Null findings

And after obtaining null results, or reading about null results in publications, how can we assess how informative they are? How much do we let them change our beliefs and inform our own work? In this article, we discuss these issues with the still dominant frequentist inference framework in mind.

But we also discuss an alternative statistical framework, Bayesian inference, which is not subject to the same formal limitations. We first outline factors that make NIBS null results particularly difficult to interpret, and how to address them. In part this might be attributable to the constraints of frequentist inference, but we suggested there were additional concrete arguments against null result interpretation specifically in NIBS: the localization argument, the neural efficacy argument, and the power argument.

According to the localization argument , one cannot be sure that the correct anatomical, or more importantly functional, area was stimulated with NIBS. With TMS, error additionally contributes, with shifting or tilting coils, moving participants, or human error in initial coil placement. With TES, selecting electrode montages is not trivial. Even if a large electrode is placed on the skull, almost certainly covering an underlying functional hotspot, the exact individual anatomy as well as reference electrode placement may determine which neurons are most affected and how effectively they are modulated Miranda et al.

The neural efficacy argument appears related but reflects a separate concern. In each participant, or even the whole sample: did the NIBS actually modulate neural activity? In TMS, the infinite parameter space number of pulses, pulse shape, pulse width, intensity, nested frequency, coil geometry, etc.

Moreover, between participants anatomy differs, in terms of gyrification or distances between coil and cortex Stokes et al. The power argument is more general but applies to NIBS research also. Perhaps a positive finding was not obtained, simply because the experimental design lacked statistical power. Aside from the usual sources of noise in experimental data, the methodological uncertainties inherent to NIBS research, of which localization and neural efficacy are examples, only exacerbate this concern.

Moreover, it appears that inter-individual differences in response to NIBS are substantial Maeda et al. For instance, inter-individual differences in network states Rizk et al. If unknown, or not taken into account, such differences can contribute strongly to reduced statistical power on the group level.

The power argument leaves one with the uncomfortable question: perhaps more trials per condition, or more participants in the sample, or even a small change in experimental tasks or design, could have yielded a positive result after all. So how meaningful is a null result in NIBS research, really?

These arguments indeed make it difficult to draw strong conclusions from null results in NIBS research.

Above, we argued why such a dichotomy would be unfortunate and even wasteful, given the original mission of NIBS to determine whether a brain process is, or is not , functionally relevant for a task.

One way to combat the localization argument is through hardware selection. Figure-8 TMS coils stimulate more focally than some older model circular coils Hallett, , electrical currents are more concentrated under the central electrode in a high-density TES montage compared to conventional large electrodes Edwards et al. But focality does not help if it is aimed at the wrong cortical target. The localization argument against interpreting null results becomes less problematic as the localization procedure becomes more sophisticated.

We previously compared the statistical power inherent to different TMS target site localization procedures, including anatomical landmarks, Talairach coordinates, individual MRI-based landmarks, and individual fMRI-based functional localizers, using frameless stereotactic Neuronavigation to determine and maintain coil positioning Sack et al.

The number of participants required to obtain a statistically significant effect calculated based on obtained effect size for each method rose rapidly, from only 5 using individual functional localizer scans, to 47 using the anatomical landmark EEG 10—20 P4 location approach. As power rises with localization procedure sophistication, for a given sample size the interpretability of a potential null result rises also although see e.

For TES, exciting developments in computational modeling of current flows, in increasingly realistic head models, similarly decrease the strength of the localization argument. Such modeling provides insight about how strongly, and where, electrical currents affect underlying neuronal tissue e. Clearly such modeling in TES also has a bearing on the neural efficacy argument: modeling increases confidence that current was sufficiently strong to reach and affect the cortical target.

This is not to say that all problems are solved for TES, because firstly modeling is not trivial, and secondly a model of current density across cortex does not yet reveal what the neural effects are of this current density. To combat at least some of these concerns, one might implement what we previously called a neural efficacy check de Graaf and Sack, Specifically for TMS, if the target region has a behavioral marker motor response, phosphene perception , both the localization and neural effects of a TMS protocol can be verified using such markers independently from the behavioral tasks of interest.

Hunting procedures, using independent tasks known to be affected by certain TMS protocols over the target regions, can also be used to achieve the same thing Oliver et al.

Ideally, however, the experimental design includes not only the main experimental condition of interest, on which a positive or null result can be obtained, but also a second experimental condition on which a positive result is expected. For example, we applied offline rTMS to frontal cortex in a bistable perception paradigm with a passive viewing condition and a voluntary control condition using the same stimuli de Graaf et al.

TMS modulated bistable perception in the voluntary control condition positive result but not in the passive viewing condition null result. The presence of the positive finding made the null result for passive bistable viewing more meaningful to us, since it inspired confidence that our TMS protocol and procedures indeed had neural effects with the potential to affect behavior.

In that study, passive bistable viewing behavior was very much unchanged. It was not a case of a small effect in the hypothesized direction not reaching significance. And this is really all one can do against the power argument: ensure sufficient power in the experimental design through a priori sample size calculations, and evaluate the effect size after data collection. The possibility that an even larger sample size, and more reliable estimation through more trials, could eventually lead to a statistically significant positive finding, is irrefutable.

In fact, it is inevitable: in classical frequentist hypothesis tests, with large enough sample sizes even true null hypotheses will be rejected Wagenmakers, This is not unique to NIBS research. What may be to some extent unique to NIBS research, and indeed an exciting development, is the inclusion of individual markers that predict response to NIBS.

