Absence of Evidence Can Be Evidence of Absence

 The phrase "absence of evidence is not evidence of absence" has long served as a caution against premature conclusions from inadequate searches. Popularised by Carl Sagan and others, it rightly warns against appeals to ignorance in contexts where detection methods are weak. Yet it is frequently misused as a rhetorical shield, allowing midwits to evade judgement and perch indefinitely on the fence. In a Bayesian framework, absence of evidence is evidence of absence to the precise degree that evidence would have been expected had the claim been true.

Bayes' theorem formalises this: the posterior odds of a hypothesis given no observed evidence equal the prior odds multiplied by the likelihood ratio, P(H|~E) / P(~H|~E) = [P(~E|H) / P(~E|~H)] × prior odds. When a thorough search would almost certainly have detected evidence if the hypothesis held (low P(~E|H)), while absence is expected under the alternative (P(~E|~H) ≈ 1), the lack of evidence substantially weakens the hypothesis. The update's strength hinges on the test's sensitivity and statistical power. An insensitive or absent search yields mere absence of evidence; a high-powered one constitutes genuine evidence of absence.

This principle underpins the scientific method. Hypotheses must generate testable, falsifiable predictions (per Popper), while statistical tools—power analysis, confidence intervals, Bayes factors and equivalence testing—determine when a null result supports absence of an effect. Underpowered studies cannot prove "no effect," a common error highlighted by Altman and Bland; well-designed trials excluding meaningful effects do provide evidence of absence.

The slogan has devolved into intellectual laziness, protecting extraordinary claims, ineffective treatments and flimsy excuses from scrutiny. Science does not treat missing data as neutral. It requires updating beliefs in proportion to the available evidence and its absence, calibrated by prior probability, detection sensitivity, and statistical power. Absolutist slogans are not epistemology; they are evasions.

In practice, absence often functions as evidence precisely because evidence should exist.

Consider everyday excuses. Someone claims there was a “massive traffic jam,” yet live navigation apps show free-flowing roads, traffic cameras are clear, and no alerts appear on local feeds. Where corroboration should be abundant, its complete absence becomes informative—it strongly suggests the jam never existed.

Or take the classic “the dog ate my homework.” The paper is pristine. The dog is healthy. There are no vet visits, no torn scraps, no mess. When an event would almost certainly leave traces, the lack of any trace is itself powerful evidence against the claim.

The same reasoning governs serious domains. In court, an alibi of being “home alone all night” is not supported by silence when silence is unexpected. Phone metadata, utility usage, CCTV, transit records, and location pings normally generate footprints. When multiple independent systems—each sensitive enough to detect presence—produce nothing, that absence meaningfully updates beliefs against the alibi.

Scientific history offers parallels. The 1887 Michelson-Morley experiment detected no ether-induced variation in light speed despite sensitive apparatus where drift should appear; the null result provided decisive evidence of absence, advancing relativity. Modern drug trials demonstrate the point: high-powered Phase III studies showing no serious side effects (where detectable) support safety, while large RCTs with confidence intervals ruling out clinically meaningful benefits evidence ineffectiveness.

The phrase retains validity where detection is genuinely limited—such as current spectroscopy for biosignatures on distant exoplanets, or early hunts for rare phenomena—reflecting technological constraints rather than disproof.

Rigour demands rejecting both credulity and blanket scepticism. The scientific method equips us to assess when absence is probative: formulate predictions, test with adequate power, and update via likelihoods. In Bayesian terms, we routinely judge evidence of absence statistically. Midwits embrace ambiguity; truth-seekers calibrate the update and act. The slogan has its niche, but indiscriminate use excuses bad faith and stalls progress. Prioritise evidence quality and expectations over comforting fence-sitting.

Appendix 1: Glacial Transport of Bluestones to Stonehenge – When Absence Constitutes Compelling Evidence

The principle that absence of evidence can constitute evidence of absence applies powerfully to long-running debates in archaeology and geology. One prominent example is the claim that Pleistocene glaciers transported the bluestones of Stonehenge from the Preseli Hills in west Wales (approximately 225–240 km distant) to Salisbury Plain. Popularised by geologist Brian John, this hypothesis posits that Irish Sea ice streams carried the stones (mainly spotted dolerites, rhyolites and other lithologies) as erratics, depositing them locally for later Neolithic use. Proponents argue it explains the stones' distant origin without invoking implausible human effort.

In a Bayesian sense, this claim generates clear, testable predictions. If glaciers transported specific bluestone lithologies over such distances to a precise location, we should expect observable traces: glacial till or diamicton containing bluestone fragments; scattered erratics of matching petrography and geochemistry along plausible ice-flow paths (e.g., via the Bristol Channel); moraines, striations or landforms consistent with ice advance from north Pembrokeshire across southern Britain; and a broader erratic train reflecting unsorted glacial deposition rather than highly selective clustering at one site.

