to the original studies – some smaller but also some larger. One effect received weak support. Only two studies consistently failed to replicate and both involved what are described as ‘social priming’ phenomena. One study where ‘accidental’ exposure to a US flag resulted in increased conservatism amongst Americans [11]. Participants viewed four photos and were asked to just estimate the time-of-day in the photo – the US flag appeared in two photos. Following this, they completed an 8-item questionnaire assessing their views toward various political issues (e.g., abortion, gun control). In the second priming study, exposure to ‘money’ had resulted in endorsement of the current social system [12]. In this study, participants completed demographic questions against a background that showed a faint picture of US $100 bills or the same background but blurred. Each of these two priming experiments had a single significant p-value (out of 36 replications) and for flag priming, it was in the opposite direction to that expected.

Turning to the special issue of Social Psychology edited by Nosek & Lakens [44]. This contained a series of articles replicating important results in social psychology. Important was broadly defined as “…often cited, a topic of intense scholarly or public interest, a challenge to established theories), but should also have uncertain truth value (e.g., few confirmations, imprecise estimates of effect sizes).” One might euphemistically describe the studies as curios. The articles were first submitted as Registered Reports and reviewed prior to data collection, with authors being assured their findings would be published regardless of outcome, as long as they adhered to the registered protocol. Attempted replications included the “Romeo and Juliet effect” – does parental interference lead to increases in love and commitment (Original: [17]; Replication: Sinclair, Hood, & Wright, [53]), does experiencing physical warmth (warm therapeutic packs) increase judgments of interpersonal warmth (Original: [58]; Replication: Lynott, Corker, Wortman, Connell, Donnellan, Lucas, & O’Brien, [38]), does recalling unethical behavior lead participants to see the room as darker (Original: [3]; Replication: [10]); does physical cleanliness reduce the severity of moral judgments (original : [49]: [28]). In contrast to high replication rate of Many Labs, the Registered Reports replications failed to confirm the results in 10 of 13 studies.

In the largest crowdsourced effort to date, the OSC Reproducibility project involved 270 collaborators attempting to replicate 100 findings from 3 major psychology journals Psychological Science (PSCI), Journal of Personality and Social Psychology (JPSP), and Journal of Experimental Psychology: Learning, Memory, and Cognition (JEP: LMC). While 97 of 100 studies originally reported statistically significant results, only 36 % of the replications did so with a mean effect size of around half of that reported in the original studies.

All of the journals exhibited a large reduction of around 50 % in effect sizes, with replications from JPSP particularly affected - shrinking by 75 % from 0.29 to 0.07. The replicability in one domain of psychology (good or poor) in no way guarantees what will happen in another domain. One thing we know from this project, is that “…reproducibility was stronger in studies and journals representing cognitive psychology than social psychology topics. For example, combining across journals, 14 of 55 (25 %) of social psychology effects replicated by the P < 0.05 criterion, whereas 21 of 42 (50 %) of cognitive psychology effects did so.” The reasons for such a difference are debatable, but provide no licence to either congratulate cognitive psychologists or berate social psychologists. Indeed, the authors paint a considered and faithful picture of what their findings mean when they conclude “…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”. (Open Science Collaboration p.4716-7)

The studies that were not selected for replication are informative – they were described as “…deemed infeasible to replicate because of time, resources, instrumentation, dependence on historical events, or hard-to-access samples… [and some] required specialized samples (such as macaques or people with autism), resources (such as eye tracking machines or functional magnetic resonance imaging), or knowledge making them difficult to match with teams”. Thus, the main drivers of replication are often economic in terms of time, money and human investment. High cost studies are likely to remain castles in the air, leaving us with little insight about replicability rates in some areas such as functional imaging (e.g. [9]), clinical and health psychology (see Coyne, this issue), and neuropsychology.

The ‘Pipeline project’ by Schweinsberg et al. [50] intentionally used a non-adversarial approach. They crowdsourced 25 research teams across various countries to replicate a series of 10 unpublished moral-judgment experiments from the lead author’s (Uhlmann) lab i.e., in the pipeline. This speaks directly to Lykken’s [37] proposal from nearly 50 years ago that “…ideally all experiments would be replicated before publication” although at that time, he deemed it ‘impractical’.

Pipeline replications included: the Bigot–misanthrope effect – whether participants judge a manager who selectively mistreats racial minorities as a more blameworthy person than a manager who mistreats all of his employees; Bad tipper effect - are people who leave a full tip, but entirely in pennies judged more negatively than someone who leaves less money, but in notes; the Burn-in-hell effect – do people perceive corporate executives as more likely to burn in hell than members of social categories defined by antisocial behaviour, such as vandals. Six of ten findings replicated across all of their replication criteria, one further finding replicated but with a significantly smaller effect size than the original, one finding replicated consistently in the original culture but not outside of it (bad tipper replicated in US and not outside), and two findings effects were unsupported.

The headline replication rates differed considerably across projects – occurring more frequently for Many Labs (77 %) and the Pipeline Project (60 %) than Registered Reports (30 %) and the Open Science Collaboration (36 %). Why are replication rates lower in the latter two projects? Possible explanations include the choice of likely versus unlikely replication candidates. Amongst the Many Labs studies, some had already previously been replicated and were selected knowing this fact. By contrast, the studies in the Pipeline project had not been previously replicated (indeed, not even previously published). Also important from a different perspective is whether each study was replicated only once by one group or multiple times by many groups.