As we continue to discover sources of inter-individual variability, we can either select participants Drysdale et al.

In Figure 1 , we distill the discussion so far into a conceptual model to help us evaluate null results in NIBS. The model contains two orthogonal axes. Figure 1. Orthogonal gradients of surprise and interpretability. A null result in an experiment aiming to replicate a well-established finding is very surprising. A null result that was hypothesized is not at all surprising.

A null result in an exploratory study with no prior expectations can be received neutrally middle of the continuum, not shown. The level of surprise vertical axis essentially reflects how a null finding relates to our prior expectations. Orthogonal to this, one might evaluate the experiment and its parameters in terms of localization procedure, neural efficacy checks, and power and effect size, together making up a gradient of interpretability horizontal axis.

This continuum reflects how informative we should consider the null result in isolation , ignoring expectations, theory, or previous research. The figure displays our view on how design choices impact the interpretability of a null finding along this dimension toward the right is more informative, see legend top-right. A few caveats are important. This figure aims to visualize concepts discussed in more detail in main text, and how they relate to each other. The visualization of Level C through Level A evidence is meant to make intuitive how they roughly fit into this overview, our proposal for what exactly differentiates Level A through C evidence is in main text.

Note also that the figure reflects how design factors influence how informative null findings are, it does not apply to positive findings in a straightforward way. Along the gradient of surprise , we find Replication nulls on one end, Exploration nulls in the middle, and Hypothesized nulls at the opposite end.

Sometimes a positive finding is strongly expected, based on previous research or strong theoretical background, but not found. For instance, a null result in an experiment explicitly designed to replicate a well-established finding seems most surprising Replication null.

Thus, Exploration nulls sit in the middle of the continuum. At the other end of the gradient are Hypothesized nulls. These may be something of a rarity still, since not many experiments are explicitly designed to obtain null results in the experimental condition.

Perhaps this is because null results seem less interesting or impactful, or simply because negative findings are a priori considered meaningless for reasons discussed above.

Either way, a null result that was expected is of course least surprising. Along the gradient of interpretability, multiple factors contribute to null result interpretability. The effort is being announced Friday as President Joe Biden tries to showcase how his policies are delivering for the public. President Biden may soon be forced to take action amid threats from an increasingly aggressive North Korea, which has flexed its military might in recent days with provocative missile launches.

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Krot told the man. Angela Simmons caught fans by surprise on Jan. In the Instagram post, the year-old […]. The former Miss Universe had her wardrobe-shaming moment chronicled on Instagram. The city council has […]. Republican Sen. Roger Marshall Kan. The "Daily Show" correspondent returned to the scene of the insurrection — where he found the Florida lawmaker. The former couple announced their separation after 16 years together. Soon, both the Prime Minister and the leader of the opposition were confined to their sickbeds and London hospitals were struggling to cope.

Despite the frizz, "The Morning Show" star stunned fans. Regardless of the outcomes, new research requires time and financial resources to complete. At the end of the process, something is learned — even if the answer is unexpected or less clear than you had hoped for. Nevertheless, these efforts can provide valuable insights to other research groups.

Independent verification of the results through replication studies are also an important piece of solidifying the foundation of future research. This also can only happen when researchers have a complete record of previous results to work from. By making more findings available, we can help increase efficiencies and advance scientific discovery faster. This lack of information affects the entire scientific ecosystem. Readers are often unaware that negative results for a particular study may even exist, and it may even be more difficult for researchers to replicate studies where pieces of the data have been left out of the published record.

Some researchers opt to obtain specific null and negative results from outside the published literature, from non peer-reviewed depositories, or by requesting data directly from the authors. The authors summarized their disappointing findings:. This new explanation… failed to account for the fact proved by experiment that the aberration was unchanged when observations were made with a telescope filled with water.

But why is it such an unusual example? The majority of negative results serve this purpose — to add to our knowledge and function as a collaboration tool. But some, like the Michelson-Morley experiment, turn out to have huge significance. When he looked back over his work to chronicle his career, Prof.

Anthony Cerami , translational medicine pioneer and the Hermann Boerhaave Visiting Professor of Medicine at Leiden University, said he was surprised to see how significant his negative results had been:. Many of the biggest discoveries of my career were the results of failure of another research project.

Failure strikes a negative tone, but it appeared in my personal history that it was an essential experience on the path to important discoveries. Cerami describes one of these failures. He and his colleagues had come up with a number of compounds with the potential to fight trypanosome infection, a parasite that affects cattle.

They travelled to Kenya to test one particular compound in cattle, which promptly died within minutes of administration. Cerami saw the value in the results, noticing that there must be something other than the parasite causing wasting in the cattle.

He was right, and the protein they eventually isolated was tumor necrosis factor TNF. He continued to work on the protein, eventually revealing its important role in inflammatory diseases including rheumatoid arthritis. Despite their potential, negative results are repeatedly relegated to the lab books, the drawers and the trash bins.

This is not a new phenomenon — research published in Controlled Clinical Trials in showed that statistically significant clinical trial results were three times more likely to be published than those supporting the null hypothesis.

Perhaps surprisingly, the researchers concluded that rather than being a result of editorial decisions, this was because scientists were failing to write up and submit papers describing their negative results. How can this culture be shifted towards valuing negative results?