Status: educational explainer. This page reports no experiment results. Project S.P.H.E.R.E. is at the proposal stage, hypotheses are not findings, and nothing here amends the registered LOC-1 protocol.

What is a null result?

A null result is an experimental outcome in which the data do not show the effect the study was designed to detect. The term is often used dismissively — as though a null outcome were a failure — but this reflects a misunderstanding of how scientific inference works. A well-powered, well-controlled null result is a positive contribution to the literature: it bounds how large any real effect could be, rules out hypotheses, and narrows the space of plausible mechanisms. The absence of evidence, under the right conditions, is indeed evidence of absence.

The key qualifier is "under the right conditions." A null result from a study that lacked the statistical power to detect a plausible effect size, or that used measurement equipment too noisy to resolve the expected signal, is uninformative. It neither confirms nor disconfirms the hypothesis; it simply fails to address it. This is why reporting a null result well requires stating the sensitivity of the measurement and the range of effect sizes that were ruled out, not just reporting a non-significant p-value and moving on.

The publication-bias problem

Publication bias is the systematic tendency for scientific journals and individual researchers to favor positive results over null or negative ones. Its effects compound across the literature in ways that are now well-documented. Journals have historically accepted papers reporting statistically significant effects at much higher rates than papers reporting null results on the same questions. Researchers aware of this have historically been less likely to write up and submit null results in the first place. The cumulative effect is a published literature that contains a disproportionate number of positive findings — many of which are false positives, inflated estimates, or highly specific results that fail to generalize.

The problem is particularly acute for small effects in noisy measurement environments, where underpowered studies can produce false positives through chance. If ten research groups independently investigate a true null effect, statistical chance alone predicts that roughly one will find a nominally significant result. If only that group publishes, the literature records a positive finding. The nine null results, sitting unpublished in nine file drawers, never enter the record. This is the "file-drawer problem" originally described by Robert Rosenthal.

Meta-analyses — systematic reviews that pool results across multiple studies — are particularly vulnerable to publication bias because they can only analyze what was published. A meta-analysis estimating the average effect size from a biased literature will systematically overestimate it. Methods like funnel plot analysis and trim-and-fill estimation attempt to detect and correct for this bias, but they are imperfect and rely on having a large enough body of published studies to analyze statistically.

How to report a null result well

A null result that is reported poorly contributes little more than a non-significant p-value. Reported well, it provides real scientific value. The key elements are:

State the smallest effect of interest in advance. Before data collection, specify the minimum effect size that would be scientifically meaningful. This is sometimes called the "smallest effect size of interest" (SESOI). This number, combined with the study's sample size and measurement noise, determines whether the study was actually powered to detect meaningful effects. A null result from a well-powered study with a clearly pre-specified SESOI is informative; a null result from an underpowered study is not.

Report effect estimates and uncertainty intervals, not just p-values. A p-value tells you the probability of seeing data at least as extreme as the current data if the null hypothesis is exactly true. It does not tell you how large the effect is or how precisely it was measured. Effect size estimates (such as Cohen's d, η², or a regression coefficient) combined with confidence intervals convey what the study found and what range of effects are consistent with the data. A tight confidence interval around an effect size near zero is strong evidence; a wide interval centered near zero is not.

Describe conditions, equipment calibration, and sensitivity limits. A null result is only interpretable in the context of the study's measurement sensitivity. In physical science, this means specifying the noise floor of the measurement system, the range of conditions tested, the calibration state of the instruments, and any confounds that could have masked a real effect. Readers need enough information to judge whether the null result came from a system capable of detecting the effect if it existed.

Share the raw data. Open data allows other researchers to re-analyze the results, apply different analysis methods, pool the data with other studies in a meta-analysis, or check for errors. This is particularly important for null results, where readers may reasonably want to verify that a nonsignificant outcome did not result from an analysis choice that was unfavorable to detecting a real effect.

Structural fixes to incentive problems

Individual researchers cannot solve publication bias on their own. The incentive structure that produces it — where positive results are more publishable, more citable, and better for careers — requires structural remedies.

Registered reports are a journal publication format where peer review and a provisional acceptance decision happen before data collection. The journal evaluates the introduction, methods, and planned analysis for soundness and relevance, and commits to publish the results regardless of outcome. This eliminates the mechanism that drives publication bias, because acceptance is based on the quality of the design rather than the direction of the result. Registered reports also prevent p-hacking and outcome switching because the analysis plan is fixed before the data exist. More than 300 journals now offer registered report formats.

Preregistration repositories like the Open Science Framework, AsPredicted, and ClinicalTrials.gov create a public record of studies before they are conducted. Even without journal commitment to publish, preregistration makes it possible to identify the gap between planned and published studies — the size of the file drawer — and to apply statistical corrections for it.

Dedicated null result journals and special issues provide a publication venue for well-powered null results that traditional journals decline. Examples include PLOS ONE (which accepts papers based on methodological soundness rather than novelty) and the Journal of Articles in Support of the Null Hypothesis.

S.P.H.E.R.E.'s commitment

The research charter commits Project S.P.H.E.R.E. to publish its results regardless of direction. This means that if the LOC-1 protocol produces data showing no statistically significant location-correlated effect on copper sphere resonance frequencies, that result will be reported and published with the same care as a positive finding would be. The data, analysis code, and uncertainty budget will be released under open licenses in either case.

This commitment reflects both the requirements of good scientific practice and the specific evidentiary situation. The locational variable hypothesis — that geographic or spatial position systematically affects measured resonance — carries a low prior probability under standard physics. An honest null result from a sensitive, blinded, well-controlled protocol would be a meaningful contribution to the literature: it would characterize the conditions under which no location effect was detectable at the precision of the measurement. Until any measurements are conducted, no result of any kind — positive or null — is claimed or anticipated. Related: replication crisis and reproducibility.

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