In the Many Labs and Pipeline projects, 36 and 25 separate research groups were replicating each of 13 and 10 studies respectively. Multiple analyses lend themselves to meta-analytic techniques and analysis of the heterogeneity across research groups examining the same effect – the extent to which they accord in their effect sizes or not. The Many Labs project reported I2 values, which estimate the proportion of variation due to heterogeneity rather than chance. In the majority of cases, heterogeneity was small to moderate or even non-existent (e.g. across the 36 replications for both of the social priming studies: flag and money). Indeed, heterogeneity of effect sizes was greater between studies than within studies. When heterogeneity was greater, it was - perhaps surprisingly - where mean effect sizes were largest. Nonetheless, Many Labs reassuringly shows that some effects are highly replicable across research groups, countries, presentational differences (online versus face to face).

Counter-intuitive and even fanciful psychological hypotheses are not necessarily more likely to be false, but believing them to be so may influence researchers– even implicitly – in terms of how replications are conducted. In their extensive literature search, Makel et al. [40] reported that most direct replications are conducted by authors who proposed the original findings. This raises the thorny question of who should replicate? Almost 50 years ago Bakan [2] sagely warned that “If an investigator attempts to replicate his own investigation at another time, he will inevitably be under the influence of what he has already done…He should challenge, for example, his personal identification with the results he has already obtained, and prepare himself for finding both novelty and contradiction with respect to his earlier investigation” and that “…If one investigator is interested in replicating the investigation of another investigator, he should carefully take into account the possibility of suggestion, or his willingness to accept the results of the earlier investigator. …He should take careful cognizance of possible motivation for showing the earlier investigator to be in error, etc. [p. 110].” The irony is that as psychologists, we should be acutely aware of such biases - we cannot ignore the psychology of replication in the replication of psychology.

The wriggle room is fertile ground for psychologists to exploit the disjunction between belief and evidence that seems quite pervasive in psychology. As remarked upon by Francis “Contrary to its central role in other sciences,it appears that successful replication is sometimes not related to belief about an effect in experimental psychology. A high rate of successful replication is not sufficient to induce belief in an effect [8], nor is a high rate of successful replication necessary for belief [22].” The Bem [8] study documented “experimental evidence for anomalous retroactive influences on cognition and affect” or in plain language…precognition. Using multiple tasks, and nine experiments involving over 1,000 participants, Bem had implausibly demonstrated that the performance of participants reflected what happened after they had made their decision. For example, on a memory test, participants were more likely to remember words that they were later asked to practise i.e. memory rehearsal seemingly worked back in time. In another task, participants had to select which of two curtains on a computer screen hid an erotic image, and they did so at a level significantly greater than chance, but not when the hidden images were less titillating. Furthermore, Bem and colleagues [7] later meta-analysed 90 previous studies to establish a significant effect size of 0.22.

Bem presents nine replications of a phenomenon and a large meta-analysis, yet we do not believe it, while other phenomena do not so readily replicate (e.g. bystander apathy [22]) but we do believe in them. Francis [23] bleakly concludes “The scientific method is supposed to be able to reveal truths about the world, and the reliability of empirical findings is supposed to be the final arbiter of science; but this method does not seem to work in experimental psychology as it is currently practiced.” Whether we believe in Bem’s precognition, social priming, or indeed, any published psychological finding – researchers are operating within the methodological and statistical wriggle room. The task for psychologists is to view these phenomena like any other scientific question i.e. in need of explanation. If they can close-down the wriggle room, then we might expect such curios and anomalies to evaporate in a cloud of nonsignificant results.

While some might view the disjunction between belief and evidence as ‘healthy skepticism’, others might also describe it as resistance to evidence or even anti-science. A pertinent example comes from Lykken [37] who described a study in which people who see frogs in a Rorschach test – ‘frog responders’ – were more likely to have an eating disorder [48] – a finding interpreted as evidence of harboring oral impregnation fantasies and an unconscious belief in anal birth. Lykken asked 20 clinician colleagues to estimate the likelihood of this ‘cloacal theory of birth’ before and after seeing Sapolsky’s evidence. Beforehand, they reported a “…median value of 0.01, which can be interpreted to mean, roughly, ‘I don't believe it’” and after being shown the confirmatory evidence “…the median unchanged at 0.01. I interpret this consensus to mean, roughly, ‘I still don’t believe it.’” (p. 151–152). Lykken remarked that normally when a prediction is confirmed by experiment, we might expect “…a nontrivial increment in one’s confidence in that theory should result, especially when one’s prior confidence is low… [but that] this rule is wrong not only in a few exceptional instances but as it is routinely applied to the majority of experimental reports in the psychological literature” p.152. Often such claims give rise to a version of Feynman’s maxim that “Extraordinary claims require extraordinary evidence”. The remarkableness of a claim, however, is not necessarily relevant to either the type or the scale of evidence required. Instead of setting different criteria for the ordinary and extraordinary, we need to continue to close the wriggle room.