A study with low statistical power has a reduced chance of detecting a true effect, but it is less well appreciated that low power also reduces the likelihood that a statistically significant result reflects a true effect. Here, we show that the average statistical power of studies in the neurosciences is very low. The consequences of this include overestimates of effect size and low reproducibility of results. There are also ethical dimensions to this problem, as unreliable research is inefficient and wasteful. Improving reproducibility in neuroscience is a key priority and requires attention to well-established but often ignored methodological principles.

/pdf/power-failure-why-small-sample-size-undermines-the-4ftwwuexp7.pdf

Power failure: why small sample size undermines the reliability of neuroscience

Reproducibility is a defining feature of science, but the extent to which it characterizes current research is unknown. We conducted replications of 100 experimental and correlational studies published in three psychology journals using high-powered designs and original materials when available. Replication effects were half the magnitude of original effects, representing a substantial decline. Ninety-seven percent of original studies had statistically significant results. Thirty-six percent of replications had statistically significant results; 47% of original effect sizes were in the 95% confidence interval of the replication effect size; 39% of effects were subjectively rated to have replicated the original result; and if no bias in original results is assumed, combining original and replication results left 68% with statistically significant effects. Correlational tests suggest that replication success was better predicted by the strength of original evidence than by characteristics of the original and replication teams.

/pdf/estimating-the-reproducibility-of-psychological-science-1en4um03nt.pdf

Estimating the reproducibility of psychological science

Cobb’s concern was a long-worrisome circularity in the sociology of science based on the use of bright lines such as p< 0.05: “We teach it because it’s what we do; we do it because it’s what we teach.” This concern was brought to the attention of the ASA Board. The ASA Board was also stimulated by highly visible discussions over the last few years. For example, ScienceNews (Siegfried 2010) wrote: “It’s science’s dirtiest secret: The ‘scientific method’ of testing hypotheses by statistical analysis stands on a flimsy foundation.” A November 2013, article in Phys.org Science News Wire (2013) cited “numerous deep flaws” in null hypothesis significance testing. A ScienceNews article (Siegfried 2014) on February 7, 2014, said “statistical techniques for testing hypotheses...havemore flaws than Facebook’s privacy policies.” Aweek later, statistician and “Simply Statistics” blogger Jeff Leek responded. “The problem is not that people use P-values poorly,” Leek wrote, “it is that the vast majority of data analysis is not performed by people properly trained to perform data analysis” (Leek 2014). That same week, statistician and science writer Regina Nuzzo published an article in Nature entitled “Scientific Method: Statistical Errors” (Nuzzo 2014). That article is nowone of the most highly viewedNature articles, as reported by altmetric.com (http://www.altmetric.com/details/2115792#score). Of course, it was not simply a matter of responding to some articles in print. The statistical community has been deeply concerned about issues of reproducibility and replicability of scientific conclusions. Without getting into definitions and distinctions of these terms, we observe that much confusion and even doubt about the validity of science is arising. Such doubt can lead to radical choices, such as the one taken by the editors of Basic andApplied Social Psychology, who decided to ban p-values (null hypothesis significance testing) (Trafimow and Marks 2015). Misunderstanding or misuse of statistical inference is only one cause of the “reproducibility crisis” (Peng 2015), but to our community, it is an important one. When the ASA Board decided to take up the challenge of developing a policy statement on p-values and statistical significance, it did so recognizing this was not a lightly taken step. The ASA has not previously taken positions on specific matters of statistical practice. The closest the association has come to this is a statement on the use of value-added models (VAM) for educational assessment (Morganstein and Wasserstein 2014) and a statement on risk-limiting post-election audits (American Statistical Association 2010). However, these were truly policy-related statements. The VAM statement addressed a key educational policy issue, acknowledging the complexity of the issues involved, citing limitations of VAMs as effective performance models, and urging that they be developed and interpreted with the involvement of statisticians. The statement on election auditing was also in response to a major but specific policy issue (close elections in 2008), and said that statistically based election audits should become a routine part of election processes. By contrast, the Board envisioned that the ASA statement on p-values and statistical significance would shed light on an aspect of our field that is too often misunderstood and misused in the broader research community, and, in the process, provides the community a service. The intended audience would be researchers, practitioners, and science writers who are not primarily statisticians. Thus, this statementwould be quite different from anything previously attempted. The Board tasked Wasserstein with assembling a group of experts representing a wide variety of points of view. On behalf of the Board, he reached out to more than two dozen such people, all of whom said theywould be happy to be involved. Several expressed doubt about whether agreement could be reached, but those who did said, in effect, that if there was going to be a discussion, they wanted to be involved. Over the course of many months, group members discussed what format the statement should take, tried to more concretely visualize the audience for the statement, and began to find points of agreement. That turned out to be relatively easy to do, but it was just as easy to find points of intense disagreement. The time came for the group to sit down together to hash out these points, and so in October 2015, 20 members of the group met at the ASA Office in Alexandria, Virginia. The 2-day meeting was facilitated by Regina Nuzzo, and by the end of the meeting, a good set of points around which the statement could be built was developed. The next 3 months saw multiple drafts of the statement, reviewed by group members, by Board members (in a lengthy discussion at the November 2015 ASA Board meeting), and by members of the target audience. Finally, on January 29, 2016, the Executive Committee of the ASA approved the statement. The statement development process was lengthier and more controversial than anticipated. For example, there was considerable discussion about how best to address the issue of multiple potential comparisons (Gelman and Loken 2014). We debated at some length the issues behind the words “a p-value near 0.05 taken by itself offers only weak evidence against the null