Yet the record shows comprehensive absence. No in-situ glacial deposits or till occur on Salisbury Plain; Pleistocene river gravels draining the area contain no bluestone erratics; no matching erratic train has been identified between Preseli and Stonehenge despite decades of fieldwork; and ice-sheet models indicate the Irish Sea Ice Stream did not extend far enough south or follow a path delivering these specific stones to the monument site. The lithological assemblage at Stonehenge is restricted to a dozen or so rock types with precise geochemical matches to discrete Welsh outcrops (e.g., Craig Rhos-y-Felin rhyolite, Carn Goedog dolerite), inconsistent with the random scatter expected from glaciation.

The most decisive recent evidence comes from detrital zircon–apatite fingerprinting of river sands near Stonehenge (Curtin University / Nature Communications Earth & Environment, January 2026). Analysis of over 500 zircon and apatite grains revealed no mineral signatures diagnostic of Welsh or Scottish glacial sources. Glaciers never reached the area; the absence of expected glacial mineral grains in thoroughly sampled sediments rules out ice delivery and supports deliberate human selection and transport.

Radiocarbon-dated quarrying evidence at Preseli sites (c. 3400–2900 BCE), stone tools, wedges and parallels with other Neolithic long-distance movements (e.g., sarsens from West Woods, Altar Stone from the Orcadian Basin) align with human agency. The glacial hypothesis, lacking empirical support and contradicted by high-powered negative results, has been effectively falsified. Its persistence despite the absence of expected traces exemplifies how the slogan "absence of evidence is not evidence of absence" is misapplied when searches are thorough and predictions specific. In this case, the evidence of absence is strong and probative: the bluestones arrived at Stonehenge through human endeavour, not ice.

Appendix 2: Glacial Transport of Bluestones to Stonehenge - How the Evidence Against Glacial Transport of Stonehenge’s Bluestones Builds Up Step by Step

Imagine you start with an open mind about whether glaciers moved the bluestones 225 km from the Preseli Hills in Wales to Stonehenge. You begin with a fair starting belief — a prior probability of 20% (or 1 in 5) that glaciers did the job. This is generous: ice did reach parts of the Bristol Channel region long ago, but the idea that it neatly delivered exactly these stones to one spot has always been a minority view.

We will now update this belief one piece of evidence at a time. Each new finding is independent and comes from careful fieldwork, mapping, or lab analysis. For each, we ask: “How likely is it that we would see this complete lack of glacial traces if the glacier hypothesis were true?” (Usually quite low.) And “How likely is this absence if humans moved the stones instead?” (Very high.) Each time, the probability of glacial transport drops. The actual calculations are below.

Starting point Probability glaciers transported the bluestones: 20%

Evidence 1: No glacial till (sticky clay-like deposit) or bluestone fragments found on Salisbury Plain despite many boreholes and surveys If glaciers had dropped the stones here, we should see layers of glacial debris mixed with stone fragments. None appear. This halves our belief. Updated probability: 9.3% (why not 10%? - see below for the Baysian calculation)

Evidence 2: No bluestone fragments in ancient river gravels or along possible ice-flow routes Glaciers scatter debris widely into rivers and valleys. Extensive gravel mapping found nothing matching the bluestones. Updated probability: 4.5%

Evidence 3: No trail of erratics (scattered boulders), moraines (ridged debris), or bedrock scratches linking Preseli to Stonehenge A 225 km journey by ice should leave a visible “breadcrumb trail” across the landscape. Decades of searching found none. Updated probability: 2.3%

Evidence 4: Modern ice-sheet computer models (including the major BRITICE-CHRONO project) show the Irish Sea ice did not reach far enough south or follow the path needed to deliver these exact stones The models are based on extensive data about past ice movement. They rule out the required route. Updated probability: 1.4%

Evidence 5: The “Newall boulder” once thought to be a glacial erratic was re-examined with modern lab techniques (petrography, electron microscopy, and portable X-ray analysis) It turned out to be a broken piece of a Preseli bluestone with no signs of ice grinding or transport scratches. Updated probability: 1.0%

Evidence 6: The decisive 2026 study — analysis of more than 500 tiny zircon and apatite mineral grains from river sediments right beside Stonehenge These durable minerals act like fingerprints. If glaciers had brought Welsh material, their signatures would appear in the sediments. None were found. Analysing hundreds of grains makes it extremely unlikely the signal would be missed if glaciers had been involved. Final probability: 0.13% (roughly 1 in 770)

Overall picture After all six independent lines of negative evidence, the chance that glaciers moved the bluestones collapses to about 0.13% — effectively ruled out. The combined effect is like multiplying six separate “this is unlikely if glaciers did it” factors together. Even though early absences cause the biggest drops, the final mineral study delivers the knockout blow.