https://www.tandfonline.com/doi/pdf/10.1080/00031305.2016.1154108

The ASA's Statement on p-Values: Context, Process, and Purpose

In 1974 an article appeared in Science magazine with the dry-sounding title “Judgment Under Uncertainty: Heuristics and Biases” by a pair of psychologists who were not well known outside their discipline of decision theory. In it Amos Tversky and Daniel Kahneman introduced the world to Prospect Theory, which mapped out how humans actually behave when faced with decisions about gains and losses, in contrast to how economists assumed that people behave. Prospect Theory turned Economics on its head by demonstrating through a series of ingenious experiments that people are much more concerned with losses than they are with gains, and that framing a choice from one perspective or the other will result in decisions that are exactly the opposite of each other, even if the outcomes are monetarily the same. Prospect Theory led cognitive psychology in a new direction that began to uncover other human biases in thinking that are probably not learned but are part of our brain’s wiring.

Thinking fast and slow.

The measurement of meaning

In this article, we accomplish two things. First, we show that despite empirical psychologists' nominal endorsement of a low rate of false-positive findings (≤ .05), flexibility in data collection, analysis, and reporting dramatically increases actual false-positive rates. In many cases, a researcher is more likely to falsely find evidence that an effect exists than to correctly find evidence that it does not. We present computer simulations and a pair of actual experiments that demonstrate how unacceptably easy it is to accumulate (and report) statistically significant evidence for a false hypothesis. Second, we suggest a simple, low-cost, and straightforwardly effective disclosure-based solution to this problem. The solution involves six concrete requirements for authors and four guidelines for reviewers, all of which impose a minimal burden on the publication process.

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False-Positive Psychology: Undisclosed Flexibility in Data Collection and Analysis Allows Presenting Anything as Significant

Because scientists tend to report only studies (publication bias) or analyses (p-hacking) that "work," readers must ask, "Are these effects true, or do they merely reflect selective reporting?" We introduce p-curve as a way to answer this question. P-curve is the distribution of statistically significant p values for a set of studies (ps < .05). Because only true effects are expected to generate right-skewed p-curves-containing more low (.01s) than high (.04s) significant p values--only right-skewed p--curves are diagnostic of evidential value. By telling us whether we can rule out selective reporting as the sole explanation for a set of findings, p-curve offers a solution to the age-old inferential problems caused by file-drawers of failed studies and analyses.

/pdf/p-curve-a-key-to-the-file-drawer-1237pz4gnm.pdf

P-curve: a key to the file-drawer.

Because scientists tend to report only studies (publication bias) or analyses (p-hacking) that “work”, readers must ask, “Are these effects true, or do they merely reflect selective reporting?” We introduce p-curve as a way to answer this question. P-curve is the distribution of statistically significant p-values for a set of studies (ps

P-Curve: A Key to the File Drawer

Research shows that evidence-based algorithms more accurately predict the future than do human forecasters. Yet when forecasters are deciding whether to use a human forecaster or a statistical algorithm, they often choose the human forecaster. This phenomenon, which we call algorithm aversion, is costly, and it is important to understand its causes. We show that people are especially averse to algorithmic forecasters after seeing them perform, even when they see them outperform a human forecaster. This is because people more quickly lose confidence in algorithmic than human forecasters after seeing them make the same mistake. In 5 studies, participants either saw an algorithm make forecasts, a human make forecasts, both, or neither. They then decided whether to tie their incentives to the future predictions of the algorithm or the human. Participants who saw the algorithm perform were less confident in it, and less likely to choose it over an inferior human forecaster. This was true even among those who saw the algorithm outperform the human.

/pdf/algorithm-aversion-people-erroneously-avoid-algorithms-after-3tn58idk12.pdf

Algorithm aversion: people erroneously avoid algorithms after seeing them err.

Research shows that evidence-based algorithms more accurately predict the future than do human forecasters. Yet, when forecasters are deciding whether to use a human forecaster or a statistical algorithm, they often choose the human forecaster. This phenomenon, which we call algorithm aversion, is costly, and it is important to understand its causes. We show that people are especially averse to algorithmic forecasters after seeing them perform, even when they see them outperform a human forecaster. This is because people more quickly lose confidence in algorithmic than human forecasters after seeing them make the same mistake. In five studies, participants either saw an algorithm make forecasts, a human make forecasts, both, or neither. They then decided whether to tie their incentives to the future predictions of the algorithm or the human. Participants who saw the algorithm perform were less confident in it, and less likely to choose it over an inferior human forecaster. This was true even among those who saw the algorithm outperform the human.

/pdf/algorithm-aversion-people-erroneously-avoid-algorithms-after-2jhdchywh6.pdf

Joseph P. Simmons

Papers

False-Positive Psychology: Undisclosed Flexibility in Data Collection and Analysis Allows Presenting Anything as Significant

P-curve: a key to the file-drawer.

P-Curve: A Key to the File Drawer

Algorithm aversion: people erroneously avoid algorithms after seeing them err.

Algorithm Aversion: People Erroneously Avoid Algorithms after Seeing Them Err