What if we change the starting assumptions? (Sensitivity check) Even if you begin much more optimistic (50% prior) or treat each absence as less decisive, the final probability rarely rises above a few percent. For example:

• Starting at 50% and treating every absence as only mildly surprising → final ≈ 5% at most
• Realistic starting belief and careful likelihoods → stays well under 1%

Simple takeaway Start reasonably open-minded. Add up the missing evidence, piece by piece. Each gap where something should have been found chips away at the glacier idea. By the end, the total weight of absences — from landscape features to microscopic minerals — makes glacial transport vanishingly unlikely. This is how we turn “absence of evidence” into strong evidence of absence when the search is thorough and the predictions are clear.

Sequential Bayesian Updating: How Each Line of Evidence Affects the Odds

We update the probability of glacial transport (H) step by step. Each piece of evidence is treated separately in logical order. We start with a generous prior probability P(H) = 0.20 (odds 0.25 : 1).

For each absence of evidence (~Ei), we assign:

• P(~Ei | H): the probability of missing that specific trace if glaciers had transported the bluestones (kept relatively generous).
• P(~Ei | ~H): the probability of observing this absence if humans transported the stones (very high).
• Likelihood ratio (LR) = P(~Ei | H) / P(~Ei | ~H) — always < 1, reducing the odds of H.

The new posterior becomes the prior for the next step.

Prior: P(H) = 0.2000 (20%) Odds (H : ~H) = 0.25 : 1

Evidence 1: No in-situ glacial till or diamicton containing bluestone fragments on Salisbury Plain If glaciers deposited the stones, till should be widespread and detectable via boreholes and mapping. Missing it entirely is moderately unlikely. P(~E1 | H) = 0.40 P(~E1 | ~H) = 0.98 LR = 0.408 After E1: P(H | ~E1) = 0.0926 (9.26%) Odds = 0.102 : 1 (The first major downward revision, as the absence of expected deposits halves the probability.)

Evidence 2: No bluestone erratics in Pleistocene river gravels or along plausible flow paths Glacial transport would scatter fragments in river systems draining the area. Extensive gravel mapping shows none. P(~E2 | H) = 0.45 P(~E2 | ~H) = 0.98 LR = 0.459 After E2: P(H | ~E2) = 0.0448 (4.48%) Odds = 0.0469 : 1 (Further halving, as independent sediment records add strong negative weight.)

Evidence 3: No erratic train, moraines, or striations linking Preseli Hills to Stonehenge A transport path of 225 km should leave geomorphic traces (moraines, scratches on bedrock, a trail of erratics). Decades of fieldwork found none. P(~E3 | H) = 0.50 P(~E3 | ~H) = 0.98 LR = 0.510 After E3: P(H | ~E3) = 0.0233 (2.33%) Odds = 0.0239 : 1 (Continues the steady decline; landform evidence is expected but entirely missing.)

Evidence 4: Ice-sheet models (e.g., BRITICE-CHRONO) show the Irish Sea Ice Stream did not extend far enough south or follow the required path Modern reconstructions indicate the ice did not reach or route material precisely to Salisbury Plain for these lithologies. P(~E4 | H) = 0.60 P(~E4 | ~H) = 0.98 LR = 0.612 After E4: P(H | ~E4) = 0.0144 (1.44%) Odds = 0.0146 : 1 (Models carry some uncertainty, so the LR is less extreme, but still reduces belief.)

Evidence 5: Re-analysis of the Newall boulder (petrography, SEM-EDS, pXRF) This small welded tuff, once cited as a glacial erratic with supposed striations, matches a Preseli source exactly and shows no diagnostic glacial transport features. P(~E5 | H) = 0.70 P(~E5 | ~H) = 0.98 LR = 0.714 After E5: P(H | ~E5) = 0.0103 (1.03%) Odds = 0.0105 : 1 (A specific refutation lowers probability modestly, as it concerns one artefact rather than landscape-scale evidence.)

Evidence 6: January 2026 detrital zircon–apatite fingerprinting of river sediments near Stonehenge (>500 grains analysed) No mineral signatures diagnostic of Welsh or Scottish glacial sources. Zircon and apatite are highly durable tracers; analysing hundreds of grains makes missing a glacial signal extremely unlikely if ice had deposited material. P(~E6 | H) = 0.12 P(~E6 | ~H) = 0.99 LR = 0.121 After E6: P(H | ~E6) = 0.0013 (0.13%) Odds = 0.0013 : 1 (approximately 769 : 1 against H)

Final posterior: ≈ 0.13% (roughly 1 in 769).

This sequential approach shows how each independent negative result compounds the evidence against glacial transport. Early absences (till, erratics, landforms) drive the largest initial drops, while the powerful 2026 mineral fingerprinting delivers the decisive final blow. The overall likelihood ratio across all evidence is approximately 0.005, consistent with the composite analysis.

In Bayesian terms, the cumulative absence of multiple specific, high-sensitivity predictions constitutes strong evidence of absence. Human quarrying and transport from the Preseli Hills is now overwhelmingly supported.